Slashdot Mirror
Help Me Get My Math Back?
nwm writes "I am trying to refresh my math skills back to the point that I can take college-level statistics and calculus courses. I took everything through AP calculus in high school, had my butt kicked by college calculus, and dropped out shortly thereafter. Twenty+ years later, I need to take a few math courses to wrap up a degree. I've dug around some and found a few sites with useful information, but I'm hoping the Slashdot crowd can offer some good resources — sites, books, programs, online tutors, etc. I really don't want to have to take a series of algebra-geometry-trig 'pre-college' level courses (each at full cost and each a semester long) just to warm my brain up; I'd much rather find some resources, review, cram, and take the placement test with some confidence. Any suggestions?"
They want you to pass calculus for a reason. No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics but you will need to use calculus every day.
Calc II, Calc III, Diff Eq, I II or III. Linear Algebra, Statistics,
There's a huge difference.
There's always MIT's Open Courseware.
This book uses programmed learning that goes step by step through everything you will need and more. It is designed for self study. There is also a sequel book that goes into some much higher stuff. I used just this book as preparation for classes requiring calc 3 as a prerequisite.
Hi,
Working scientist here. Ph.D. I've been working 20+ years doing scientific research, getting grants, publishing papers in peer-reviewed journals.
I haven't done ANY calculus since I was an undergrad.
you're more than welcome to do my taxes for me...
If you haven't needed a degree or calculus in 20 years, why bother now?
If you're job hunting, your time would be better spent making yourself relevant to current employers or starting a consulting business than trying to match your calc and trig skills with a recent grad and get a degree.
A degree is a nice "filter" when hiring new applicants, since it proves that they were able to deal with BS for at least 4 years, however with 20 years of actual job experience, you'll do much better off trying to differentiate yourself from the recent grads than you will if you try to "look better on paper."
That said, if you want to do this just because it's "unfinished business" lots of community colleges have entire departments dedicated to getting us old folks "up to speed". Just stop by and talk to someone.
It's essential that he pass calculus I, III, III and Diff EQ without the use of a calculator.
Just in case we are bombed back into the stoneage, he wont have to worry about losing his job as a scientist.
This tutorial site helped me through 6 years of school. Hope it helps you too! http://tutorial.math.lamar.edu/
Helpful handouts from Germanna Community College's tutoring Center. (I used to work there a few years ago; these resources are not only helpful, but free.)
Drexel's Math Forum (full disclosure: I'm a current Drexel employee and student -- but the Math Forum strikes me as pretty cool.)
Project Euler(more oriented toward programming and numerical methods, but interesting site for developing your math skills. The problems range from not-too-hard to mind-boggling.)
Purple Math
Paleotechnologist and connoisseur of pretty shiny things.
Most text books have practice questions for each chapter, and some answers in the back. Why not just work through some of those on your own? Math is the kind of subject that you can only learn by doing problems, so I don't think there's any shortcuts. But I suppose if you work on problems, it's nice to have a teacher to help if you get stuck, but perhaps a reasonable substitute would be forums.
Just do Community college summer sessions or something similar, should be enough and they only cost like 60 bucks a class. Taking the college level calc classes would be good too at CC unless they are upper division differential equations or something as those are not offered.
Eat sleep die
Keith, I would start with YouTube. Crazy as it sounds, but there are many free training videos there. Especially, look up channels maintained by the universities like i.e. MIT or Yale, etc etc. They have recordings of lecture sessions available for free to watch, of course. And some of them are of finest quality. Anyway, that is just a start... Good luck, KW
cheat! and the TI-89 series makes it easy!
Just get review books for the New York State Regents exams.
What you're mostly going to find in these replies are codices. Not teaching. Not knowledge. You're going to get information sources. What you do with those sources, that will be the teaching, the learning and the progress. No one's going to help you get your math back but you. You're going to get static nonliving information and it's going to be up to you to bring that alive. Frankly, on your part it's going to require the will of a volcano otherwise I suggest a tutor or precalculus class.
The course I can refer you to echos my sentiments:
This material could conceivably be studied by a student on his or her own, but this seldom works out. Students tend to get stuck on something, and, having no goad to keep them going, they try to get past it with decreasing energy, and ultimately develop mental blocks against going on. Having an organized course prevents this by forcing them to face obstacles like exams and assignments.
If you attempt this and get stuck, as is almost inevitable, you could try emailing us and we can try to unstick you.
Did you catch that last part? You're going to need help. Whether it's bribing your nerdy friends with cases of beer or Star Wars Galaxy Series Five collectible card packs (*cough* *cough*) you are going to need guidance at certain points in time. Don't be afraid to ask those around you or -- and I recommend this only in dire cases -- dressing up like a student and rolling into your local university asking to see the precalc professor for help.
Your codex might be Wikipedia. Your codex might be Wolfram's MathWorld. My codex sits three feet in front of my face as I type this. My codex (and this is purely personal) Bronshtein et al's Handbook of Mathematics. The binding is acceptable. The paper is not the greatest. The content is priceless. This is not a teaching device. This is my starting point. If I were you my ending point would be at my college's library pouring over all calculus textbooks. The great thing about this starting point is that I like how it lays out all the starting points leading up to that starting point in case I need to start backwards. Another great thing about this particular resource is that it has nearly everything imaginable and is well organized. The bad thing is that it costs $71.97. I think I paid $60 for mine but either way it's not free like Wikipedia.
I don't know where you are comfortable starting from but if I were you I would simply research what your learning institutions pre requisites are and spend your free time now acquiring their books and notes in order to make sure you have them covered. All of my old University of Minnesota syllabuses are online although I cannot find the Math department equivalent (aside from the registration listings).
If you could name your courses, I'd suggest books like The Annotated Turing which has been a page turner for me and actually starts with basic set theory to work up to automata. I'm guessing you're aiming for more Multivariable and Diff Eq type stuff. Let us know what the courses are and perhaps more human readable works can be suggested that aren't as laboriously mind numbing as reading a codex would be.
My work here is dung.
http://lmgtfy.com/?q=refresh+algebra+and+calculus+skills
Second hit seems pretty good, it's called SOS math. http://www.sosmath.com/
I've been studying for the FE exam (Fundamentals in Engineering) and bought the Lindeburg FE Review Manual. It has a lot of explanation and practice problems, but includes a lot more than just math (thermodynamics, physics, etc.). I bet there are similar review manuals for just math though. You could also pay for a tutor, I've seen adds on craigslist before.
A site that I have used to great effect is this: http://www.phy.ornl.gov/csep/CSEP/BMAP.html
Sometimes, real fast is almost as good as real-time.
and check out all of the relevant math textbooks. Make sure there are exercises for each chapter for which answers are provided somewhere in the book.
Then, read the chapters, and do the problems. Keep doing the problems until you get every . single . one . of . them . right and you understand what you've previously done wrong in each case.
Pour over it until you really understand the relationships between the quantities.
It is very hard work, but there is no shortcut to understanding math and science, and if you don't understand them, you'll never be good at them, even if you manage to solve a few problems using memorized patterns.
STOP . AMERICA . NOW
My advice is go for cheap and easy classes that count for your degree, especially if the classes are useless for your job (as most will be) try taking them at a community college, or see if a "degree mill" offers the course for cheap that will transfer. Many universities will take community college or other sub-par classes if they are for general education or basic requirements. Now, if you are, say, a biology major, taking all your biology classes through a community college might not transfer, but taking math classes should.
Taxation is legalized theft, no more, no less.
You might like:
Khan Academy http://www.khanacademy.org/
(Get an account for the review software if you have forgotten college algebra skills as well.)
MIT's Open Courseware http://ocw.mit.edu/
Many of these courses now have full video libraries of lectures, homework and exam solutions, etc. You can buy a text and take the course.
I am interested to see other finds out there, though.
In my experience in school, if you are motivated to pass, you will find a way to pass (most of the time). But if you are motivated to learn, passing the class will come as a pleasant side effect. Not knocking your stated intentions, but approach this as a learning experience, a thoroughfare in self-enlightenment, and you will reap the test-score rewards.
'We are trying to prove ourselves wrong as quickly as possible, because only in that way can we find progress.' RPF
A tutor can move at exactly your pace, and answer exactly your questions. This is A LOT faster than anything self guided. I'd do it myself if I was in your area.
Oh bullshit. Those are both overt and ridiculous generalizations. First off, many scientists use statistics every day (at the least, much more than "never"). Second, not all scientists use calculus "every day", and many use it almost never.
As a calculus teacher, I can tell you this: you need skills in symbolic manipulation. Your algebra needs to be rock solid before you attempt college level calculus. In my experience, you need dozens of hours of practice before you get it. Buy an algebra textbook, and do every odd problem in every section until you are reliably getting everything right. My experience = flunked high school math and went back to college 10 years later, and am now working towards a PhD in math.
Obtain all four books from the Gelfand Correspondence Program in Mathematics. Read them carefully and do all the exercises.
The titles are:
Algebra
Trigonometry
Functions and Graphs
The Method of Coordinates
Dunno about college placement tests, but to start thinking about maths in general there's nothing like just buying a couple of books and going at it (but make sure you have the answer booklet/solutions are in the back of the book). If you're feeling a little panicky you might even want to start with something really un-threatening ('Statistics for dummies' exists for that). You might want to see what the standard textbooks would be for the courses that are prerequisites for the ones you're looking to study, and perhaps ask which areas you would be expected to be comfortable with.
Also, the MIT opencourseware site is probably your friend: http://ocw.mit.edu/OcwWeb/Mathematics/
As regards an online tutor, depending on whether you currently live near a college/university/miscellaneous site of higher learning, you might want to see if there are any postgrads in applicable subjects who are willing to tutor. In my experience online tutors are seldom worth half as much as talking to a real live actual human being, and they are usually more expensive. YMMV - especially if you are extremely busy an online tutor may actually suit you better than scheduling another real live person into your week.
Finally - good luck :)
I agree do community college, check out http://yaymath.org/, this guy is the best he helped me with college algebra. I am going to move onto calc soon.
I've found karlscalculus.org to be a useful site. for my brushing-up needs.
you can't say such a thing without knowing what specialization a person would have. Statistics is the bread and butter of some work, for others just plugging numbers into formulas that have been known for a century or two (my job at national lab was like that for 10 years!), for others the heavy duty tensor calculus or partial diffy-Qs. Same situation in engineering.
I was in the same situation as submitter. In fact, it was the reason why I switched majors from CompSci - being in a hurry to get a degree in a science and too much bullshit math I'd never use. I'll go back for Compsci when I can learn on my own terms, for fun.
However, you were spot-on about this: Calc 1 is 90% algebra(with 20-30% of the problems involving trig)and you're gonna be fucked if you don't have a good grasp of algebraic manipulation. My recommendation to submitter is to take online calculus(where available) at an accredited junior college and use a computer algebra system to help them through the homework visually, especially with regards to roots and asymptotes.
Constructing Maple worksheets gives one a good step-by-step process for visualizing the steps necessary to solve the problems. Iterative methods like Newton's, Simpson's, Trapezoid rule etc. would come naturally to a programmer.
Submitter - stats is just arithmetic and basic algebra, it's the concepts and knowing what to do with the data that are the hard part. Again get a T.I. and learn all of the functions, there is a LOT of tedium. Don't be afraid of the weird greek variables and big formulae...it's just arithmetic and algebra 1, you will hate it when you take it, but you will love it when you pass it.
Ethanol-fueled
I find it profoundly unsatisfying that you have to ask this question.
It's not your fault; it's the structure of the educational system. You are clearly not interested in mathematics, since you just want to cram and pass some test. You don't specify exactly for what you need mathematics, but I'm guessing it's for some other thing, possibly something computer related.
It's a big lie that you'll ever use calculus for anything except for specialised degrees (and if you were to use it for anything you personally would want to do in your future, you would already be interested in it). It's also profoundly strange that calculus seems to be pinnacle of mathematical education if you're not going to go on to study something like mathematics itself or physics.
To put my frustration another way, why doesn't anybody ever ask similar questions for sculpture, or Schaum's Outlines on Basket Weaving or all the other myriad useless things we humans do for our edification? Why is western society obsessed with mathematics, deluded into thinking it's useful in general, and why are people so stressed over learning this useless and dryly-presented subject? Why aren't you required to achieve a certain level of chess expertise before you can complete a computer science degree? A lot of early computer science was concerned with chess playing, let us not forget!
It's pointless. It's pointless to cram for exams about subjects you don't care about in order to satisfy requirements you don't genuinely need.
My recommendation is, are you really interested in learning this stuff? If so, just spend hours and hours in your local university library in the math section browsing books you're interested in. If you're not really interested, go grab some Schaum's Outlines or the Complete Idiot's guide or whatever, and use that to pass whatever bureaucratic and pointless requirement your educational institute imposes before you're allowed to study what you really want to study.
Were did they say they were getting a science degree? Needing to take a few math courses to wrap up a degree implies that most of the course work is done. I can't think of a science or engineering major that would allow you take the required courses without having completed calculus first.
more cowbell
As a scientist I learned a long time ago not to make general and unsubstantiated claims like "No matter what kind of scientist you plan to be, your knowledge of calculus will be essential." As a practicing molecular geneticist and cell biologist I use statistics quite often. I cannot remember ever having to (directly) use calculus in the last 20 years for any of my research. I really enjoyed all of the calculus (and linear and set theory and ...) that I took a long time a ago. When I look back at it what I really got out of all my math classes (and O-Chem too for that matter) was the the knowledge that I could learn anything I really set my mind to - if I have to.
You must be a scientist, because apparently you have no sense of humor.
It depends on your overall plan whether you need new dead-tree books. But the Schaum's outline books are good, with plenty of worked problems. Look in a college bookstore or do a web search on Schaum's outline .
And what field might that be in? Not all fields will have much use for calculus in the real world, but I am still curious.
SSC
Another thing that you might want to brush up, in addition to those things the parent post mentions, would be trigonometry. A healthy portion of the various calc courses I've taken have used trig identities fairly heavily. It also helps to remember the values of trig functions for common angles. Depending on the college, you may have to be decent at mental arithmetic. My school frowned upon using calculators in class.
SSC
There is a new edition, edited by Ian Stewart, which Amazon has:
What is Mathematics?
I like the book because it is geared to an intelligent adult reader; it doesn't assume much technical math knowledge, but it gives (IMHO) an excellent overview of the concepts through calculus. It has exercises, too.
Your slacktard approach to effort and accomplishment is a theme in your life. Don't waste any instructors time, or take any seat from someone more willing to work. Go watch TV.
I remember Newtonian mechanics as the best applied calculus class. If you didn't like calculus as math, maybe this will work out better for you. It links math with more physical (useful?) phenomena.
If not, I don't have a clue what would help you, since I found college calculus much better than AP high school stuff.
Fuck systemd. Fuck Redhat. Fuck Soylent, too. Wait, scratch the last one.
I have gone through those at MIT, just for fun. I also found that Khan Academy was really interesting and perhaps is easier for some. Strang at MIT is awesome and also the courses at Yale are good.
UCLA has some great courses too.
science and magic was very informative. It doesn't hurt that some of the profs are also quite entertaining.OR science and magic on youtube
I'm on my second college level calculus course for a computer science degree, ten years after graduating with a liberal arts degree. I took calculus in high school with no problems. My advice is not to be too worried about it; just take the class. It'll take you a few weeks in class to catch up on the algebra, but it will come back to you. You'll have 20 years more experience than your classmates learning things.
Also, chances are you had your butt kicked the first time 'round because you weren't spending enough time asking the professor to clarify things you don't understand, doing homework, or studying. I will stare at my textbook and reread a section until it makes sense. Sometimes things are easy and sometimes I spend a few hours more than I planned.
I'm at a top tier university and am having no problems so far getting A's in Calculus... while working full time.
My dad got a degree in a technical field--CS or something related, IIRC--and he never even had to take a calculus class at all. He took classes overseas while in the military through UMUC. It does happen.
SSC
Really... No business getting a degree in ANYTHING? That's a rather closed and inappropriate (IMO) view. If he's worked in a field for years that doesn't require he use any algebra how's he supposed to keep up with his skills other than doing algebra problems in his spare time? He never indicated the degree he's completing was heavily math-biased or math-dependent. Stats and Calc may be akin to gen-eds.
When you paint such ridiculously broad statements you risk your own image before anyone else's.
Still, if you can't even pass calculus then there's something wrong. And that's not even the problem- he's looking for help preparing for the placement test. If he's let his skills deteriorate so far that he forgets algebra, then he has no business getting a degree in anything.
And what field might that be in? Not all fields will have much use for calculus in the real world, but I am still curious.
Ah biology, the humanities of the science world...
I'm not sure to what extent this site would help:
www.ThatQuiz.org
But I like to go back there from time to time and run through various tests just for "the fun of it." I'm not only surprised by the simple things I've forgotten over the years, but I'm also surprised at some of the things I never use but still remember.
I would go to www.teach12.com and try out their 'joy of math' class, or try some Math Tutor. The joy of math is a 24 lecture series, each is 30 minutes long, and it goes all the way from basic math to basic integral calculus. That will teach you all the theory you need. Then the Math Tutor calculus classes will easily fill in the exacting skills you need.
Or, if your not into lectures, I would highly recommend the textbook 'Calculus 6th Edition' by James Stuart. It is in easy to understand language and goes from the beginning of calculus 1 to the beginning of differential equations in the last chapter.
Also, if you want to understand 3d space in a calculitic way, just buy matlab and play with surfaces for a few weeks.
Really, I think calculus is easy if you understand the concepts, the rest is just bookkeeping. But spend enough time playing with that bookkeeping, and beautiful patterns about the very nature of the world in which we live arise, and you will be flabbergasted. The importance of numbers like pi and e become obvious, and all the frustration seen in math is gone.
The practical use is also great, besides the enhanced understanding of the world. You might not use Statistics and Calculus every day, but the concepts will change the way you see the world, and how you think. When you run into any kind of issue or problem, your tools to deal with it will be far better than before. And what once kicked your ass will be kick ass to practice.
Try not to cram to much, reading a calc textbook or watching some of those classes will let you understand what you are doing, so you won't have to worry about trying to cram.
Hope I helped, just remember to give yourself the chance to learn. Without learning, what do we have after all?
Where is the mod rating for "scary"? Also,
Up until right now, I just used http://www.purplemath.com/, and had no idea that other resources existed so extensively.
I enjoy math, but I'm also an unmedicated ADHD child - lectures frequently just bounce off of me; and attempting to learn from a course assigned textbook is a joke... these are designed around a lecture format that doesn't work perfectly for everybody. Nothing is more frustrating than hitting a wall due to not fully processing a lecture, and having the textbook be worthless ($180 worth of worthless, too.)
I think the best suggestion is just to wander your way through some of the recommended books and sites and not force it; as others have mentioned, if you're actively enjoying the learning experience, it'll just flow naturally. Or, it'll fail miserably... either way, progress (not necessarily forward) will be made!
Really for me the main trick was understanding exactly what a derivative was. It sounds obvious I know but you really have to get your head wrapped around exactly what it's doing and the basic idea of summing an infinite series of slices. Do some mental exercises like the speed of a car and how a speedometer works, imagining the rate a pool of different shapes would be filling up as the water rises, etc...
Once you get the concept clear and what it means the rest is just memorizing the various transforms with the Sin, Cos, etc... and getting in good practice doing it. Then years later when you've forgotten all of those (as I have) and you run into a calculus problem you'll at least recognize it and know what the basic formula is, then use a TI calculator or whatever.
Cwm, fjord-bank glyphs vext quiz
Translation: I'm so smart, look at me. If you didn't do things the way I did, you are not smart and should be a ditch digger.
Seriously, mods, can we start modding down these ego masturbation posts? They are way too common here.
It's the same deal as people who say others can't learn to do art. Their skill makes them feel special and if someone else can learn to do it also, their specialness is threatened.
And saying that someone should not be awarded a degree because they don't know algebra is extremely arrogant and ignorant. There's a reason why they TEACH algebra in colleges.
When I had to do well on the GRE before entering graduate school, I used the prep book from The Princeton Review and kicked the hell out of the math section.
They have prep books for SAT Math 1 & 2 which covers (ironically) more complicated stuff, and I think that's what you really want. For getting your mind back in mathematics mode, I'd pick up both of those (twenty bucks each or less) and work through all the exercises you need to in order to jog the memory banks. Start with the GRE math and good luck!!!
Many scientists misuse stats.
Fuck systemd. Fuck Redhat. Fuck Soylent, too. Wait, scratch the last one.
No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics
This has to be about the worst piece of advice about a science education I've ever seen. Like anything, it depends. Calculus is extraordinarily useful to someone in physics, but less so in biology. Statistics is insanely important in an experimental science (actually it's insanely important in just about any science I can think of). Hell, statistics should be a mandatory class taught in High School. It's far more applicable to everyday life than trig is.
AccountKiller
I would mod you up if I had any points. Sad as it may seem calculus was where I *learned* trig. For me, trig is one of those subjects that you beat your head against for months and years and one day *POOF* it makes sense. My first semester of college level calculus was were I learned trig. The second time I took that first semester of calculus - man I got it.
Don't forget to brush up on the basics - algebra, trig, analytical geometry as well as your calculus.
goes looking for an old text book just to tinker around with it.......
Another working scientist PhD here. Unless you are going to be involved in hardcore theoretical physics or math work then calculus won't crop up very often. However, you DO need to know what it means and how it works - software solutions generally can do the hard yards after that. Statistics crops up a LOT more often and that really pays off.
Just my experience guys.
Yeah, bleh. All that useless stuff like discovering the causes and cures of disease.
If you had to do any linear regression or error analysis, knowledge of statistics is important (e.g. being able to answer questions like "Is this a good datapoint or an outlier"). And Calculus is used to derive the formula for linear regression. I didn't touch it since I was an undergrad, but I still know and can use it. My sister-in-law who got the same B.S. in chemistry asked me why I remember this stuff when she was studying for a nursing degree. It trained my mind. Being able to do algebraic manipulation should be send nature to you. Do whatever you need to do to learn that cold. You'll need it for calculus and statistics.
If you're looking for geometry learning, try to make an asteroids-like game.
It's not too challenging as to turn someone down, but lots of fun and you'll learn how to apply geometry. Specially sine and cossine, which my teachers did a terrible job in teaching what that was all about (only teached transformation formulae, never applying them). I only learnt what it was meant to do when I tried to do a subspace-like game.
You haven't specified what kind of degree, and therefore, what kind of coursework is required. Moreover, even the same level of coursework taught at different institutions can vary widely in difficulty. "Undergraduate calculus" at, say, Caltech is nothing like "undergraduate calculus" two blocks away at Pasadena City College. The same goes for statistics.
If your intention is to obtain a degree, the best starting point is to figure out which text(s) are being used in those courses that are required for that degree. This will give you some idea of the scope and level of difficulty to expect. Otherwise, you could end up studying a great deal of ancillary information. Such things may be good to know, but will not contribute to your stated goal.
Regarding your plan to dive right in, I appreciate and understand your enthusiasm but I also think it is misguided and potentially counterproductive. You could very easily make it much more difficult for you to obtain your credits by not reviewing basics beforehand. Mathematics is not a subject that is easily cherry-picked, nor is it amenable to rote learning. It is more like a vast edifice, a tower whose foundations support increasingly complex and abstract concepts. Furthermore, it is a topic which is best learned through actual understanding. For instance, if you understand what integration actually means, rather than viewing it as a mechanical operation on a function, you will find it easier to interpret other concepts that employ integration, such as the calculation of moment-generating functions of continuous probability distributions.
On some level, it's possible to "get by" with simply learning the mechanics of computation and symbolic manipulation. That is pretty much what calculus is (as opposed to analysis). But if you want to make it as easy as possible on yourself, at the very least I advise you quickly review nearly everything at the high-school level, from algebra to trigonometry. Then take a more detailed look at the AP Calculus curriculum; any gaps in knowledge should be readily apparent and immediately addressed before continuing further. From there, you should compare against the aforementioned college coursework and texts.
Success in learning mathematics is not so much about the details of what you know as it is about how to think analytically and abstractly.
That's rather amusing. What I've noticed is that in the life sciences, it's very rare to see someone who didn't struggle with physics and calculus. Conversely, statistics are used all the time. There are two main reasons for this. First, biology is more memorization and less mathematical, and requires a different skill set than math or physics. Second, biology is messy, most numbers are inexact, and everything follows a normal distribution.
That said, not being proficient in math means that you'll also likely struggle with statistics. I've heard estimates that more than half of research articles in the life sciences have at least one statistical error. When I say "everything follows a normal distribution", that's because everything is assumed to do so. I have yet to see a research article actually verify or check to see if that assumption is true. Last year I read a paper concerning some high profile discovery in medicine that actually reported a negative p value (reminder: probabilities range from zero to one).
They want you to pass calculus for a reason. No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics but you will need to use calculus every day.
Are you wooshing me here?
Having an understanding of what a derivative or integral of a function is a good insight to have, no doubt.
But I would argue that statistics is much more broadly applicable, and extremely important for a clear understanding of scientific discourse and all the 'facts' that the poster will encounter.
In reply to the original query, what you're going to need to do is a lot of problems. You need to look at this like getting in shape--you can't do it overnight.
I returned to college after about 5 years off and needed to take placement exams myself. Turned out the test allowed using a Ti-89. I cheated myself out of really 'placing' myself by being able to approximate/calculate all the multiple choice answers and placed highly.
After a few attempts in the classes I was placed in, in the end, I re-took precal and calculus.
I could have avoided that if I had actually done a large volume of problems rather than skimming some books and looking at the answers and deciding that it was 'easy enough'.
Never look at the answers of problems until you try them. Once you know the right answer, you convince yourself the problem was easy and that you didn't need to do it. This will fuck you over in the end.
Find an approach to doing math that makes it enjoyable for you. One thing that helped me a lot was getting a large whiteboard. I find I enjoy doing math more pacing back in front of a board and whatever else comes along with doing work on a board rather than a piece of lined paper. Chalk would have been better.
Lastly, ignore the assholes here who are going to berate you for not knowing what they think is simple, obvious knowledge. Math is rife with 'tricks' and non-intuitive methods to solving problems that come through experience. Someone who had a good experience with math through school and went straight into college is not going to understand your position.
Good luck to you, and if you really want this, do problems and problems and more problems. Put on some music you love and shred through a book or two. Get help at local colleges. Bribe a friend to help you study, or just hire a tutor.
Otherwise, you're going to end up doing it by taking the classes (as I did). One way or another, you have to do the work.
Long live the BSD license
The parent is absolutely right. You need practice. Actually, you need what Anders Ericcson calls 'deliberate practice'. Solve every example in the book as follows:
Write down the problem. Close the book and try to solve the problem. If you got it right, go on to the next problem. If you didn't get it, look at how the example is solved. Close the book and try again until you get it right. Repeat until you have solved every example in the text.
Check out this article: http://www.conestogac.on.ca/~bcoons/readings.html
BTW, Jamie Escalante, http://en.wikipedia.org/wiki/Jaime_Escalante, just died. He was the real life teacher who proved that you can teach calculus to just about anybody. They made the movie 'Stand and Deliver' about his life. Ability is highly over-rated. Most people can, as Escalante proved, learn math to quite a high level of accomplishment.
Most people think math is some magic thing that some people just can't get. They are wrong. Almost everyone is wired to learn math. If you are missing some important skills, go back to the level where you were good and start from there. John Mighton points out that most people discover that they have no math ability the same year they have a bad math teacher. ;-)
If you want, you can learn math as long as you practice, practice, practice.
While the initial parts of the book may be too easy for you, many people have found "Arithmetic and Algebra Again" by Immergut and Smith to be wonderfully helpful. It will help you get back into the habit of doing math (especially algrebaic functions) in an easy, tidy way, and is designed for adults. That should give you a good baseline jumping-off point.
The book "What is Mathematics?" by Courant and Robbins, despite its cushy-sounding name, would be my recommendation. First of all, it's written by two world-class mathematicians. Second, it's not a textbook; rather, it's what you might call a celebration of how awesome math is. If you want to succeed in college math without being miserable, why not try to see the subject as thing of beauty, rather than a burden? This book will definitely help you do that. If you read through the first half of the book (it shouldn't take long) you will have a chance to warm the math parts of your brain back up, and you'll learn some extremely cool shit along the way. (A bit of geometry, a bit of topology, a bit of algebra, etc.)
When you get to the authors' lucid explanation of the main ideas behind calculus, you'll realize that (1) calculus isn't scary, (2) the computations you need to learn how to do are fun, not hard, and (3) everything comes down to a few very intuitive ideas -- it may have taken geniuses like Newton and Leibnitz to come up with them in the first place, but they are part of our common intellectual heritage, not erudite ideas reserved for mathematicians and physicists.
And, although it's not a textbook, there are some exercises which will give you the chance to test your understanding. Again, though, they are fun, not grueling.
I do a lot of molecular biology. I've never thought of it as like the humanities at all. It's always seemed a lot more like computer programming to me.
Buy yourself a Schaum's calculus guide and work through all the problems. That should get you through single variable calculus with few problems.
my mom posts on slashdot.
Khan's Academy is Great. Strangs linear algebra is great. MIT's Calc III is great.
I know it sounds a little weird, but check out iTunes U. There are a lot of courses (many by some very well known academic establishments) including a full library of math and science. Best part is, it's free.
They want you to pass calculus for a reason. No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics but you will need to use calculus every day.
These days, biology is 100% statistics.
I compute derivatives every day. That's why my compute farm draws a couple of megawatts when I want a number.
Glad to hear people are still doing it by hand. Arts and crafts should been encouraged, even in the modern age.
Last I checked the average scientist uses statistics.
I was told how much math I'd need since I wanted to get in to technology. Math teachers always kept on about how important it was. Well, they are dad wrong. I need a good understanding of arithmetic, and some basic algebra is also useful. Past that, I use nothing. Had I stuck with CS, linear algebra would be good (since a lot of programming relates to it) but certainly not calc. Knowing calc is kinda neat, it allows me to understand how some things are done, but they aren't things I need to do, a program does them for me.
We really need to refactor how much of what subjects we teach people. Math is one in particular we need to get real about. I think it is a leftover of the red scare, the "Oh my god the Soviets will crush us technologically all our kids have to be math whiz kids!" That was dumb then and even dumber now. Trying to cram more math down the throats of every person does nothing. It doesn't turn someone in to a brilliant engineer. The kids that love math, well they'll discover that by having math taught to them. That love should then be nurtured and they should be taught all they can hold. The rest? Teach them what they need to know and leave it at that. What that is will vary, an engineer will need more and different kinds than a sociologist, but teach what is needed, don't just teach math for math's sake.
We should be focusing more on presenting a well rounded education, particularly at lower levels. Expose kids to a LOT of different things. Why? Because you want them to find the thing that clicks with them, the thing that they are interested in. Maybe it's math, maybe it's computers, maybe it's drama, maybe it's biology, whatever. Expose them to a lot, let them learn about all kinds of things, and then they are in a much better position to choose what they want to learn more about during secondary education.
Of course you need to include things that everyone needs to know. English is very important as all jobs demand communication, some math is for sure important, etc. But teach the amount needed and useful, don't just teach more for the sake of teaching more.
In university, this should be even more the case. Universities need to evaluate their degree programs and say "How much of what non-degree material does this really need?" Math is NOT degree material for CE or CS. It is necessary to understand some of the degree material, but it isn't actual material relevant to the degree. As such you should be teaching the level needed. You shouldn't say "Well this is a math heavy field so make them take 6 math classes." No, it should be "These are the kinds of mathematics necessary to properly understand the things they are being taught, as a result they will need to take math course A before class X and math course B before course Y and so on." Maybe that ends up being a lot of math, sure will be for some degrees, but make sure it is because it is needed and useful. Don't insist CS people take calc because computers are about math.
You'll never use statistics but you will need to use calculus every day.
Statistics is great for figuring out when you're being lied to, so go ahead and learn it or prepare for a lifetime of being easily manipulated with real-sounding BS.
Reboot macht Frei.
I was pretty much in the same boat you are. This book, and the accompanying videos, helped me to 'get my math back' after 15 years away. However, you might have to take a pre-calc refresher. It's amazing how much gets away from you after that much time.
Many public libraries subscribe to a paid database called Learning Express Library. This resource gives access to multiple practice tests and courses including all levels of math including preparation for the AP Calculus test. Contact your local public library to gain access. My public library has it at http://skokielibrary.info/s_info/databases_alpha.asp#l
As a calculus teacher, I can tell you this: you need skills in symbolic manipulation. Your algebra needs to be rock solid before you attempt college level calculus. In my experience, you need dozens of hours of practice before you get it. Buy an algebra textbook, and do every odd problem in every section until you are reliably getting everything right.
I couldn't agree more. My better students are invariably the ones who can do basic algebra in their sleep. Those who struggle are those who never learned high school algebra (or god forbid, arithmetic) well.
Statistics is one thing you will use often. Calculus... umm depends on your specific job.
Depends on your field. In mine I use statistics far more than calculus.
I suggest Schaum's Outlines myself. Cheap, comprehensive, mostly well-written.
...that was a pretty asinine thing to say, beyond the fact that such a vague blanket statement is, for all intents and purposes, almost completely useless.
your use of calculus really depends on what you're going to be doing in life. while i would agree that calculus, and even higher maths such as modern algebra, topology, discrete, are good for the soul, they aren't for everyone. most biology majors don't even have to take the calculus for scientists and engineers, for example. and then math majors have to take calculus that makes engineering and scientist calculus look "soft".
but, having taught at a community college for some time, i would say that even the most math-fearing students can succeed in calculus if they want to. it really just takes patience and time. i know this will sound a bit odd, but calculus really isn't even that hard. most of the time, it's the algebra that kicks people around more than anything. you MUST be good at algebraic manipulation in life.
at the end of the day calculus is just about two things, both of which are highly intuitive and useful. [a] tangent lines (i.e. rates of change) and [b] total change (i.e. areas under curves). these concepts are ubiquitous in every day life, it's just that math takes the time to formalize them.
approach the subject calmly, and with an open mind and you should be fine. and don't let any jerks tell you that you're less than human if you struggle with it. just make sure you get a good teacher and put in the time.
Use it or lose it. Just like most people after studying a language in high school can barely remember to say hello in it years later. Good thing is they can relearn it faster than first time around.
you'll never use statistics... HA
I haven't found a field of math I HAVEN"T had to use yet. (double negative: I've used EVERYTHING I Heard of in college and more)
Want to see stats in use, look at image processing where people aren't trying to use learning algorithms. Adaptive? sure, use stats.
As for an answer to the op, try playing with vedic mathematics for a warmup. It's (asian, not US) indian tricks to solving simpler math problems quickly.
Calculus is mostly symbol mapping. I kept the book I used in College and just review when I'm getting rusty.
Start with polynomials, exponentials (and sine/cosine). Practice on weird trig manips, then move to higher dimensional spaces.
Should be fun! Yes, I realize I'm insane. Pardon the AC post.
I went from 0 to Quantum Mechanics, here's how: 1. Get a reference book which is easy to flip through and has all the main things like fractions, decimals, scientific notation, logarithms, etc. This will save you a ton of time. I suppose wikipedia will do these days. 2. Go straight into algebra 101. 3. Go take trig 101 4. Take Calc 101, 201, 301 5. Take Differential Equations and Linear Algebra 6. Take 2 years of Math Methods in the Physical Science 7. Take Quantum Mechanics I know it sounds simple but it takes a lot of time. The idiot guides are helpful for reviewing thoroughly.
Ahhh yeah, I'm in biology and I'm computing non-trivial derivatives and integrals (what's the distribution of the protein location patterns in response to drug x?), in addition to setting up differential equations left and right (enzyme kinetics driving reactions left and right, what are those rates?).
"I'd just like to emphasise that taking a million years isn't a metaphor here..." -Rich Bradshaw
The easiest way to get your math back is to contact the Math department, get a list of Math tutors and work with them to get back up to speed.They will know all the tricks and current books to use.
http://www.lanecc.edu/math/reviewsheets.html
PDF viewer required, blah blah blah.
I studied some stuff in the months before class, but was not really prepared at all. The first half of the first day of class covered all of algebra and pre-calc, the second half was new material. She put up stuff on the board the first day like x^(y/z) and expected us to know what it meant. The next few classes we were expected to already know what the quadratic equation was. Some of my lowest grades were in that class, and I studied all the time for it. I got a 670 on my Math SAT, and am doing math tutoring for grammar school kids right now. I am not bad at math, it is just too much to expect to remember this stuff 20 years later.
I would suggest auditing a pre-calc course, or even taking a non-credit pre-calc course outside your college. Or take one there. It is a lot more work than I had anticipated. It is cumulative as well so if you fall behind I would have been screwed. We also barely covered asymptotes in class but half the test questions were on asymptotes.
Also - almost everyone I know who is short a few credits in college to graduate is almost always short for the math classes. There must be a reason math is always the subject people are short a few credits to graduate in. I myself have been pushing off Calc II since Calc I was so hard.
Thanks! I've been wanting to refresh my maths from college again and this is really useful
Idiots and politicians don't need statistics. Anyone else that wants to do real science does.
I would have guessed sociology, economics or psychology.
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It's so funny that this question has been posed. I thought for a second that I had actually posted this! :)
I'm pretty much in your same situation. I dropped out of college back in the late 90s, and the last math class that I successfully passed was Calculus II. I took a Calculus III class, but stopped going around the time I dropped out. This puts me at almost 15 years since I've attended a structure math class at the university level. Before that, I look Precalculus in high school...in 1991. I haven't had an Algebra class since 1990.
I can recall many things, but definitely NOT enough to pass a college exam. I decided that I would go back to school and start with Calculus I. After all, SURELY if I've had this material before I could easily get an A! Ahem. I could remember the basics, I could remember the rules of derivation and integration, but I couldn't remember the Trigonometry. Finding the derivative of something involving sine, cosine or tangent confounded me. At the behest of the professor, I enrolled in Precalculus. After the first week, we had a test covering the basics of Algebra. I flunked that. I couldn't remember every last detail, and it's been nearly 20 years since I've seen this material directly in a classroom environment.
After consulting with a friend, I decided to take matters into my own hands. I'm not willing to spend the time (and money) in a classroom retaking math classes, so I headed to my local Half Price Books. I'm fortunate enough to live in Dallas where we have several large stores with a massive stock of older college texts. I picked up a book on Algebra, Trigonometry and Precalculus. I also acquired the teachers manuals and student's solutions manuals for these texts, giving me a nice base of information to jog my brain. Math hasn't changed a whole lot in the last few years, and the main thing that I find that dates the books is the calculator requirement. Some of these books use a TI-85 or TI-86 in their chapter sample exercises, but these are the calculators I have lying around since my college days.
iTunesU is also an awesome source. Go search on Algebra and other math subjects to get full courses on any subject you lack. You can get older courses and cheap textbooks on Amazon if you want to precisely follow along. Th Algebra videos from Harrisburg Area Community College have helped me immensely.
As mentioned above, MIT's OCW can help you, but if you were so inclined to teach yourself mathematics with MIT's material you probably wouldn't be posting on Slashdot asking for some assistance. I don't mean this as an insult in the slightest; I'm not one to learn this type of material on my own, either!
In summary: hit iTunesU and get some FULL courses to fill you in. Go get some used, older textbooks either online or at a local used bookstore if you have such a resource in your area. Outside of these self-help options, you can always enroll at a local community college to basically start over. I know the Dallas area colleges sometimes have rolling enrollment and/or compressed schedule courses. You may find that you can plow through classes like College Algebra, Trigonometry and Precalculus in a shorter time since you're basically refreshing your knowledge.
Good luck!
Try MIT OpenCourseWare.
And stats is pretty useless
That has to be one of the most useless statements I've read on Slashdot. Statistics is one of the most applicable branches of mathematics; it does the best job of allowing us to model our observations of events, since we understand 0% of the world around us well enough to say with 100% confidence what the outcome of a certain event will be.
Not only is it an extremely important field, it's an extremely understudied and undervalued one. I avoided statistics until I began my master's degree, and if there was anything about my educational career I could change it would be taking an intro to statistics course in my undergraduate years, or even AP Statistics while in high school because of how applicable it is to everything.
"I'd just like to emphasise that taking a million years isn't a metaphor here..." -Rich Bradshaw
You couldn't learn it with a teacher - now you want to learn it on your own? Go back to bagging groceries.
Go take a couple of courses for non-credit or "enrichment" at your local community college. Start a little bit behind where you think you are at the moment. It will air your brains out in a non-pressurized environment, give you some idea of what you need to be doing, and won't cost much. I did it years ago, about ten or twelve years after I finished college. It rebuilt my confidence, sharpened my skills after ten years of disuse, and was highly enjoyable in the bargain. The fees were very affordable. I never regretted it for a minute and considered it time well spent.
"Here's what's happening. You're starting to drive like your Dad..." - Red Green
Sorry, thats crap. I entered into college 10 years after high school, not even having taken a math my senior year. I hadn't done any significant math since. I took one look at the placement test and decided not to even bother - I could only remember how to do one or two problems on it. So I had to start at math 0900.
Oh and almost a senior and I've been on the deans list every semester, and I have a new love for math (it used to be one of my most despised subjects).
Jump over to the cramster.com answer board and work out problems people are asking. If it becomes clear that you need even more help, try a textbook.
I would add - get a college physics text. There's almost no better way to get some algebra/trig/basic calc practice than to work on physics problems. I remember thinking that my Physics 1 class at the University level was really just an algebra/trig class in disguise. Helps to get some practice.
An interesting thing to note about calculators - in my math department Calc classes, we weren't allowed to use any calculators, but because of this, basically all the problems they gave use used 'perfect' angles - i.e. angles that corresponded to the small table of trig values we were expected to memorize - 0, Pi/6, Pi/4, Pi/3, Pi/2 (and the other angles around the rest of the circle which are really just those angles reflected across an axis).
In the calc class, since you could use a calculator, they could somewhat randomize angular values, because you could use your calculator to calculate sin(23 deg), arcTan(47 deg), etc. Actually, a lot of the problems in Physics didn't even care about concrete values - the answers were more about deriving the correct formula to find an answer, and you just left x or y or whatever as the symbolic parameter values (which is also an important lesson in mathematical thinking - formulas which solve a problem are usually more interesting than concrete numerical answers - because once you have the formula, you just plug in your values, and it spits out an answer [though as a comp sci major I might have been a little biased - that's how I tend to think anyhow: people solve problems, computers calculate answers]).
Well, yes, of course it is. That's why it's called a "normal distribution."
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If you did any real work (instead of panhandling for state money), you would have used your calculus.
If $2/hr Indians can get you 100% on your assignment and homework, then you can still bomb the exams and pass.
Correction: s/In the calc class, since you could use a calculator/In the Physics class, since you could use a calculator/
http://www.gcflearnfree.org/default3d.aspx Many FREE classes, many topics, all skill leavels.
Google has answers.
TNR - Typical Nerd Response
It might be that you just need some minor warming up, but a more heavyweight solution would be to take appropriate math classes at your local community college.
While it would obviously be costly and take substantial time, it is far less costly than taking such classes at a university and you can pick a nearby one even if there's not a good university nearby (or go there cheaply while attending your university if you're already attending one). You may also be able to find a particular series of classes that suits you well time-wise. In particular, when I started out I was unsure of my ability to take on Calculus I so I took Precalculus I and Precalculus II in the same semester so I could take Calculus I the next semester. I'm glad I did it because I learned a lot and was ready for Calculus I when I took it. It also has the advantage of giving you college credits for your effort.
Of course, there's a lot of variability here. It may be that there isn't a local community college or math program that fits you. It could be that even one extra semester is too much time for you. The cost may still be too high if you're on a tight budget. etc. Still, you should at least consider the idea.
You're in luck, there are tons of options. Use online courses, cheap textbooks (look for teacher editions), and community college courses.
If you were an AP student in high school and enjoy math, you'll do fine the second time around in college. I had to work a lot harder at calculus than I expected during my first undergrad degree. Five years later I returned for another degree and found it much easier and more enjoyable. Suffer through Calc I, II, III, they're basically computation. The fun comes with applied calculus, linear algebra, and finite topics.
either got to khanacademy.org or to youtube -> kahn academy.
It is by far the best course in mathematics I have ever seen.
To fortify your knowledge, get yourself some textbooks with lots of problems in them, and do them all.
For me, I bought some textbooks and used MIT's Open Course Ware to get back up to speed on calculus. For precalc I was able to use Sullivan's book. It's very well written with great explanations and lots of examples that walk you through things step by step so you actually understand how it all works together. For calc I'd recommend either Stewart for practical application, or if you are big on the theory/proof end of things, I still haven't found a better book than Apostol's, but it's a difficult read and uses a rather archaic method of teaching the subject. Still, it's very rewarding if you're going to be getting into the theoretical end of the sciences.
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I did the math courses for engineers, which was lots of calculus. Actually 4 semesters math with a focus on that doing calculations. (Uni in Germany). I also did the math for computer science, which was completely different: 1 semester was stochastics and statistics, 1 semester numerics, 3 semesters things like calculus, linear algebra, number theory, graph theory etc. with a focus on proving theorems rather than doing calculations.
Physicists also had their own math courses taylored to their needs with a big amount of caculus, too.
Math for biologists and chemists was more compact.
Lockhart, famous for his critique on “mathematics” “A Mathematician’s lament” is currently writing a book, to teach math the way it’s supposed to be taught.
I decided to wait for it, since all the other stuff on the market is the same retarded backwards-“teaching” shit, with the same stupid “learning rules by heart”.
Any sufficiently advanced intelligence is indistinguishable from stupidity.
It's the same deal as people who say others can't learn to do art.
Speaking as a former art major (which is why I'm a truck driver now, BTW), people who say that really used to piss me off. Sure, some folks have a huge natural artistic talent but the rest of us have to learn how to do art. When someone suggested my skills were due to a magical innate ability, I'd get ticked off and tell them no, everybody has the innate ability. My skills, in fact, came from many hours of tedious practice, doing the same thing over and over until I got it right.
This ain't rocket surgery.
I had a similar experience, returning to college after 10 years out of school.
...and then crashed and burned in Calc II, because that -required- a full understanding of the groundwork on which it was based.
Even though I didn't (in theory) -need- to take it, I started with College Algebra, and worked my way up through the math courses.
Algebra was a breeze.
I could do Trig and Analytic Geometry without any trouble, though I didn't really understand them.
I got my first B (as opposed to straight As) in Calc I, being able to apply what I knew without understanding it...
That was 17 years ago. I never did finish my degree, and haven't had any great need for math above the Algebra level since.
I'd love to go back and finish my CS degree, just to have it - I've been working in the field for over 30 years (yes, I started on mainframes) and it would be nice to have the piece of paper, though it isn't likely to do me any good at this point.
Statistics are, absolutely, one of the most useful. I'd wager you can improve your performance and ability to "get it done" in pretty much any professional field with a mastery of statistical analysis: anything from field biology/naturalist to burger flipper, really.
No, it might not be immediately or daily pertinent, but if you've got a non-trivial data set, you've got enough data to find a trend. Being able to prove a trend is better (by far) than an "instinctual" hunch, observation, or crudely derived "educated guess".
I use some form of statistical analysis almost weekly in my work (sysadmin for a small company). It's never a big study or anything like that; it's rarely even much more than "hmm, we've got a pattern" and deriving a result, but just the same, it's useful. It's actually one of the few "educational" things I wish I'd put more effort into due to its regular pertinence.
~/ssh slashdot.org ssh: connect to host slashdot.org port 22: too many beers
Most colleges now use two sites for their online coursework. MathLab and Math XL. Both cost to join. Of course, you need to be in a class to get actual homework assignments(so no assignments - no big deal). But they do have full online tutoring, examples, and so on for you to review from the book. Some textbooks also have similar programs or access to them in a CD in the back.
Log in, select "I am studying on my own and need to select a textbook" Then search for the author. Go to course home at the top.
There are study plans, coursework, sample tests, and the text of the book online.
For $50 or so, nothing's better to get you up to speed. When you are done with one course, start the next. Each enrollment is good for a full year.
If you're looking for a general introduction/remedial/refresher resource, you could do a lot worse than the MathTutor series of DVDs. They're not particularly cheap, but they are cheaper (and quicker) than full-scale courses. You would probably need to find a source of exercises/quizzes/tests to reinforce the learning though - I would expect any university entry-level text should give plenty of those.
http://www.online.math.uh.edu/HoustonACT/ My high school teacher used these slides last year. I thought they were helpful.
I suggest you get a copy of Richard Courant's What is Mathematics?. It covers a wide range of topics so you can pick and choose what you want to learn about. You don't have to read it from cover to cover like most text books. IMO the key thing is that it makes math interesting. Math is like sex in that if it isn't fun then you are probably not doing it right.
Also, don't feel bad about having trouble with college calculus. IMO people seldom learn calculus in college when it is taught by the math department. This is because most mathematicians aren't interested in calculus. You are best off either learning it in high school or, if possible, learning it from the physics department. Many physicists use calculus day in and day out (especially grad students) so they are really into it.
We don't see the world as it is, we see it as we are.
-- Anais Nin
And stats is pretty useless, especially in light of the fact it exists mostly to provide the cover of math to people who wish numbers weren't being used against them.
Ignorance abounds. Statistics is used and needed far more than calculus is. You clearly didn't go far in your studies of statistics, or perhaps never learned it.
Beetle B.
Many scientists misuse stats.
57.5% of all scientists would agree with you. 40.5% wouldn't comment. 3% of all readers will realize these stats are made up without being told... ;-)
The sharpest blade is no match for the sharpest mind.
purplemath.com
all you need to brush up on the basics / get a solid foundation
After working 25+ years, I was approached by my manager to take course work in Statistics. It seems they had determined they needed another statistician and wouldn't I like to be it? After some consideration and talking it over with my family, I agreed. Before I could enroll in grad school, however, the math department decided I needed to retake Calculus since it had been almost 30 years since I took Calculus in college. I took the first semester at a local community college for about $150. I took the second semester at a local private university for about $4,000. (Fortunately, the company paid my tuition!) Despite the difference in tuition, I found the CC version of Calc I to be at least as thorough as the more expensive semester at the private university. In some ways, it was more rigorous, although your mileage may vary. I would suggest that a CC probably has more experience in teaching calculus to students that are struggling with the concepts than a larger university where the students are expected to have some level of expertise. I was lucky - I remembered much of my calculus and got As in both classes, then started classes in Applied Statistics. I completed my degree in 2.5 years with a 3.86 GPA while working essentially full-time as well and raising a family. It's fortunate -- the company and I parted ways due to being outsourced, so if nothing else, I have additional fodder for the resume and proof the old dog still knows a few tricks.
Calc in high school as soph and junior (graduated early). Had 2 semesters calc in 1979 for BS in micro bio , then in 91-93, did BS in CS. What I found is that in the decade, my learning skills had dropped and I lost information. How do you recover? You do not. What you need more than anything is to focus on learning. you should be 40 or so. You will be slower at picking up info. On the first degree, I never studied for anything and it was all AP. I got a 3.0. On the 2'nd, I studied until 5 am, and had 1 B and that was due to working 30-40 hrs/week and carry 18 credit hours (big mistake: do not do it). For the first semester, I had only 3 classes for a total of 11 credits. And it was calc, and several CS courses. That will allow you to focus on that calc course. Keep in mind that if you were AP, then you were probably brighter than most and likely lazy. As such, you now have to re-develop your learning skills. This is IMPORTANT. THings are NOT going to come easy to you. At this point, the majority of the 20 y.o. have it easier than you do. the only real advantage that you have, is that getting laid and having fun is not a top priority. Focus on your studies.
I prefer the "u" in honour as it seems to be missing these days.
I am in the same boat ... going back to school after 20 years.
I decided to do a junior college, because those are cheap, and start at the beginning to give me the best chance to get through the higher level classes.
I know it is not what you want to do but it would give you the best foundation.
Or combinatorics (generating functions, graph theory, probability theory, topology, optimization, etc.). Applications in cryptography, CS, etc. But there are many other branches of math... is it relating to sciences ...physics/chem/biology... when I was studying electronics, we did a lot of differential equations/laplace transforms/z transforms/fourier transforms/fourier analysis (along with calculus ..Reimann integrals and such) but in university I studied other/different kinds of calculus ie predicate calculus, discrete propositional calculus, etc. for artificial intelligence and tupple relational calculus for databases (but not the calculus the dentist scrapes off your teeth). So once again, what the heck is the direction you are heading? Your description "I'm going up" is as wide open as the clear blue sky. Balloon? Rocket? Hiking up a mountain? Elevator? Step ladder? Rolling up on your tiptoes? Abstract questions get abstract answers, concrete questions get concrete answers.
probably because of the odd mixture of superiority and inferiority complexes (are they the same thing? who knows...).
Anyway, I commend you on your efforts to get back into mathematics. I started taking mathematics courses well after I received my B.A. (in Philosophy) and my friends and colleagues gave me no shortage of grief over this. I don't complain when they want to spend their free time painting or water skiing, and yet-- they seem to think there's something wrong with a grown man studying mathematics. The best advice I can give you is: ignore them. Mathematics is a fulfilling and beautiful subject. At the risk of sounding like a stoner, it will open your mind to new possibilities.
You already have the important part: motivation. But motivation is not quite enough. Until you understand the weird (or I should say, counterintuitive) ways of mathematics, you really need a teacher. This is worth the money. I was in your same position about five years ago, and what I did was: start at precalculus. I signed up for a summer course in precalc and trig at the local Uni (UMass Lowell, in case anyone is wondering...), and then I worked my way through calculus, stats, discrete math, set theory, algorithms, and formal languages. I threw in a physics course for kicks, and I found that it reinforced my calculus immensely.
Remember: math is hard. But not for the reason you think. It's hard because you need to change the way you think. The problem sets are essential, because they make you understand what assumptions can be kept, and which must be thrown away. You will be a better person for it. Once you change the way you think, math is easy. It sounds trite, I know, but it is very true.
Also, Bach helps during homework.
Good luck, and do not let your friends and family discourage you. I personally believe that if you are not challenging yourself, you are not living. I would do it again in a heart beat.
Thinkwell courses are pretty awesome,
With video and a whiteboard type presentation together.
Thinkwell.com
http://khanacademy.org/
You must be a "scientist". ;)
Fuck systemd. Fuck Redhat. Fuck Soylent, too. Wait, scratch the last one.
Your post suggests that the cost of tuition for math make up courses is a problem.
That comment indirectly suggests to me that you live a long way from a Junior College.
You need a nearby Junior College to supply reasonable cost preparatory courses and you also need a nearby 4 year College to award a degree.
I suggest you explore moving to put yourself and your family as close to your chosen college and a nearby junior college as possible.
I presently live in an "educational saddle" place that is 8 airline miles distant from any Junior College and any 4 year institution.
While the rugged coastline is beautiful, nobody I know is keeping up the commute to get a degree. I also don't know anybody going to Junior college for career change education either.
I got my BA by commuting from a parent's house that was 4 miles airline to college.
Every time I have lived close to a college, I wound up studying something. Distance makes it much more difficult to pursue formal education.
n/t
I don't want to be mean, but if the submitter "took everything through AP Calculus in high school" and still "had [his] butt kicked by college calculus", then I can only conclude that the AP Calculus class he was in was a total joke.
I wonder WTF they taught the kids in the regular Calculus class...
Are all AP courses that crappy?
I, too, had to use Strang's linear algebra text. I know bunch of you think the world of him/his text, but I couldn't stand that shit - yammering on and on instead of getting to the point.
If I ever meet that dude, I'd kick his ass all the way out to China.
And then I fly to China, and kick his ass again to Australia.
And then I fly to Australia and...
Fuck systemd. Fuck Redhat. Fuck Soylent, too. Wait, scratch the last one.
Economics? Are you kidding? Economics is full of mathematics and mathematical models.
In sociology, and psychology some scientists build models for phenomena and those models are sometimes mathematical. I am a CS scientist but I work on building such models (models for human behaviors) and most of those models are mathematical.
Find an approach to doing math that makes it enjoyable for you. One thing that helped me a lot was getting a large whiteboard. I find I enjoy doing math more pacing back in front of a board and whatever else comes along with doing work on a board rather than a piece of lined paper. Chalk would have been better.
I disagree on chalk, but only because I have the visual acuity to see the dust floating on the air, the finkckyness to be unable to stop imagining that breathing the dust I can see would be harmful, and juuust enough sensitivity to high-pitched scraping sounds that every stroke is torture to me. If you get a good chalk-board (real slate, btw, or one of the expensive synthetics. paint just doesn't cut it. It takes a lot of effort to find a good chalk board.) some of that is mitigated.
Otherwise, markers are better. They dry out quicker, but if you care for them they're just as easy to see, allow multiple, vivid, colors, and have a significantly lower coefficient of friction across the board (so you can write more stuff in the same amount of time. Or just bigger stuff.)
More importantly, you can get a good quality marker board for cheap. By cheap, I'm talking $12 for a four foot by eight foot rectangle from the local big-box home supply store. One cut free if you live in a small location. Just get a plain white tile board panel and mount it anywhere you care to. It's a little harder to clean the first couple of times but after that the standard fuzzy styrofoam markerboard eraser will work fine. Considering the same size board from staples would, if I'm extrapolating correctly) cost about $450, I'd say it's a pretty reasonable compromise.
Can you be Even More Awesome?!
If you are really worried about it, why not give the Manga guide to Calculus and Manga guide to Statistics? I wish I had read them while in school.
Check this web site: http://nostarch.com/manga/
The guide to Calculus actually covers the following:
* Use differentiation to understand a function's rate of change
* Apply the fundamental theorem of calculus, and grasp the relationship between a function's derivative and its integral
* Integrate and differentiate trigonometric and other complicated functions
* Use multivariate calculus and partial differentiation to deal with tricky functions
* Use Taylor Expansions to accurately imitate difficult functions with polynomials
Based on the preview, it looks like a good intro to calc.
In molecular, that is pretty true, but you have to suffer through the acquisition of serious chemistry knowledge. However, what about the biology specialists that hate chemistry?
I have nothing to add but to say that you are all sorts of awesome in my book. My story is similar: sharp cookie, dropped out of high school to pursue women then eventually programming (aha, there was my mistake), blah blah, now I'm in my mid-30s finishing a math degree. Couldn't be happier. People like you inspire people like me.
It goes from God, to Jerry, to me.
For example:
theassayer.org
freetechbooks.com
I remember thinking that my Physics 1 class at the University level was really just an algebra/trig class in disguise.
You got that one backwards.
"Educate the mind but never at the expense of the soul."~Blessed Basil Moreau
I took a 300-level stats class for my bachelor's, and I found practically every element of the field to be pointed toward providing backing data as opposed to proof.
I'll take a second derivative over a chi square any day of the week. At the end of the day, the second derivative tells me when to act. That beats the ass off of telling me what already happened.
There's only one thing I learned from stats: correlation is not causation. And that sort of indicts the field itself.
My admission: by trade I'm a programmer. Any field of study that's more about finding outliers than determining right where the curve is tends to be of less use to me.
I scream. You scream. I assume that means we're both acquainted with the problem. We proceed.
I'd agree, but the kick-ass products would be "How to Ace Calculus" and "How to Ace the rest of calculus". Then the Schaum series make sense (like the College Mathematics book for example.
The "How to Ace" series make me madder than hell that it wasn't published twenty-five years ago.
Tubby or not tubby. Fat is the question
Hell, statistics should be a mandatory class taught in High School. It's far more applicable to everyday life than trig is.
But then how is little jimmy gonna know how tall the statue is on top of the building from 100 yards away.
"Educate the mind but never at the expense of the soul."~Blessed Basil Moreau
Well, it is a fairly fundamental and basic bit of modern mathematics and it you can't grasp the basics of it you probably will have a lot of trouble getting a degree in anything, let alone science.
There are many subjects where it can crop up unexpectedly and you wouldn't be able to progress in what you really want to know without a bit of the mathematics used to describe it. About all the lecturer can do is show you the door and tell you to come back later when you've learnt what your high school should have taught you.
For the simple stuff all it takes is time and a small amount of dedication, and there's some really good books that take you from zero to advanced.
Wow. Don't hate on it just because you thought "hey I'm 'good with computers' and this major says Computer in it" and got burned by math expectations. If you don't love math, you have no business being in CS. Computer Science is a of field mathematics, not an engineering program where you learn to fix and build computers!
For (potential) CS freshmen, I recommend going through the classic SICP video lectures. It's very appropriate how Sussman says over and over things to the effect of "we don't care how this would actually work, we're studying the theory." If that doesn't excite you, or you think functional programming is stupid and inconvenient, or if you can't follow a word he's saying, for your own good switch to a different major because it only gets harder and more theoretical. That course was given to freshmen. Clearly you weren't a good fit for CS, but that's because you couldn't handle the math, not because it was bullshit you'd never use.
It's really alarming to me how hostile a lot of posters are to academia. A bachelor's degree isn't a fast-track to get into a career, it's a period of academic study. You really have no business claiming that you completed four years of post-secondary study without some basic understanding of math- and calculus is really, really basic.
Good books can really help. I suggest _How to Ace Calculus: the Streetwise Guide_ and it's sequel if you are taking more than a first course in calculus. One really good thing you can do once classes start is to work with a classmate or start a small study group. It can be hard to stay motivated when you are working on your own - I recommend using CLEP exams to obtain credit and work at your own pace. Set a deadline for each test, and a definitive one for starting school again too. Good luck!
I would recommend Engineering Mathematics by K A Stroud. I guess these days it comes with a companion CD. The book covers almost all topics in a very clear and interesting fashion. All the best!
Calc:
Books!, get some good ones and read all theory, solve every example, do as much problems as you can and you shall pass. Particular suggestions? well I used stewart's calculus for theory, I am sure that there are better ones but it did the trick (for multivariable calc I prefer Espinoza Ramo's analysis vectorial dont know if it is available in english), those two will explain the theory quite well, try to do every doable proof for the identities you might have to use, it will help you remember them and and understand what they are about.
Buy them used, you can find the for less than a cup of good coffee, most books dont change that much from edition to edition, dont be afraid to buy a book more than five years old, get the compendium, at least with stewart's calculus you can get a book which includes single and multivariable calculus or two with each topic.
Lectures!, there are plenty of online lectures from many universities available online, I really enjoyed the mit ones available at mitocw and academicearth.org there are also lectures from berkley, I first red the book then listen to the lectures, with the mit ones there is even material such as examples and exercises available (at mitocw)
Practice!, as much as you can, concepts are sometimes easy to gasp, examples easy to solve, but many problems require certain math skill which you can only get by practicing, for this I recommend a series of books: Schaum's outlines, they are available for almost any course and provide an extensive array of solved problems to help you get the skill, dont look at them! solve them, and just when you are stuck look at the book. practice practice practice! (these books also come with a theory but sometimes too resumed and dificult to get without a proper background)
Stat:
Currently taking the course with university provided material, cant really help you that much, google a bit and I am sure that you will get some good book recommendations and adequate video lectures, there are also shaum's outlines for statistics, in this case I have found the thery available on the outlines to suffice.
Ps: you can get the books really cheap at betterworlsbooks.com dont bother with the last editions, an old book in good condition will be much cheaper and almost as good as the latest one.
No, many science journalists and/or activists misuse statistics. A very slim fraction of scientists do so. Those that do are often stripped of the title "scientist" when the fraud is discovered.
So if this is the future...where's my jet pack?
Saxon Math. It's used by a good number of people who homeschool. Usually any edition will work for you--just make sure the answer key is the same edition.
Three years ago I was in the same situation. Now I'm working on Calculus III.
First, I recommend investigating your local community college. Prices are cheaper than the more prestigious schools nearby. I've been told by my professor that the Calculus textbook (Thomas' Calculus Early Transcendentals) is also used at the Colorado School of Mines. The courses are evaluated and transfer programs exist. Your employer may offer reimbursement.
Take the school's math placement exam and it will slot you into a class suitable for your skill level. Trust the recommendation. It was spot on for me.
Most of the mathematics classes at my school use a Web based program for homework and online quizzes. It may take some time to adjust, but overall I believe it is worthwhile. It also offers immediate feedback which is very useful. The quizzes are annoying, but instructors are good about granting partial credit if you show and grade your missed problems.
Personally, I think the calculus textbook sucks. Many reviewers on Amazon agree. On the plus side, the same text is used for calculus I, II and III so the cost is not too bad.
Amazon pointed me to a few useful supplementary books.
How to Ace Calculus by Adams Thompson and Haas
How to Ace the rest of Calculus - same authors
The Humongous book of Calculus Problems -Kelley
I found a few useful web sites.
http://khanacademy.org/ had a large number of 10 to 15 minute free presentations covering many subjects. Khan is *very* good at explaining the concepts, and working simple problems. But he does not cover the more difficult ones. This is an outstanding site to browse or brush up.
http://midnighttutor.com/ is another very good free resource.
http://calc101.com/ provides free step by step solutions to derivatives and many other types of problems. They charge $25 for step by step solutions to integrals. This is money well spent when you are stuck on homework problems.
I've also heard of websites offering worked out solutions to every problem, but I have not used them.
The TI-89 calculator will solve almost every problem thrown at it. But only dumb, non graphing calculators are permitted on exams.
If you are a Mac user, check out grapher. It's installed by default and very useful.
Good luck!
Man -- you got my hopes up there. Not the same Khan, I guess. I was hoping for either Genghis, Kublai, or the one from ST...
Still, pretty cool-looking site, though. Thanks.
Paleotechnologist and connoisseur of pretty shiny things.
.
Bullshit - remember an integral is as simple as the area under a curve. Even just finding the area or volume of something can benefit from calculus. "Specialised degrees" comes down to pretty well everything where a concept involving numbers is mentioned.
Usually calculus is used as a tool to convey information about some physical thing or behaviour - for instance the relationship between displacement, velocity and acceleration. You might not need the numbers but you need a way to grasp the concepts.
For an analogy consider heat transfer. You don't need to work out the actual numbers to operate a PC but you do need to know the trends so you don't block up all the air vents and reduce heat loss from convection. You can't make a very rough estimate that something will be good or bad without a way to know about the trends of behaviour.
I think your view of statistics comes from a misunderstanding of it on a fundamental level (not that this is your fault). Statistics and probability theory are the basis for interpreting any kind of quantitative measurement. Beware: trying to interpret measurements without knowing this stuff is perfectly analogous to the way people used to build large buildings (sometimes successfully) without using any mathematical modeling, before things like Hooke's law were well known. Sure, plenty of buildings would collapse, but some fairly sophisticated buildings were built anyway, by people who would be grossly incompetent by today's standards.
patrickJMT on youtube has a plethora of tutoring videos for math from pre-algebra through calculus concepts.
After 10 years away, not even remembering how to do differentiation or integration, I've gone back to do statistics.
Honestly, I think you should just go back and do it - it's actually quite easy the second time around even if I have to relearn things.
When someone suggested my skills were due to a magical innate ability, I'd get ticked off and tell them no, everybody has the innate ability. My skills, in fact, came from many hours of tedious practice, doing the same thing over and over until I got it right.
I don't think it has to be one or the other. I've never been able to draw worth shit. I probably could learn if I really wanted to, but even as a kid my skills were mediocre at best. Rational thinking and separating out bullshit from what's real I've always been very good at, even as a kid.
I think there most certainly are innate talents. The idea that "anyone can do it" might be true if we all had infinite patience, time, and motivation. We don't of course, so we gravitate towards things which we develop at with less effort. If you work at subject A and get half as far as the average person, but work at subject B and get twice as far.. which one do you think most people will pick?
It's not magic, it's just how our brains are wired.
AccountKiller
To rephrase: it is assumed that a normal distribution is normal. Besides, there are always things that are abnormal.
I have yet to see a research article actually verify or check to see if that assumption is true.
I won't join Slashcott. OTOH, If Beta goes live, I just won't be back until it's fixed. Sorry Dice.
If you want to get started on calculus, check out what textbook the nearest University uses and just go with that. It breaks degeneracies when choosing the book, and you can assume it is as reputable as the school who uses it. It's not a perfect system, but it'll get you going; once you have a book, really getting to know it inside and out is the best way I know of to master a topic. It may seem weird, but many of the graduate students in my program have emotional connections to certain pages in textbooks because of how much time we spend with them.
I'm posting AC, because I'm embarrassed.
I am a researcher/professor. My work is heavily statistics-based. I teach research design.
But you know what? I can barely handle multiplication. I'm not kidding. I make so many errors that I won't do it in front of anyone. I can't factor. I routinely make addition and subtraction errors. I'm totally hopeless. I'm 35 years old; I don't think I'm going to get any better. It very literally feels like I'm retarded, and it's really embarrassing, especially at my level.
I didn't really start liking (or getting good grades in) math until it got more symbolic and we could use calculators. Concepts are no problem for me.
What I'm saying is that I have come to the conclusion that those are discrete cognitive skills. Algebra is not a superset of arithmetic; it's a different thing altogether. This is probably why so many people hate it at the beginning--it's a total gear-change from arithmetic.
And this is why I have spent my education career avoiding the GRE. With no calculator, I cannot do the math questions with any reliability, unless they really are just symbolic. I feel like I scammed my way into a career, but I actually am very good at statistics... Just not math.
Amen. I didn't take any stats until I was doing my master's either, and the learning curve was steep, but before my first class was over, I was virtually shouting to anyone who would listen, "Hey! Do you know about statistics???" That should be the primary mathematics taught from high school on. It is applicable to everything.
I look back on all the math I had in high school, and I think, "Okay, I use geometry every time I build or repair something, I use trig every time I... launch rockets at the moon... or something... I use calc... Shit, what is calc even for?" I think that if we replaced a lot of those kind of physics-related math classes with stats, people wouldn't give up on math so soon, and they'd also learn to be more critical thinkers about the world.
How could anyone ever claim it was useless???
I had no real impetus to relearn a lot of my forgotten math from engineering until recently. I've been helping my gf get through a Calculus I class.. she approaches me when she really gets stuck, and I usually end up finding a similar problem on the internet.. Yahoo Answers in particular... and then between that and the resources she's provided, I have confidence in my ability to do all of it. Not sure if this is applicable in your situation, but it worked for me.
I suggest you do an interlibrary loan on the 3 volume programmed course Pre-Calculus Mathematics by Vernon E. Howes, copyright 1967. Furthermore, I suggest again to do an interlibrary loan on the 5 volume A Programmed Course in Calculus. The latter is from the 60's also. Both sets of the books allow you to quickly get up to speed or review forgotten concepts.
And Computer Science should most definitely be considered a Liberal Art, mainly as a derivative and/or specialization of Logic.
The study of "Humanities" would also fall within a Liberal Arts degree, it might not be pertinent to your specific Liberal Art.
But a liberal art none the less. However, you may find more direct applications by looking into Digital Humanities, a task of multimedia archiving, collating and presentation, you tube could be such an application.
The actual Computer Science (CS) degree at UMUC requires calculus, the Computer and Information Science (CMIS) does not, although it still requires algebra.
I started in CMIS and recently changed to CS. Taking calculus online was a real gut check but very satisfying when I finished.
Yay me! ^^
The problem with this is two-fold: many high school math teachers fail to fully grasp statistics and learning from one without a complete understanding can be worse than no class for students; the other issue with statistics is that half of it relies on calculus, much the same way Newtonian physics. The normal distribution makes no sense without an understanding of integration, the same with other continuous distributions. While I work in a discrete field myself, for many applications, an ability to deal with continuous variables is a must.
Before you decide, ask yourself... if you needed brain surgery, would you prefer the doctor who actually read-up on how to perform it, invested the time and practiced, got good at it, or the one who logged onto slashdot and asked the community how to perform brain surgery? No one can learn your math for you. What you do about this depends on why you need the higher level math course. Option One, you take the easy way out, and then you crash and burn in the math class, having cheated yourself out of the foundation knowledge you need to succeed in the course, or... Option Two, you bite the bullet, and purchase a textbook for each of the classes you need a refresher on, and work every problem in each book, which if you still have the knowledge dormant, shouldn't be all that hard. If you are unable to solve the problems, refer to the text. If you still can't figure it out, go to the learning center/tutoring center, and ask for help there. If you go with option one, and by some miracle pass, hopefully neither your future, nor anyone else' future, actually depends on your skill at math. BTW: I know whereof I speak. I took College Algebra in 1996, and Trigonometry in 2002. Before enrolling in Pre-Calculus, I got a college algebra book and a trig book at a used bookstore ($2.95 for the algebra, $4.50 for the trig) and went through them. I had forgotten more than I'd realized, and if I'd tried to walk into PreCalc without remembering what Completing the Square was, or the Bernoulli Triangle, etc., I would have been in deep trouble.
This is exactly why we need more engineering schools offering majors in "Software Engineering". Computer scientists like to masturbate with theoreticals quite a bit, and those who like to masturbate the most are mostly those who have no business designing and writing software.
For the majority of us, a year of calc, a semester each of stats, linear, and discrete are quite enough. And no, those aren't "hard" maths.
These are the sites I used to get me through the end of my college mathematics courses.
http://tutorial.math.lamar.edu/ - Used during first year calculus
http://khanacademy.org/ - found these for multivariable calc and differential eqs.
I'm a Computer Scientist/Software Engineer (I dropped out of the research end a few years ago - my current job is R&D in the commercial realm so I'm not sure what to call myself), before that I was a land surveyor. My parents owned that business and I started work there when I was 12 (apparently that is legal for your own kids - they payed me minimum wage so at 12 I was the richest kid in school and was happy :)). As a Computing researcher I can't say I did much calculus at all. Most everything was heavily discrete math. Lots and lots and lots and lots of discrete math.
I have, however, used calculus a few times as a land surveyor even though they are less likely than a computing professional too.
We had done a topographic map of a local gas depot's containment pits for their tanks. At the time some new regulations for the pit had passed and (I'm going to botch these numbers - fine details like that were too long ago) they had to go from 105% the volume to 115% the volume and they wanted to know what their current containment was. Most surveyors know very well how to draw topo's and with software how to calculate volumes and such, this was before said tools were widespread. So I basically did an integral to calculate the "area under the curve" with the curve being a close approximation of the contours (which were smooth and a spline was highly accurate). They ended up with ~90% of the volume contained (I know it was around that - I recall a little over 10% spill over). After me redoing my numbers (still in college - who am I to contradict a licensed engineer who designed the thing) I realized the person had simply made the containment pit "square" - that is the side sloped to the bottom at around a 45 degree angle and a several hundred foot long pit dropped about 3 foot from one end to the other. The engineer took the highest point on the burm, the lowest point in the pit, and the dimensions around the outside of the pit and calculated a volume. I had less than a .5% error from his numbers from the one we produced if I used that method.
After calling their head engineer and telling her what we found she went back to the person who originally did that and asked - I was correct. I had also submitted a full accounting of how I came to my conclusion on the area. They asked me to calculate how much more needed cut, I did so, they signed off and built it, and I'm still not sure how that makes me feel. I was a college student and not *remotely* qualified to do that. I figure they had me do it for the same reasons the person screwed up - it was cheap. They payed my parents 50 dollars an hour for me to do that, their staff drew it up, and their engineer signed it. It was good money for me (they gave that financial part of the job to me) and no liability on us - we were clear we were not able to do that or sign off on it and had it in writing. In that sense I'm OK with it, in another I hope the other parts of the system were done better than that was originally. They just lucked out that I could do what they wanted and had enough knowledge to do so
I'm lucky enough to both have had the correct schooling and ability to apply that - since then I've learned a great deal and know I inferred the correct things. Yet, I really shouldn't have been put in that position, but it at least gives me an amusing story I guess. Indeed, as I have aged since then I have become more and more aware of how truly lucky they were that I still know I did a working design. I clearly recall long phone conversations where I kept saying I was still in school and they didn't care.
Then, none of this helps the OP. I do not know the answer to his/her question. Calculus was always a struggle for me due to dyslexia and an insistence on memorizing forms (thats about like demanding an armless person catch a football with their hands). I never once had the issues they stated - I was in graduate level math (graph theory and formal languages/computability) before I made it through calc II. It took
------- Sorry about the spelling, I suffer from two problems. Dyslexia makes it difficult to spell well, lazy makes it
Learning the tools is only half the job.
Skill is being able to pick the right tools throughout the process.
For me, at least, it's never been enough to learn the tools and techniques.
As you've already learned, use it or lose it; if you want it back, start working the exercises.
"Reality is that which, when you stop believing in it, it doesn't go away." - Philip K. Dick
Hell, even psychologists employ statistics!
Even MIT has stopped teaching functional programing in most of their CS courses. They switched to a combination of Python and Java.
Frosty piss posts are worthless, GNAA posts are worthless and hurtful, but they are the least of this site's neuroses.
I've never been able to draw worth shit. I probably could learn if I really wanted to, but even as a kid my skills were mediocre at best.
If I really wanted to. That's the key right there when it comes to learning anything, not just drawing.
It's not magic, it's just how our brains are wired.
You're right, it's not magic at all. When I started to draw, I was also mediocre at best. I became pretty decent at it--although no one would have ever mistaken me for a Great Artiste--because I wanted to learn. The point I was trying to make is that you or anyone else could have become at least as good as I am at drawing if you'd been willing to put in the time to learn the skill. You weren't interested in doing that, which is fine, but my experience has led me to believe that almost everyone has a certain level of drawing ability hardwired in and they just need the training to develop it. However, that training requires commitment and a lot of tedious work, which was the part I was proud of and why I'd get ticked off when people suggested it was some sort of mystical craft that came without effort.
Of course, just as in any field, there are people who do excel, seemingly without effort, but people like Picasso only come around once a century and, besides, you don't have to be able to work at that level to make art worth doing.
This ain't rocket surgery.
I didn't see anyone post a link to http://justmathtutoring.com/
The videos are posted on YouTube but that website maintains the index so you don't have to search around. These videos helped me immensely when I was taking calculus.
Yay me! ^^
The Teaching Company is a great resource for lifetime learners. I've used a fair number of their products over the years and they have a lot more positives than negatives. The only thing I dislike about their course offerings is there is too little to acquire with regards to MBA-style courses, but that's neither here nor there.
I think the two courses you want are:
Understanding Calculus: Problems, Solutions, and Tips by Dr. Bruce Edwards, and
Change and Motion: Calculus Made Clear, 2nd Edition by Dr. Michael Starbird
I have the second course and although I haven't gone through it yet, it does not look too shabby.
You might also do well to consider a calculus book by Schaum's.
http://www.mathehilfe.biz/
nachhilfe zu mathethemen als youtube videos
Also, don't forget the best mnemonic of them all, very useful in trig:
some old hippie caught another hippie tripping over acid
(sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, tangent equals opposite over adjacent)
I had to wonder if my alter ego was posting this question, but I knew it couldn't be me since because I'd been out of school for 30 years before returning last fall. Statistics is now a required course for CS at my school and took it first thing (the academic adviser signed me up) and I did struggle a bit because I couldn't follow the proofs involving calculus without help, but I still got an A (we didn't have to know the proofs for the exams). But when I saw the text (Pattern Recognition by Bishop) for the Machine Learning & Data Mining class the next quarter I knew I had to seriously (re)learn some calculus. I looked through a number of books and when I found Calculus for Dummies by Mark Ryan I knew I'd found exactly what I needed, the workbook is helpful too but not essential. Don't bother with Calculus II for Dummies though, it just an ordinary (which is to say useless for the non-naturals) calculus text (although I did pick up PDE from it in a brief look through).
And as it happens, the rules on AP Calculus transfer have also changed and I'm probably gonna wind up taking first year calculus anyhow, although pretty much too late for it to do me much good (it would have been helpful to do that before those classes I mention above). I will probably take it online from a community college rather than at the university though, which is what I'm also doing for the foreign language requirement. Thirty years ago the university didn't make CS majors take a foreign language reasoning that computer languages were foreign. We knew that was a joke then, of course the joke on me is that they fixed it in the interim.
For free online resources, the Kahn Academy videos are pretty good if that form works for you. http://khanacademy.org/'
Don't listen to all the noise on in this thread. You're totally The Man for braving the slings and arrows in returning to school. It's actually pretty cool in a lot of ways. Among other things you get treated with a rather large measure of respect as a result of being old(er). That is probably on account of the kids thinking you're likely to be a professor or at least a grad student.
No, you've just been doing it wrong. A lot of the humanities require one to imitate, study and analyse the work of masters. It's like programming; without looking at some good code and studying the logic and design patterns, anything non-trivial that comes out of your keyboard is going to be a lump of mud. Don't let the ethos that the humanities are 'soft', magical, arbitrary things; they are art in the sense of Latin ars in their very technical essence; they are founded on great skill, practice, and a tradition of heroes who strive to attain aesthetic perfection.
I was using Calculus by steward for my college classes: http://www.stewartcalculus.com/ It covers calc 1-4, and most likely a bit more as well. calc 1 is equivalent to ap ab, while 2 is equivalent to the bc test. If you go through that book, you should be covered rather well. And the solution manual is available for half the problems, and works them out too.
In my experience, you need dozens of hours of practice before you get it. Buy an algebra textbook, and do every odd problem in every section until you are reliably getting everything right. My experience = flunked high school math and went back to college 10 years later....
Precisely my experience too. Being ten years wiser and more motivated made all the difference in the world.
Do -not- just read about the stuff, practice! Make errors, figure out what you did wrong, do it over again. And again. Though this may sound terrible now, finally getting the hang of these things will actually feel nice.
I also found it useful to make my own quick references (cheatsheets). The formulas stick better when written down by yourself. It's a bonus if you are allowed to use them on the exam, but if you really practice a lot you won't need them anyway.
Remember the AHSME? American High School Mathematics Exam? Now it's known as ACM10 and ACM12. Try to take a sample test and/or a full test, do the problems until you are stuck, then seek help. This is the fastest way for you to get up to speed IMO.
A lot of these math problems requires knowledge from multiple high school math courses, but yet don't need calculus to solve. It will help you refresh your geometry, trigonometry, and algebra all in one go. If you are determined to solve the problems, you will find ways to look up the necessary knowledge to solve them, it's a good way to refresh your math knowledge as well as get some problem solving exercises for your brain.
Once you try a few problems, you might realize which areas of math need more remedy, and just dive into the text books for those sections. I think this is a fun way to get your math skills back up to speed. But remember that nothing can replace hard work, you just have to go over a lot of problems like you did back in high school.
Me too. I studied at the University of Manchester University.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Did anyone notice, everyone is so busy squabbling that no-one really answered the question?
I'm 60 this year and have the same problem, I got quite a long way in that I studied some quantum machanics about 40 years ago. As i'm in the UK, I'll probably do an Open University course: http://mathschoices.open.ac.uk/routes/p5/index.html I'm not sure what the equivalent institution is elsewhere.
On y va, qui mal y pense!
Calculus is particularly useful for calculating ballistic trajectories.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
"The point I was trying to make is that you or anyone else could have become at least as good as I am at drawing if you'd been willing to put in the time to learn the skill. "
The problem is the amount of time and the rate at which you learn, learning to draw is about observation and _conceptually_ grasping techniques and tools. Some people have _natural_ unconscious understanding of techniques and tools and if you asked them outright "how do you draw so good?" they couldn't tell you exactly why. The artists that are thinkers (ones that focus on observaiton) and technique can usually tell you use x tool for this, to do this you do that.
Drawing is a process you learn by mimicking and lots of the best artists could speed up other peoples learning by posting videos on youtube and tutorials about how they go about drawing things.
But there *are* naturally talented artists who don't need training wheels or line of sight lines who can simply 'draw' from memory or their imagination, go watch something like this and check out other artists on youtube.
http://www.youtube.com/watch?v=ssOJQXdwmrI
Many times you get a drawing wrong is because you missed a step somewhere or someone somewhere else has figured out the *best set of steps* to draw certain things in order because of problems that may crop up later if you need to change anything.
This kind of info is learned from years of experience from both trial and error.
Often I find learning math from humans is the best way to go. If you have some colleague who would be willing to tutor you, that might be the most efficient use of your time. At the least, they could give you some basics and tell you what concepts are particularly important.
http://www.artofproblemsolving.com/ might be worth a look - it is intended as enrichment, but has a rather active community of problem solvers and problems that may be more stimulating in relearning the alg/pre-calc material.
But then how is little jimmy gonna know how tall the statue is on top of the building from 100 yards away.
He will look it up on wikidpedia or read the plaque in front of the building pointing it out.
Wow... the firehose is in full spray mode today. First off, thanks to those of you who actually responded to my question and suggested books, sites, DVDs, etc. You've given me plenty to look into. I don't know if it's worth it to even mention it at this point, but here's a little more information. I didn't mention it earlier because I was trying to keep the post short and focused (not that it helped, with all the arguments about calc vs. stat I started!). I worked in IT for ten years doing everything from electronic form designs to help desk to network administration to database administration to network engineering to phone cabling to basic web design. Since I have the work background, I want a piece of paper to go with it. It's as simple as that. Well... that and I'd really like to finish a degree at some point in my life. Current degree program: Associates in Information Technology at a community college, all online. Reasons: 1) cost (not going to throw my money away on lower level courses) and 2) I live in Albania right now, and in Mexico before that (and who knows where in another couple years - my wife's job will move us every few years). So, access to English speaking tutors - limited; access to local college resources - very limited; access to good US libraries - none. I might go on to a bachelor in IT at some point, but at this point I just want to wrap up this degree. Am I willing to do the work and learn the material? Yes. I simply do not want to waste my time on entire semesters of material that I might be able to refresh myself on in a few weeks to a month. If I hit a spot where refresher material just isn't cutting it, I'll take a full course. I don't want to test out of calculus - I want to slay that particular beastie with my own two hands! I enjoyed math in grade school and high school. Who knows? Maybe I'll learn to enjoy math again and get a degree in it. And to respond to the "bag groceries" comment, been there, done that (worked six years in a grocery store after dropping out of college, also a car wash and fast food). :-)
Check out Kahn Academy http://khanacademy.org/. They have short 10-15 minute video on all types of math in easily digested servings.
I really agree with the sentiment of doing problems. That is why Chinese students seem smarter at math. Not because they are, but because the do problem after problem after problem after hour after hour. Also, they tended to hang out with others that could speak their own language (aka other Chinese), who would also be doing math. Which no doubt they played off each other for help and encouragement.
Take the cheese to sickbay, the doctor should see it as soon as possible - B'Elanna Torres, "Learning Curve"
Go back to college and pay for it like I have to. Why should anyone give free education away when we're forced to go into debt to acquire it ourselves.
we understand 0% of the world around us well enough to say with 100% confidence what the outcome of a certain event will be
I'd say that if an event is certain, we know 100% what the outcome will be.
The question of whether a computer can think is no more interesting than the question of whether a submarine can swim.
Computer Science is a of field mathematics, not an engineering program where you learn to fix and build computers!
Funny thing is, I knew a person who repaired computers for a living who said he quit studying Engineering because of the Math. It seems you don't need math (i.e. calculus) for a lot of things, including even science.
You really have no business claiming that you completed four years of post-secondary study without some basic understanding of math- and calculus is really, really basic.
Clearly, like one study here on Slashdot demonstrated, mathematics can chloroform your brain. As for "hate" I think the poster was thinking more about expectations, which brings us onto the next paragraph:
It's really alarming to me how hostile a lot of posters are to academia. A bachelor's degree isn't a fast-track to get into a career, it's a period of academic study.
That is a problem with high school. People go through (generally, in North America) four to five years of high school with no idea how useless a university education is to the vast majority of the population (no matter how "bright" they may appear to be). There's clearly something very wrong with high school if teenagers aren't taught that university is (more) about academic ideals and not about real world jobs. For decades I've been hearing that there is a shortage of "trades"; tool-and-die makers, machinists, plumbers etc. I'd have thought that most high schools these days would have adapted to the job-market and would be primarily offering courses in these trades.
As an idealist myself, I'm university and college educated (with even more at-home self-study), but don't let that be an example to anything but idealism; I find it difficult to find (even) manual labour work (which is very under-rated, both in terms of pay, prestige and in difficulty).
My school frowned upon using calculators in class.
My elementary school frowned upon ball point pens to. Something about penmanship. So we used fountain pens. The nuns would whack us with a ruler if they caught someone with a ballpoint.
Thankfully they still make fountain pens, so I am able to write.
Parts of biology are getting insanely mathematical. Very recently, say the last five to ten years, there has been a large influx of mathematicians into biology. They use stochastic analysis to model various processes such as transmission of genes to offspring and growth of cell populations.
A decent fraction of the PhD students in my department (maths) are involved in biology.
Slashdot: news for Apple. Stuff that Apple.
If you live at or near a college town, go to the math department itself. See if they have a preferred tutors list. Pick 3 names off the list, generally the senior the better.
Write each of them an email, explaining to them your particular quandry. Let them know what statistics/math course you want to take to graduate. Ask them about the pre-reqs and what you have to know from them. Let them know you will be looking for a tutor to help them out, tell them what your rates are (generally 20 bucks an hour in a midwestern university is fair. Youe also being tutored really easy math classes).
For example, whilst my Alma Mater numbers their engineering/science statistics course above calc I/II/III and diffy-q, one only needs to make calc I and II to get the pre reqs out of the way. In all honesty, the level of integration is simple enough (and it not like you actually have a clue of what is going on anyway) to warrant only calc one to follow the instructions. The necessity of calc II is part training you to follow instructions better, and part bureaucracy trying to siphon more money from you.
From your story, you seem most likely needing refreshers on college algebra, trig, pre calc and then business calc one and two, if not more, depending on the difficulty of your statistics course. You cant actually talk to an academic advisor, because they will try for good reason to get you to enroll in the courses that they think you need. That is their job, nothing you can do about it.
From the pre-reqs, either obtain the list of text book(s) from said TA or find the syllabus elsewhere, generally from emailing the instructor of a running class. If you tell an instructor that you would like to freshen up on the material but not take the class, if you could get a copy of the syllabus or audit, most of them would be most obliging. Do the problems on your own. If you want, go on Amazon/Half/Ebay and find the instructors manual. Push comes to shove, if you still cant make heads or tails of a problem, email your Tutor TA about setting up a time.
I suspect if you are diligent, i.e. 2 hours a day, you will drill through most of College Algebra in two months. After that if you remain diligent, you can expect to move through trig and pre-calc in another 2-4 months. Set goals and remain diligent at keeping them by eschewing wine, song, gaming of all sorts. It going to require a great deal of discipline, but if you follow through, youll end up wanting more. Best of luck.
I'm sorry, but how did you test this theory at a confidence level of 100%? :-)
Eliminating all uncertainty would be really handy, and I could thoroughly use this 100% confidence level (given this level isn't infinity, since I can't do shit with that).
Those who struggle are those who never learned high school algebra (or god forbid, arithmetic) well.
Like me. I failed my way up through high school with C's and D's. Except I proceeded to continue learning math on my own after high school, through my hobbies. When I got to college, I breezed through algebra, calculus and trigonometry with A's. I took college seriously and did the homework. The only thing high school taught was how to deal with boredom, and how to do the minimum amount of work.
I actually freaked out a math teacher in high school once when he saw what I was scribbling on the back of some papers (in a math class I was failing). I had rediscovered Pascal's Triangle, while doing some heavy programming and I was half hoping he'd see it, so he could tell me what the heck field of math it was. At the time, I was digging into Combinatorics (unbeknownst to me), because I thought my "two to the power of a prime number minus one" formula, was yielding larger primes. I hadn't tested it thoroughly yet, but it looked promising... 2^2-1=3, 2^3-1=7, 2^5=31, 2^7-1=127, 2^11=2047... obviously it doesn't make larger primes 100% of the time, but it's an amazing thing to find as a 17yr old kid.
Lemme guess... sociology? No wait, surely even that uses calculus...
I'm a Masters student, and I do a LOT of calculus. Almost any useful model can be hugely simplified using it.
Granted, computer tools can do a lot of it for you these days... but not always, and you still have to understand what's going on.
If you don't understand the model, you're probably not doing proper science.
What Garridan said about symbolic manipulation and rock-solid algebra is probably true about the majority of current calculus courses. However, I like to take a different approach to calculus. You start with general ideas explored somewhat qualitatively. The ideas include limits, series, convergence, and manipulating "infinities of different sizes." Once the ideas are in place, you gradually fill in the computational apparatus for them.
I do this with kids in Math Clubs, and they can be as young as six when we start. You can find parent descriptions of some of our meetings at the Natural Math email group: http://groups.google.com/group/naturalmath/topics There is also a good book about this approach, called "Calculus by and for young people" by Don Cohen: http://www.mathman.biz/html/chapters.html If this approach makes sense to you, consider getting Don's book from the library.
(no mod points, never took stats, now use it for a living)
there is no thing
what else could you want?
Try one of the "Algebra for Dummies" books.
They're not only educational, but entertaining.
I have Masters in both Economics and Comp. Sci. Any math you can apply to one can be applied to other. It's pretty foolish to assume there aren't smart people in both fields that find ways to use mathematics in either one. That said, I teach economics at a few colleges/universities around my area (full-time and part-time). Once you get into the junior/senior level econ. classes, I use calculus and statistics on a daily basis in the lecture. It all depends on what you are going to use the classes for though if you expect to be continually using it into the future (building economic models, lots of calculus, differential equations, linear algebra... forecasting them? More statistics based...)
I have never let my schooling interfere with my education.
I bought a DVD a few years ago that I thought might be useful for my son in a few years...
Here's a preview: http://video.google.co.uk/videoplay?docid=-1873635453969513506
Auto-check your UK lottery lines
It is nothing like Programming. It is either high-paid labor, or it is cutting edge math and chemical.
Back in the early 80's, I was working on sequencing DNA using Maxim-Gilbert and the new sanger-nickols (dideoxy) approach while doing my BS. What we did was to follow the papers laid out by others. It was nothing more than a repetitive type work. At the time, I approached my boss at CDC and suggested a different way to sequence: fragment them using the dideoxy approach, and tag with luminosity, and then use HPLC to sequence and of course, use a computer to put the fragments together. At the time, my boss felt that it was not possible. A decade later, the automated machine was done. Of course, it simply automated the lab rat approach lowering costs and improving QA. It did nothing to improve the speeds
The 2006 X prize is now going to get my HPLC approach going. What will it take to design this HPLC approach? SOLID MATH. Why? Because you have to design the columns in different strategies, which will require one to figure out rates on the design of the columns, as well as a shifting binary or possibly terinary solution. The solutions can be simply edged triggered (count off x number of BP, and then increase solution b), but the columns are a whole different thing. They will require several sintering sizes as well as different chemical matrix. This is pretty much the ONLY way that somebody can win that X-Prize.
I prefer the "u" in honour as it seems to be missing these days.
Here's an interesting concept.
I suck at math. I was never good at it in school. I fought viciously for every concept I grasped. Yet I loved every minute of it, and eventually got past two calc classes (Calc 1 and Descrete structures of Calc). I probably would've gotten farther if I didn't drop out of college to take a job in software dev.
I was always good at English and drawing. When I was a toddler my aunt (who teaches illustration at a pretty prestigious university) taught me the basics of how to look at things when I draw. From then on drawing came easy to me. For some reason English comes easy to me as well. I actually spent most of my time in English and writing classes doodling, working on math, and getting A's.
Drawing is easy, Math is hard. Guess which one I took farther? (Being on slashdot right now should give you a clue). You're not 'born' with a hard limit that says no matter how hard I try I can't ever learn calculus, or how to write a novel, or learn to draw. It's all about desire to learn, and from what I've seen that's a fully learned trait.
"There is no royal road to [your math discipline here]."
That said, maybe Manga Guide to Calculus? http://www.amazon.com/Manga-Guide-Calculus-Hiroyuki-Kojima/dp/1593271948/ref=sr_1_1?ie=UTF8&s=books&qid=1270383631&sr=8-1
``Tension, apprehension & dissension have begun!'' - Duffy Wyg&, in Alfred Bester's _The Demolished Man_
Most higher math courses in college are almost all formulas. In high school math you learned about algebra/geometry and in grade school you learned arithmetic. But once you get to college most of it is just re-using those skills with various formulas. There are two approaches to learning college math. 1. You understand every formula, the derivation, the proof, and where it came from. 2. You just memorize the formulas and how to use them. Both will lead to A's. I did a hybrid with understanding the core of the math classes but memorizing a bunch of the secondary formulas.....
Anyway Calculus is the study of limits (more or less). While you may not be doing integrals or computing derivatives all the time, the concept of limits does come in handy. What if you get some formula to model a population and then want to know what happens as the animals keep multiplying? So you would want to take the limit as n approaches infinity. In computer programming I often use limits to categorize a complicated function in Big O notations. Basically I ask the question, what happens as n approaches infinity. Also rates of change in finance/physics often use calculus. I would expect biology has rates of change. Mostly I don't do the calculus because people approximate the rates of change or use average rates as opposed to the instantaneous rate.
But the idea of derivatives is that you are looking at a rate of change between two points, and then using calculus you shrink the difference between those two points to be infinitely small to get an instantaneous rate of change. And in integrals the main idea is that you are computing the area under the curve. In order to do this, you chop the area into infinitely small pieces and then add them up. The main idea being that if you use small enough pieces, then even the curviest line has each piece looking like a tiny trapezoid. But conceptually if you take some curved line and divide it into tiny sections, you will see that it is almost like a bunch of little rectangles. And it is pretty easy to compute the area of a rectangle.
And the real value in calc is that computers can cut things into small pieces, evaluate functions, and then add them up. You have to watch rounding errors. But rather than using all the calc formulas, people who actually solve calc problems often use numeric rules to have a computer do the problem. Many integrals cannot be solved with the formula and integration rules you know. But through a computer, you could use Simpson's rule to basically divide the function into tiny tiny pieces, evaluate each piece, and add them all up and get an answer.
Mostly I didn't need calculus for statistics because for computer science the focus was on discrete events. But there was one section on continuous probability where you needed to do an integral. Basically the idea is that the probability distribution is a function and to evaluate the probability of an event, you sum the area of the function (which you use an integral to do). Most likely the integrals in that class will be more simple straight forward ones, so using an integral table and understanding how to evaluate a definite integral should be enough. The rest is basically all formulas. Discrete probability, conditional probability, rules for combining probabilities, counting rules (permutations/combinations), etc.. Then there will be probability distributions which will have formulas for the mean, standard deviation, etc.
Also statistics classes are often taking by business people, and they have a watered down simple calculus instead of the engineering level calc. Sometimes they get one or two semester calc courses while engineeres get 4 or more semesters of calc (or now as is common 3 semesters of higher credit calc courses....ie instead of 4 courses with 3 credits each you get 3 courses with 4 credits each.....). The business people often get one or two semesters of 3 credit calc courses. Basically it's just enough to cover differentiation and some applications and integration with some applications. The sequences/series/multi-variable calc/etc. is usually not done.
Oh, did I mention physics, biology, and the French Revolution?
Ruby Neural Evolution of Augmenting Topologies
There is only one way I know of to learn this shit ... find a text that speaks to you and starting doing all chapters. I like a big heavy book for this. I hit Anton 6th edition when I went through.
The first time through a standard 1000 page book, read all, do the worked examples and every second exercise at the end of the chapter. The first time through you can skip some of the last few examples.
It is not as bad as it sounds. Do two hours each night and after a week your general problem skills will improve. You'll get faster.
After becoming proficient with multivariate integration with its applications it is time to go through the book a second time doing all worked examples and all problems.
Total time six months to one year depending on life necessities.
.
After reading through some text books, I found I only really learned and remembered the material if I did the exercises at the end of the chapter. I've wasted lots of time just reading a few books, understanding what I was reading, only to forget it later. And when I did tackle the exercises, I sometimes find that I didn't correctly understand the concepts, especially has the classes get harder.
Another book to check out is the classic Stewart Calculus book. It'll probably be the book you use in class. In addition, the appendix has a few dozen pages on algebra, geometry and trigonometry might be what you're looking for.
But I mostly want to stress: practice practice practice
Yeah, but Einstein was right you know. So you'll eventually replace that Bohring stuff with something more exact.
.
Don't you need calculus to do stats?
http://outcampaign.org/
So, it helps to have a strong passion to get you through the necessary time it will take.
Ruby Neural Evolution of Augmenting Topologies
As a calculus teacher
Bias alert! :D
I've loved the most this site: http://tutorial.math.lamar.edu/
What about Calculus Made Easy? "What one fool can do, another can". It was good enought to get Richard Feynman started.
http://www.pathstoknowledge.net/ has a large collection of links to math and other science videos available from universities. Look down the right side and you'll find the links way down under "Science Info Educational Videos". A lot of great courses all free, with many from major universities.
Whether you use calculus or statistics will depend on what career you end up in. Statistics are used in many industries to prove cause and effect in order to improve processes. They are very important in the pharmaceutical, manufacturing, and other businesses as well, but you could be in a position in those industries where you have no need to use statistics. Same for calculus. It was required as a prerequisite in one MBA school, but not in another. So in some business environments, it may be useful. In others, you'll never need to use it. When I was considering one MBA school that did require calculus as a prerequisite, I took a proficiency exam to satisfy the requirement. I had never had calculus before, so I asked for an outline of the knowledge required and studied the first 6 chapters of the book The Complete Idiot's Guide to Calculus. It made calculus fairly easy to understand (for me, anyway), and I passed the proficiency exam for calculus. It didn't make me an expert in the subject, but if you want a good starting point as a refresher for calculus, I can recommend this book. For statistics, I can't recommend any book on my own experience. I learned what I needed during an intensive 160 hour training course in Six Sigma techniques. But I would bet that this book would also be a good starting point for you as a refresher: The Complete Idiot's Guide to Statistics. Both are available on Amazon.com. You can get both as used books there for less than $18 including shipping.
For me, the "free calculus videos" at http://justmathtutoring.com/ made a world of difference. Things I'd struggle with for days he makes me understand in less than 10 minutes.
Here's a link that I don't think has been mentioned here yet:
http://cow.temple.edu/~cow/cgi-bin/manager
You might find this selection of stuff (calculus plus a few other bits) more tractable than some of the other possibilities.
I've gone back to school to specifically get my degree in Computer Science. After watching this lecture I have to say that I made the right decision. He's not the best lecturer in the video, maybe he's improved, but I now know I picked the correct field. Thanks for the link.
Save Pangaea!! Stop Continental Drift!!
I'm almost in the same situation as yourself. Went back to university in my early thirty's after 10 years outside of academia. One site I really liked and recommend it the Khan Academy site. It starts with basic arithmetic, allows you to work through multiple examples while grading your progress as you go along. Works it's way up to derivatives the last time I checked. I'm really not doing justice to the excellent work done by Sal (if my memory serves me well that's his first name as well as being a MIT graduate). The site linked to youtube videos explaining the concepts and back when i used it all of this was completely free. If you happen to know anyone related to this site, tell them I said thank you. S.
"You're not 'born' with a hard limit that says no matter how hard I try I can't ever learn calculus,"
You are born with a kind of hard limit you just don't see it in your lifetime because _Everyone is so average_.
Take a look at Kim Peak and Daniel tammet, these guys have _Natural_ talent things are happening and being solved automatically on a subconscious level.
Kim
http://www.youtube.com/watch?v=leBpj14h_uY
Daniel
http://www.youtube.com/watch?v=AbASOcqc1Ss
I've noticed, comparing what *I* did for math analysis (pre-calculus) and calculus in school back in the 70s and what my daughter is doing now, that, today, knowing values of trig functions is not useful. Back in the precalculator days, the problems were chosen to use "easy" angles (45, 30,60, etc.) and knowing the trig function values made working them much faster than looking it up in a table or using your slide rule. Today, though, everyone has a calculator and is expected to use it. So the problems (both on homework and on tests) do NOT use any particular angles.
You need those trig identities, though. sin^2+cos^2=1, law of sines, law of cosines, half angle formula, sum and difference, etc. Even if they give you a sheet with formulas, you are basically just using it to make sure you get the sum and/or difference correct, not to figure out which one to use.
At my school is was:
Some Old Horse Caught Another Horse Taking Oats And Thought "Santa Claus"
(The last being Tangent equals Sine over Cosine)
This may be a bit more advanced than you are looking for, but I do have a free online differential equations textbook if you need:
http://www.jirka.org/diffyqs/
What you're saying is technically true, but the cause of it can be linked to many things. Say child A enjoys drawing, and doesn't enjoy math. And child B enjoys math but not drawing.
Then logically child A is going to draw more than child B, at least a little more inevitably, because he will spend more time on each drawing, perfecting it. So he'll outpace child B at drawing.
As they go on through life and child A spends more focused time drawing, and less focused time doing math their abilities are going to spread further and further apart. Even during the times they spend doing the same activity, child A will be paying more active attention if it is a drawing activity, and child B will be paying more active attention during math. If child A makes a conscious decision to enjoy math however, and spend time thinking about it and approaching all his math problems actively, the spread will start to narrow again between them in math.
There are innate abilities, but I don't believe for most of the general population they have much meaning. I was the worst artist all the way through school, and enjoyed math, I became interested in art and picked it up very quickly to the point of selling paintings. The person with innate ability and average work ethic will always get outstretched by the person with no innate ability, but a large amount of work ethic and the need to constantly challenge themselves. As long as they both care about the subject. To quote Einstein "It's not that I'm so smart , it's just that I stay with problems longer". There will always be the percentage of the population that's much lazier than Einstein, and will frequently cry "No sense for me to try. He was just born much smarter than me. I do have work just as hard, honest," when someone has more ability than them.
Yeah, contrary to what the OP said, I'd think that far more scientists would need to know statistics than calculus.
There are far more scientific fields which involve knowing basic statistics than basic calculus.
For example: scientists should know whether the results of their experiment/study/research are really statistically significant before they make big claims to the Media.
AC, I'm posting AC since my wife *was* in the exact same situation till a month ago. She's a researcher, and had much of the same problem you described. Well, she got fed up with it and started doing online games for 10-year-olds that force you to do hundreds of multiplication and addition/subtraction problems ("bubble" something tetris clone). I had the same theory you do -- she's brilliant, just can't do algebra. Well, after 4-6 weeks of training she solves these problems in her head faster than I do. So I'll say I started off thinking like you do, but changed my mind.
I've had less trouble with Calculus since I saw it applied to real-world concepts. The classic case is the relationship between Distance, Velocity, and Acceleration. You can view Integration and Differentiation as more "general" versions of multiplication and division that you can apply to functions rather than just numbers.
If you drive at a constant speed, you can multiply your speed by the time you travel to get the distance you travelled. But what if your speed is not constant? Say you draw your speed on a chart versus, it follows a mathematical curve? If you have the function that defines that curve, the distance travelled is the area under the curve between the start time and the end time. You can do various things with geometry to roughly work out the area numerically, but Integration is an analytical method you can use to get the exact distance, by "multiplying" the function by time to get another function for the distance.
The thing they didn't tell me about Calculus is just how much of it there is to remember. At university I felt I was being examined on how much of it I could remember, rather than my skill in using it. Pointless, since out in the real world you don't get penalised for consulting a reference of some kind, since it's all about results, not being a swot.
(this is not a
http://www.amazon.com/Precalculus-Self-Teaching-Guide-Wiley-Guides/dp/0471378232/ref=sr_1_27?ie=UTF8&s=books&qid=1270389659&sr=8-27
http://www.amazon.com/Calculus-Lifesaver-Tools-Princeton-Guides/dp/0691130884/ref=sr_1_1?ie=UTF8&s=books&qid=1270389762&sr=1-1
The first one is precal. It refreshes all the stuff you have forgotten since high school.
The second one has videos that go along with it. It covers all of cal I and most of cal II.
Historically, the claim of consensus has been the first refuge of scoundrels.
I believe the OP is working towards college level and this is college level. Courses from a wide array of subjects taught at MIT. I've been looking at the Physics I and II and Calculus I and II courses myself.
http://ocw.mit.edu/OcwWeb/web/home/home/index.htm
Probably the easiest way to refresh yourself on concepts is to go the Educational Software route. There's a set of discs that cover everything from basic math through Basic Calculus concepts and the nice thing is, your kids can alsu use them to get a boost in school.
Mod me up/Mod me down: I wont frown as I've no crown
I took 10 years off to play punk music before going back to school. When I decided to go back to do my undergraduate degree, I found this text in a used bookstore:
http://www.amazon.com/Precalculus-Mathematics-Calculus-5th-CD-ROM/dp/0534492770
It turned out to be a great refresher. I went through most of in on our last tour and hit the ground running when I went back to school. I recommend it for anyone in the same situation.
Good luck!
let us rephrase the question as : If I want to work in a field where every thing is going to be discrete and static, do I need Algebra etc? If, however, I want to work in a field where every thing is dynamic and subject to errors, do I need Calculus etc. learning mathematics is learning thinking and getting a powerful tool back and one can not predict if one or all the tools will be useful in work and life. With bad teachers and bad text books one might be turned off, but the fundamental thinking patterns are always going to come and haunt us. Maths is a very specific modeling tool. The fact your learned History but you are not using in daily life does not mean you have to ignore it. History repeats, maths repeats and so on. You understand well once you have mental maturity (around about 27 for men and 23 for women when the frontal lobe matures) and as such your hard work will pay off. Statistics is party of our daily life and so also useful if you want to use it in your daily life. For example, finding alternative highway or routes to travel when there is a traffic jam is based on the statistical knowledge that more ignorant people clog the highway around the same time because they need sugar in their system and thus rush to home to eat. Anyway, learn maths and statistics and worry about it use later. Mathematics and statistics govern your life.
A good textbook is "A Course in Higher Mathematics" by Vladimir Ivanovi Smirnov, it comes in five volume although the first one is more than sufficient for you.
"No matter what kind of scientist you plan to be, your knowledge of calculus will be essential. You'll never use statistics"
You have it backwards. Statistics will show up every week or so, calculus, rarely to never.
Linear algebra shows up moderately often, and numerical methods comes in handy at times, as this is how you will solve whatever calculus does show up, which will not be intregratable by textbook methods.
It's the same deal as people who say others can't learn to do art.
Speaking as a former art major (which is why I'm a truck driver now, BTW), people who say that really used to piss me off. Sure, some folks have a huge natural artistic talent but the rest of us have to learn how to do art. When someone suggested my skills were due to a magical innate ability, I'd get ticked off and tell them no, everybody has the innate ability. My skills, in fact, came from many hours of tedious practice, doing the same thing over and over until I got it right.
though you may have your own reason, but I believe the animation industry needs you more than the trucking industry.
Submitter - stats is just arithmetic and basic algebra, it's the concepts and knowing what to do with the data that are the hard part. Again get a T.I. and learn all of the functions, there is a LOT of tedium. Don't be afraid of the weird greek variables and big formulae...it's just arithmetic and algebra 1, you will hate it when you take it, but you will love it when you pass it.
I'm spending some time with my SO, who is a math professor, she says: "To understand stats properly, you have to know calculus. You need to know what the standard deviation is, which means you need to know what variance is, and to compute the variance, you have to know how to take an integral. Granted, this is for the continuous case."
My suggestion: concentrate very hard on your algebra. It's the foundation of calculus. Have a trig book handy for when you're working on your homework.
SO's suggestion: Get the SAT 2 subject study guide for math (if you can find one).
If I read it correctly, OP wants to avoid taking the lower level courses. This happened to me when I returned to school after being out for a while. What I did was grab the study book for math competency exams, and spent a 3 day weekend studying it. Went in and passed all pre-reqs. You cannot try and re-learn all concepts they way you learned them the first time. It is way too time consuming and you don't need to. What you need is to bring forth the knowledge you already have. You also need to concentrate on what gets tested, not what gets taught in normal classes.
Have a look at www.youtube.com/khanacademy. He has videos on algebra, trig, precalc, calc, statistics, etc. They are very well done and broken into 10-15 minute sections.
I thought that this comment was hilarious but was incredibly dissappointed by all the urination-in-the-breakfast-cereal comments which followed it.
-SMC
/uses both derivatives and stats IRL
/been known to integrate ocassionally
/never had to use Green's Theorem outside of a classroom because I'm not a M.E.
This may seem like an odd suggestion, but get the relevant "for Dummies" books. Wiley puts a lot of effort into ensuring the quality of these books (they aren't really for dummies). They are peer-reviewed, fact-checked and edited. The results are better than any text books and a lot less expensive. As well, the "for Dummies" label gives them permission to use lots of pictures, comfortable fonts, and an informal tone--no pretentious, migraine-inducing tomage. I have a half-dozen stats books on my shelf; "Statistics for Dummies" is the only one getting used.
I'm a Programmer. That's one level above Software Engineer and one level below Engineer.
As a mathematician with a statistician wife, I'm surprised by the number of responses like yours. Many people here are asserting that they never use calculus but constantly use statistics. Do they never work with a continuous distribution? No z-tests, f-tests, t-test, chi^2-tests? No exponential, gamma, beta, gaussian, log-normal, logistic distributions?
Or maybe they just don't know that probability theory is based on integration, and every time they compute an expected value, correlation, variance, co-variance, skewness, kurtosis, regression, etc. they are using calculus-based techniques and results. That would go a long way to explaining why my wife is consistently busy consulting with scientists who have worked themselves into a corner with their data. They designed their experiment to produce sub-optimal data and can't do the analyses to extract the meager conclusions their design entails.
Sorry, I don't mean to pick on you in particular, but to say that one uses statistics all the time and never uses calculus is preposterous.
This thread is exactly why I'd never ask a question on SlashDot. You wanted recommendations on websites, books, and other resources. What do you get? Tons of comments about how useless calculus is, or how useless statistics is, or what sciences use which one(s), and on and on. Sure, there's probably some good recommendations in here. Is it worth digging though 343 comments to find the handful that are useful? Not to me.
Read the book thoroughly and go to your professor's or TA's office hours frequently. Every student I've had that comes to office hours does well on the exams and homeworks, it's like free tutoring, you can go several times a week, and few people show up so you get personal instruction.
I took my calc classes in 2008-2009 at UVA. None of my classes allowed calculators in class at all, and angles were chosen to be easy.
SSC
Three Standard Deviations Left of the Curve, Dumber than a Sack of Rocks, Whoa-We-Have-a-Winner-Jack, American Idol-Watching, Right-Wing Radio-Listening, Can't-Read-Slashdot-and-Chew-Gum-At-the-Same-Time, Stop me if I'm going too fast...
Revised and Corrected Edition, with fewer exercises."
C'mon, anyone can grasp the concepts behind calculus in an hour or so -- the rest is just slogging through the equations. Of course, you have to know algebra and geometry cold going in or you're dead.
Oliver's law of assumed responsibility: If you're seen fixing it, you will be blamed for breaking it.
Don't overlook your local library. Many carry textbooks and have homework clubs or even on-line homework help. Find out who runs the math part of the homework club and ask for help/advice.
If you read my original post you will see that I stated that "I cannot remember ever having to (directly) use calculus in the last 20 years for any of my research". The word 'directly' was used very purposefully. I do realize that the math that underlies some of the statistical and analytical tools that I use includes calculus. However, I have not had to directly deal with solving problems involving integration or derivatives for a long long time.
For example, for some of our PCR based genotyping assays, the data we produce is a melting curve (amount of double stranded DNA measured as fluorescence vs temperature). See Melting curve analysis for a reasonable explanation. To make the data easy to visualize we plot the derivative of the fluorescence vs temperature - this gives us nice peaks centered around the melting temperatures of the PCR products. To get the curves I click a button built into the real time PCR machine software - I never do the math myself. This is not to say that I could not do it (although it would take me a lot longer now than when I was in a math class and practiced this kind of thing on a regular basis).
Just trying not to be preposterous....
http://khanacademy.org/
Just sound out SOH CAH TOA. Not that hard.
>Having an understanding of what a derivative or integral of a function is a good insight to have, no doubt.
Learning calculus is to statistics what getting undressed is to sex.
1] You have to learn algebra so that you can figure out how to take derivatives.
2] You have to learn derivatives to learn how to integrate.
3] Once you can integrate you can integrate y=1/x from 1 to x and then learn what a logarithm is (real, Naperian logarithms, not log10 that the engineers uze.)
4] Then you can evaluate the integral of y=1/x from 1 to infinity and discover from where arises 'e' the base of logarithms.
5] *NOW* you can contemplate e to the negative x squared and understand the distribution of men's chest sizes and distributions normal and otherwise.
To claim you know anything about statistics with out knowing integral calculus is to make the silly claim that you know all about sex from having seen a few copies of Playboy. To understand sex you and a partner must get out of you clothes, and once you get good at it you will need a shower afterwards. To understand statistics is just as much work, just as messy and just as rewarding; and just like sex, not something one brings up in every social circumstance.
McGraw hill has a thing called ALEKS for $20. You can get college credit for it too, although that can be complicated (depends on the school). Technically, you can, as the math courses are approved by ACE. But anyway, it's a great way to refresh things. Free trial, too -- you might like it. It's rough though -- you've got to be willing to put in the time -- hours and hours and hours and hours. But that's what learning math is all about, right? You'll feel good once you've done it.
Mod this guy to the sky! Khan Academy can be found on Youtube as well. He helped me through numerous topics in differential calculus!
You need to sit back and let the future happen.
Purplemath.com will get you a review of everything algebra through trig and simple log functions. It includes full lessons, descriptions, examples and practice work with explanations. It's free and you can take it at your own pace and/or review only what you need.
http://math.about.com/od/mathhelpandtutorials/Math_Help_and_Tutorials_by_Subject_and_or_Topic.htm
Check it out!
I do a lot of molecular biology. I've never thought of it as like the humanities at all. It's always seemed a lot more like computer programming to me.
Since you called it computer programming, you probably don't know anything about it. No coders call it "computer programming".
There were two *great* comments prior to mine:
(1) Have rock-solid algebraic (symbolic) manipulation skills;
(2) Really know your trigonometry.
My family has been using Sylvanus P. Thompson's "Calculus Made Easy" for several generations (the book was first published in 1910). It really is a wonderful introduction to Calculus (targeted at high-school students). There are two versions:
(1) The classic text, search for "Sylvanus P. Thompson" and "Calculus Made Easy";
(2) The updated text co-authored by "Martin Gardner".
I agree about trigonometry.
I have over 20 years of experience as a software engineer, and pretty much the only school math I've ever used during that time was trigonometry -- understanding how to rotate the bitmap of a picture.
(All the other math that I use is very specific to computers -- such as hex numbers, bit shifting/masking, applying DeMorgan's law, etc.)
it seems that if YOU find a problem you want the answer for,
say the "simple" problem of finding the area enclosed by a line, which
can be represented by a function, it is much easier to learn whatever you are
trying to learn.
say you need a table, you will find and learn to use the specific tools to make
said table.
some people think it is important to understand the tools, even though you don't seem
to have a problem you want to solve with the tools.
math is the same, physics is the same in this way.
find "problems" you want answers to, THEN go look for the tools. heyya?
buy an abacus
I had the same problem. I had to take a differential equations class 10 years since my last calculus based math course. During the week prior to the course I read Quick Calculus: A Self Teaching Guide and was all set. It is a really good book for getting you back up to speed without wasting a lot of time.
Based on measurements of 1,000 other statues, that statue is 11 feet tall +/- 8 inches
Definitely my favorite for anything math/technical. The books aren't standard text books with word problems, or stupid stories, it's just formulas and problems, and all the problems have worked through examples. And at only $15 for a book, can't beat the price.
Calc: http://www.amazon.com/Schaums-Outline-Calculus-Elliott-Mendelson/dp/0070419736
Schuams site: http://www.mhprofessional.com/templates/index.php?cat=145
Differential equations measure change. Statistics measure uncertainty. Stop covering for your own stupidity by trying to pin it on others who actually do know what they're talking about. Either that or get your ass on a wambulance.
> I haven't done ANY calculus since I was an undergrad.
... Once you've got a couple of semesters of calc under your belt, the world of math opens up to you. Heck, after calc 3 you can even jump straight into engineering math courses like diff eq, if you are so inclined.
I have, and I'm just a network administrator.
But the main point of taking calculus isn't its immediate practical application.
Calculus is the gateway math. It stretches your thinking in ways that allow you to take college-level math courses, and it's a prerequisite for almost everything. Linear algebra, modern algebra, number theory, prob and stat (_real_ prob and stat, not the half-baked version they teach to business majors so they can make mathematically invalid charts for their PowerPoint presentations), analysis, non-planar geometry, topology,
That's why you have to take calculus. It's not the destination. It's the front door.
Cut that out, or I will ship you to Norilsk in a box.
I used the Stewart Calculus book through every undergrad calculus course I ever took, Great book. http://www.stewartcalculus.com/
> You'll never use statistics but you will need to use calculus every day.
I don't know about that, but you sure can't expect to pass your other college math classes if you don't have a couple semesters of calc first. It's foundational.
Cut that out, or I will ship you to Norilsk in a box.
Calculus for Dummies
Google it!
> However, you were spot-on about this: Calc 1 is 90% algebra
All math is 90% algebra. That's why they hammer algebra so hard in high school math: so when you get to college, you can take math classes. Starting with calculus.
And yeah, if you had trouble with algebra in high school, you either need to knuckle down and make yourself learn it, or else think about a college major that doesn't involve much math. Counseling, for instance. Because if you think you're going to find a college math or science program that doesn't require any algebra, I've got some nice beach-front property in Oklahoma that I can let you have cheap, since the previous owners defaulted on their last loan payment.
Cut that out, or I will ship you to Norilsk in a box.
Sometimes it's just a matter of getting over a single hurdle. I was horrible at art for the longest time, maybe it was cause I didn't get any help from art teachers. Then one year something just seemed to click and it made so much more sense.
I find there seems to be a lot of things like that, you just need to cover a single hurdle, or maybe two or three, and once you learn how to think about things they become infinately easier.
After being out of school for over 10 years, I recently started tutoring a few high school friends in Algebra, Trigonometry, and Chemistry. It was amazing how quickly these things came back to me. Not only will it help you brush up on your math skills, but it will help someone else out, too!
Well if you were a nephrologist you would need to know what a calculus is.
> A bachelor's degree isn't a fast-track to get
> into a career, it's a period of academic study.
Absolutely agreed.
> You really have no business claiming that you completed
> four years of post-secondary study without some basic
> understanding of math-
Not all post-secondary schools are liberal arts colleges. Vocational/technical training *is* also a valid thing. Not the *same* thing, but a valid thing. I mean, the world DOES need diesel mechanics and so on. That's not what I personally wanted to do, but that doesn't mean it's no good for anybody.
> and calculus is really, really basic.
Basic in the sense of being a basis for what follows, yeah. Calculus is foundational to pretty much all college-level math. You can't take *squat* for math in college until you've had a couple of semesters of calculus. It's just required. And all serious college science programs require some math. Saying "I want to major in math or science, but I don't want to take calculus" is like saying "I want to learn to enjoy Asian cuisine, but I don't want to eat any rice." It doesn't make sense.
Cut that out, or I will ship you to Norilsk in a box.
They want you to pass calculus for a reason.
Who doesn't? But calculus can be extremely painful, and the patient may not be able to pass it without assistance. When the calculus gets too big it clogs your tubes. Good luck with that.
Unfortunately, the problem with economics is that it has TOO MUCH math in it. Or rather, it has too much math misuse.
There should be a large amount of statistics, but little calculus. That's because we're dealing with human beings and their obstinate free will. So much of modern economics is about making assumptions so that you can start applying some math to the problem. But the assumptions are often unwarranted, like micro's assumption of "perfect knowledge" that can only exist in a fantasy land.
Yes, you're going to have to do a shitload of math to get a degree in economics. But you shouldn't have to. Economics is not a hard science like physics, and should not be treated as such.
Don't blame me, I didn't vote for either of them!
Go for it! Learning as an adult is surprisingly easy -- don't think you are desperately disadvantaged by your age. Actually, adult learners do remarkably well at academic courses. I guess it is about being better able to identify what matters, to focus, and to stick to things.
You need to use a method that works for you -- some people can really only learn from other people, some people can learn from standard textbooks. Good self-paced materials are great, but you have to find one with your sort of pace. So think about what has worked for you in the past, and look around you now. If what you are trying doesn't work, try something else.
And try to control a yearning for perfection -- you don't need a deep understanding of every detail, Good enough is good enough. Whichever bits you actually need in your career will get developed fully then.
I wish I had mod points. I struggled with math, algebra and trig in high-school. The concepts didn't make sense, no matter how much practice I did, how many hours I spend after school with the instructors, etc. The way things were being taught were extremely abstract; abstract and my mind don't tend to mix that well.
I was told by guidance counselors to not take physics unless I had at least a B in algebra. Not a chance, I failed out of Intro Algebra, with 13% for course. Not due to lack of effort. I spend more extra time in class trying to get these concepts than I spent working. It didn't help me at all.
Until I took physics. Everything that was so abstract in algebra and trig suddenly came into focus. Suddenly factoring made sense, and there was a reason do factor an equation other than just because it was in the textbook. Why one would use scientific notation made sense. *EVERYTHING* that I fought with so hard in trying to understand algebra and trig suddenly made sense. This didn't happen until several years after high school. Physics was my Savior (sorry Jesus).
The manner in how math, algebra, trig, calculus is taught makes all the difference in the world. I learned and understood more in the first 10 minutes with my physics teacher than I had in all my math classes, extra time, tutoring, etc. combined.
It's amazing how an instructor can make all the difference in the world
Whether or not you use calculus on a daily basis, you can't understand probability and statistics without it. To understand what a probability density is you have to understand what an integral is.
If you want to get into statistics in any depth, especially Bayesian statistics, then calculus is absolutely essential. I develop software for estimating Bayesian models of consumer preferences, and I use my calculus all the time. In a sense, practical Bayesian statistics is all about evaluating difficult, high-dimensional integrals, and Bayesian experimental design is all about working out and evaluating matrices of second partial derivatives.
http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education.html In short, the statistics show calculus sucks.
While I agree with the subject -- you really need to learn & understand calculus -- you may not end up using it day-in-day-out in engineering. In some engineering jobs statistics is orders of magnitude more important than calculus.
I end up using statistics (stdev, cp, cpk) as a basis of my job (production test engineering) & rarely resort to calculus. Where calculus is useful for me is in understanding the equations used in design, or in understanding discrete/fast fourier transform. Thorough understanding of logarithms and exponentials, trigonometry and algebra is important to my job too... but, not so much calculus.
...and by basics I mean everything from arithmetic,
all the way up until college level algebra/calculus.
Well, first year anyway.
Khanacademy.org
I see this all the time at my college. Older students come back to school, take calculus for a few weeks and drop it. A semester which should have been spent on prerequisites is wasted. Instead of jumping into calculus now (you did get your "butt kicked" 20 years ago), take a precalculus class at a community college. If there is no inexpensive community college in your area, just find a large lecture hall precalculus class at a university and hide in the back. Homeless people do this all the time without being detected :)
I have the same idea as you. I took the AP courses in high school and got my butt kicked in college. I hit Math 401, aka Differential Equations, and it hit back. I didn't have a solid understanding of the basics to really tackle diffq.
Years later, I was influenced by several things:
First was Neal Stephenson's Boroque Cycle. That novel brought home the idea that math was a tool invented to solve problems and expanded minds. The second was my growing fascination with Lisp -- specifically, MIT Scheme / SCIP. By the time I started watching the first lecture, the introduction was already echoing what I felt about calculus, that software engineering dealt with idealized machinery, much the same way calculus was tool that gives us leverage.
I chose the Schuam's Outline for Calculus and started some self-study. I had also taken AP Physics, and the teacher more or less ignored our nominal textbook and used the Schuam's Outline for Physics. Although I was able to follow the derivations on the blackboard, I retained none of it. We were assigned problems out of the Schuam's Outline, meant to be two problems per week, all handed at the end of each half-semester. There were no fancy pictures, no chatty text to wade through. It was straight up physics concepts, how the math worked, and condensed down to its essentials. And lots of problems to practice on.
Of course, I procrastinated on the assignments. The day it was due, I spent every spare break time doing as many of those problems as I could. I wasn't able to complete all of them in time, but the sheer pressure of attempting that many within a short amount of time got me to really understand the concepts and how to work the math. I had no trouble with college-level physics taught to engineering students, just the calculus that powers it.
When I picked up the Schuam's Outline for Calculus, the material was much like that for physics. The concepts were not taught from first principles so much as showing you *how* to use the tools first, then later, *why* those tools worked. I was quickly able to get a handle on basic stuff that I had been vague on -- the Chain Rule, for example. I realized there were really two parts to calculus: Describing the problem (setting up the problem) in the language of math, and then symbolic manipulation. I could generally do the first part OK, considering that I've been writing software for ten years now. The latter part was where I was more hazy on, since I simply didn't know the tool. In structuring the "how to" before the "why this works", I could dive into solving my problems, then satisfy my curiosity later.
Good luck.
There's a lot more to it than that.
I've never been a good artist...but then I studied for awhile with a good teacher. I became MUCH better than average. Lots much. But I still wasn't drawn to the field, so I've let it lapse. I could probably pick it up again with a few weeks of hard work, but I'm not likely to.
OTOH, my wife studied with the same teacher several times a long, and before I dropped it for lack of interest, she wasn't as good (technically) as I was. But she enjoys it, so she's kept on. By now she's much better than I ever was.
So skill isn't enough, and motivation isn't enough, and talent isn't enough. You need all three. But the least important is talent.
(And skill implies the fortune of having a good teacher. Most art teachers don't qualify, even more than most math teachers don't qualify. A *LOT* more.)
I think we've pushed this "anyone can grow up to be president" thing too far.
Calculus or Analytic Geometry? I can see learning trig in Analytic Geometry, but not in Calculus. (It's true some places merge the two into on course, but if it doesn't involve the theory of limits, it's not Differential Calculus. (Probably not Integral Calculus either, but I don't remember clearly enough to assert that.)
N.B.: Integral Calculus uses lots of trig identities, but it's no place to learn trig. Ditto for Differential Calculus, but less stringently "no place". Still...in Calculus trig functions were used as functions, not as geometric things. That was Analytic Geometry.
I think we've pushed this "anyone can grow up to be president" thing too far.
Hi,
Working scientist here. Ph.D. I've been working 20+ years doing scientific research, getting grants, publishing papers in peer-reviewed journals.
I haven't done ANY calculus since I was an undergrad.
I actually advocate the old adage that math teaches you more beyond the formulas and proofs of any particular area or level of math. I'm a computer programmer, and I use Calculus all the time. I don't compute derivatives or integrate anything, but I definitely use the same part of my brain to work out an algorithm that I did to determine which approach to take to solve a nasty Calculus problem. Whenever I found the solution to a math problem to be 1 = 7 or some similar impossibility, I use the same part of my brain to go back over my work and find the error that I use when debugging code.
At my engineering college, Calculus was the easy start of 4 years of hard math for Computer Science majors. It's not really the "same part of my brain" concept I just used, it's more that the math I've studied developed my abstract problem solving skills, which are extremely important in my job. I think the same skills are just as important across the spectrum of real scientists, too, at least, as far as being good at one's job goes.
Oh, and as for taking Calculus in college, just do it. You don't need to build up to it unless you don't understand the concepts of basic algebra. The professor will teach you the rest.
I would have guessed sociology, economics or psychology.
That is a horribly unfair to the field of Economics. Replace it with "Political Science" and then you've got a proper grouping.
Unfortunately, the problem with economics is that it has TOO MUCH math in it. Or rather, it has too much math misuse.
There should be a large amount of statistics, but little calculus. That's because we're dealing with human beings and their obstinate free will. So much of modern economics is about making assumptions so that you can start applying some math to the problem. But the assumptions are often unwarranted, like micro's assumption of "perfect knowledge" that can only exist in a fantasy land.
Yes, you're going to have to do a shitload of math to get a degree in economics. But you shouldn't have to. Economics is not a hard science like physics, and should not be treated as such.
Are you really an economist, because what you're talking about sounds like the classic outside perspective after having taken a couple courses. A lot of your points are accurate, but the assertion that assumptions such as "perfect knowledge" are unwarranted. It's similar to assuming zero friction in physics: it's a step to building a useful model. Physics is a strange choice to pick as an example as a hard science when on the topic of making assumptions, with so much of it happening entirely within models that explore theories using math, built off of assumptions. Within those models that math is indeed much more "hard science like" than the way models are developed in Economics, but as you say, we're dealing with human beings here, not the laws of the universe. I find the simple fact that Economics has produced successful models that accurately explain situations of how real people act (on an economic scale) absolutely fantastic.
Is this useful with Calculus 2/3 or just 1?
I'm in a major that is often sneered at as being "CS for those who couldn't pass calc" (Information Science)
I was dealing with my own issues in K-12 (Mother with cancer, physically abusive father, neurotic aunt, my own depression issues, etc). It's very easy to get stuck in the "slow" classes if you act out early in your education.
Then guess what? You're bored, so you act out more - and they keep dumping you into lower and lower classes.
By high school I decided to turn my act around, but it was way too late - I had missed out on years of math and science. I had dreamed of going to study CS at a very, very prestigious university. Instead I went to a shitty local college that didn't even look at SATs, because I thought I was dumb.
And I was bored, again. I did a bunch of clubs, ran for student government, and hacked around a bit in my free time. Still bored. After 2 years, transferred to a state school to study information science.
Looking back, I regret I didn't go to a community college for a year or two and build up my math and science skills. But it was stuck in my head that I was "bad" at math. It wasn't until I started hanging out with a group of engineers and physicists that I got more confidence. One of the them helped tutor me on algerbra so I could take a harder statistics class than what was required for my major.
And you know what? I'm actually enjoying math. It makes me sad that at this point it's too late to switch to CS (I'd have to add 2-3 years to my degree to get all the science and math classes done), but at least I can hope to study in my free time, go to night classes while I work, and maybe at some point come back and do a master's in CS.
Anyways, my point is, if you are trying to look for ways to learn on your own, you're ahead of the game. Having a passion for something will take you farther than anything else. Read Malcolm Gladwell's book "Outliers". His main point was that practice makes perfect, (10,000 hours worth specifically), but there's another implication: If you have an interest in a subject, you'll learn way more about it than someone who went into science/engineering because they're good at math and it pays well.
I didn't take the opportunity to read all the responses you have received as of yet, so I don't know if anyone has made this suggestion already. I know when I was getting back into school, I lived on Khan Academy's website. I really think it saved me in my math classes. The site address is www.khanacademy.org. I hope this helps, and good luck.
I know you're joking but I should say that calculus and error analysis (part of statistics) are quite solidly intertwined. So, yes. Any practicing scientist does use calculus, though sometimes it comes disguised as statistical analysis. How about curve fitting? Least squares analysis rests firmly on calculus. So, you might not be doing dy/dx or contour integrals but you are using calculus even in the social sciences. If you don't see that explicitly, it just means you're using a packaged tool for the purpose (which is fine - reinventing the wheel is a good exercise, but necessary only in the classroom - elsewhere it's optional).
Not a biologist, but that sounds more like chemistry to me - or biochemistry. I imagine that, essentially being an overlap between disciplines, it would share a lot of features between the two - and chemistry is high-maths.
Just because you're paranoid doesn't mean there isn't an invisible demon about to eat your face
AI tutors are infinitely patient. Not only will it work problems for you, it will explain to you how it did it.
Sorry, I just re-read my post and I sounded like a bit of a jerk compared to your completely reasonable post. I had just scrolled through enough posts like "calculus is useless! statistics 4ever!" to be somewhat irritated.
You're quite right that direct computation of derivatives or integrals is rarely done by people nowadays (and it should really be this way in calculus classes as well, but I digress). My poorly phrased point is that the knowledge of what an integral is and how it behaves is of great value when thinking statistically, even if you don't do any integration.
I think many people undervalue the conceptual understanding to their detriment, but I'm going to cut myself off before I start ranting again.
There are several avenues open to you. a) In my day we had Schaums college outline series, which included most math subjects. It was a great way to learn by oneself. b) Put an add on craigslist for a local college student to give you some guidance. It should not be as expensive as a full time back to school option c) Check your library for the dummies books. d) I would call the highschool and talk to the principal to see if they can line you up with some bright student.
Leslie Satenstein Montreal Quebec Canada
Been working on brushing up on math as well, this book has a lot of breadth and has been great for me: http://www.amazon.com/Mathematics-Nonmathematician-Dover-explaining-science/dp/0486248232
Very cheap online math lessons. I passed the CSETs 20+ years after high school math after a few months with these online classes. They solve many of the problems in several well known books that you can buy and work along with. The teachers were very good.
I have used Thinkwell's math videos since Precalculus. Edward Burger is great at explaining the lessons. It is pretty expensive, but I think that it is worth the cost.
try http://khanexercises.appspot.com/video?v=W0VWO4asgmk
try khan academy
I'm a C scientist. My dissertation was about pointers.
Learning calculus is to statistics what getting undressed is to sex.
You mean optional?
You must be BadAnalogyGuy using a different nickname. You can definitely know quite a bit about statistics without knowing anything about calculus.
No, "you" don't, in the sense that statistical software like R, SPSS, SAS, etc, can do all the calculations which require calculus for you. The software needs to know calculus, but not the users.
http://www.jamesbrennan.org/algebra/ Nicely done Algebra 1 text. No problem set, however. http://cnx.org/content/m19435/latest/ Don't let the somewhat klutzy organization of this text put you off. What this guy is doing is running you through Algebra 2 by discovering it for yourself. This is the text I use at the small charter school where I teach, and it's working well with kids who have never, ever gotten school at all! Good luck to you.
wife used it, excellent, she got an A+
I'm still not sure how that makes me feel. I was a college student and not *remotely* qualified to do that.
You shouldn't feel bad about it. It sounds like you were certainly qualified to do the computation. Once you documented your answer, the engineer was able to check your work and confirm it met their specs. He or she then certified that your math was an accurate representation of the volume.
Being in school or not, being a trained surveyor or not, doesn't matter. Your answer was based on math, which is the same regardless of who you are. Asking a kid to count apples in two boxes and tell you how many apples there are by adding the numbers doesn't invalidate addition just because you asked a kid to do it. Same thing here, only you're talking about calculus and the containment of a toxic gas where a mistake could mean environmental disaster. :-)
Also, consider that your math was within 0.5% of his rough estimate. The engineering firm might have been hoping you'd come up with a dramatically "bigger" estimate than his simple cubic volume, which might have saved the firm $$$ when it came time to dig out the extra dirt to meet the new volume requirement. As it is, since you came up with a number that was so close to his estimate, the firm was probably just as pleased to know that applying calc to future similar problems was not worth the extra effort. So if nothing else you validated their estimating methods.
John
Statistics is important because you can use it to manipulate people!
"There are three kinds of lies: lies, damned lies, and statistics."~Disraeli
Starbucks, Harbuckle of Breath.
its a question of luck, you can overcome that.
learning to draw is surprisingly easy, its more about perception than anything else really.
This probably isn't the answer you're looking for, but....adult education centers offer all their services for free; one of the things that may of them use is software programs like Plato or A+LS. Those programs can give you an assessment, and a prescribed list of lessons based on the assessment. I'm a college admin but found myself in the position of having to tutor some h.s. kids after not having done 'school' math in 20 years. Using A+LS with the students (the college uses it for remedial math courses), I 'refreshed' my memory for algebra and geometry. The math subjects goes all the way through calculus (or at least pre-calc, IIRC).
It's produced some pretty unsuccessful ones too. Now all we need is some way to work out[1] which is which.
[1] ideally in advance.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
Google "the Teaching Company"they have some nice courses on DVD that should be perfect for your purpose.
Depends on if you can study by yourself or not. I used to be the guy at the student help clinic... about 25 years ago. If you can or you want to try it, go to a campus book store. You will usually find off to the side a used book area. They often have old books and more importantly the keys. Mathematics builds on previous courses. The thing to do is to find out where you are. I'd try an algebra book and geometry. Select 10 questions (or even 5) from the chapters and see how you do with the key. Of course be honest with yourself, make sure you master those chapters. Then you can probably sell those books back to the store or put them on flea bay. Now you are ready to do the calculus. Buy a book(s) and key again. Same thing. Do 10 questions and see how you do. If you get 8 right, that's 80% of course. You are going to need more like 9/10 right. Statistics is tougher. I bought many books and keys for the Engineering grade statistics. That's all I did during a summer course. I passed it with a 95%. Problems, problems, problems. Just keep doing them and you will know it. This by the way is how to learn. Something they don't seem to teach in school. If you are having trouble, feel free to seek out campus help. Most schools have a tutor area or sometimes it's called a clinic. As a guy who used to run one of those clinics, please do your part. That is, don't expect them to be a test fairy and somehow by the mere fact you were there, you know it. That may not be you, however we had a lot of people that hadn't even looked at the chapter and thought we would teach them. I found there is no short cut for advanced mathematics. You have to train your mind how to do this stuff.
Johnsonbaugh and Pfaffenberger, Foundations of Mathematical Analysis http://books.google.com/books?id=Zi6qnkC7t0QC&printsec=frontcover&dq=johnsonbaugh+pfaffenberger&source=bl&ots=rbvLL-TuQT&sig=GTSHgC60gkmlclVJSywOxTbcs3I&hl=en&ei=ZN-5S7uJJ-KiOKDHxaEL&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBEQ6AEwAw#v=onepage&q=&f=false . Hope the link works. For algebra, try W.E. Deskins, Abstract Algebra http://books.google.com/books?id=LE4mPB-1RFQC&printsec=frontcover&dq=deskins&cd=2#v=onepage&q=&f=false or Seth Warner, Modern Algebra (http://books.google.com/books?id=jdx5K7CdL_4C&pg=PP1&dq=modern+algebra&cd=1#v=onepage&q=&f=false).
I had the same issue with advanced statistics. Took it 20 years ago and had my butt kicked. I bit the bullet and took it again after 20 years and got an A -- you'll be amazed how much better your brain works when it's been in use for a while. Fear not!
Grar II
Hmmm. You do sound like what we computer programmers used to call 'coders'. I started programming computers in 1978. Do you do any computer programming, or are you just a coder? RFT!!! Dave Kelsen -- "To have no thoughts and be able to express them - that's what makes a journalist." -- Karl Kraus
The field is too broad, and the education is too narrow.
The problem is that a software developer may be someone who writes CRUD business applications or utilizes computer processing power to predict weather patterns, earthquake damage results, manipulate images, control artificial satellite orbits, or lifelike video game AI characters. These jobs all have the same name Developer or Programmer. There's usually only one aspect of training in 4 year BS/BA programs, and they trend towards Mathematics.
In construction no one would argue that any of these are the same, Carpenter, Plumber, Stone Mason, Surveyor, Architect or Civil Engineer, but they are all aspects of "Building." I'm pretty sure they all require some pretty specialized training. Only a few of them are offered via 4 year BS/BA programs. The others are apprenticeships or offered 2 year associates technological schools. Oh, and most organizations don't expect you to self-train your self form one profession to another (unlike the business world and software development).
Maybe there needs to be a better appreciation for tech schools and computer programming. But in a world where all the hiring is done by a person in human resources with a 4 year business school degree doing the first level filtering, and little or no tech skillz, guess what happens.
I have a series of 110 math videos (free) on Youtube that can act as a refresher for you. Go to www.youtube.com and search for minkusbc to access these. I also have a math related website, www.mathhiker.com where I have uploaded some 250 math blogs for your perusal, also free.
Wayne Loutet
wloutet@shaw.ca
Jimmy could use the median of 100 guesses from those around him. That would be as close as my trig ever was.
Take this and your head will be hurting for several years: http://ppi2pass.com/ppi/PPIShop_pr_XMESM0110P
Calculus is most often used to make predictive models. Not all scientists work on modeling systems. Physicists like to joke that if biologists could just learn some hard math, they would be able to make perfect models of biological systems and stop doing experiments on them.
Statistics is used to see if data agree with a theoretical model, or with another data set. In order to use stats, you have to be doing experiments that collect data. Not all scientists do experiments. Biologists like to joke that physicists ran out of actual experiments years ago and now they just argue about untestable theories.
Chemists just add stuff until it blows up.
try the videos (the ones I used were free) http://www.mathtutor.ac.uk/
I taught my self calculus at 15 out of this book: Calculus Refresher A. A. Klaf, still available from http://store.doverpublications.com/0486203700.html ($14.95). Most of it stuck through Physics (BSc MSc) and Med School. Only use I have now is mental recreation.
online videos: algebra + calculus
http://justmathtutoring.com/
http://www.mathtutor.ac.uk/
http://www.khanacademy.org/
http://www.graderocket.tv/index.php
Uni Maths Videos
http://ocw.mit.edu/OcwWeb/Mathematics/
http://press.princeton.edu/video/banner/
http://academicearth.org/subjects/mathematics
http://freescienceonline.blogspot.com/2009/01/calculus-video-lectures-bonus-basic.html
http://www.apple.com/education/itunes-u/ (requires iTunes download)
Resources from Universities
http://www.germanna.edu/tutor/helpful_handouts.asp?menuchoice=Helpful%20Handouts (wow)
http://mathforum.org/
Free online books:
http://www.jamesbrennan.org/algebra/systems/solution_set.htm
http://cnx.org/content/m18205/latest/?collection=col10624
http://www.jirka.org/diffyqs/ (Differential eqns)
http://www.purplemath.com/
http://tutorial.math.lamar.edu/
PowerPoints
http://www.online.math.uh.edu/HoustonACT/
Tutoring services
http://www.nutshellmath.com/
Collections of Links
http://math.about.com/od/mathhelpandtutorials/Math_Help_and_Tutorials_by_Subject_and_or_Topic.htm
http://pathstoknowledge.net/
Problems
http://projecteuler.net/
Some computer Resources
http://www.graphmatica.com/
http://archives.math.utk.edu/visual.calculus/
www.sosmath.com www.interactmath.com 50 year old college freshman here. my last math class was 35 years ago, THAT I SLEPT THROUGH. Back in the day when you could do so.
That sort of depends if you are into algebra or analysis, and I take it that you are more the algebra person.
In my area, combinatorics and (complex) analysis are essential. And the usual way to learn complex analysis is to start with the real one.
It's produced some pretty unsuccessful ones too. Now all we need is some way to work out[1] which is which.
[1] ideally in advance.
One of the expectations people have about Economics is that it should serve as a predictor. This is, of course, fostered mostly by all the economists who go on news and political shows to give their opinions. I don't remember the economist (modern day) who said, to paraphrase, if someone is speaking about what we "should" do, he's not acting as an economist.
I like to make a general comparison to physics. A physicists's job is not to predict when or where two trains will collide, but rather be able to explain the forces at work if they do.
I seldom see much calculus in my Botanical research, but I am not a Real Scientist.
The cost of that cleanup, of course, will be borne by taxpayers, not industry.
You're quite right that direct computation of derivatives or integrals is rarely done by people nowadays (and it should really be this way in calculus classes as well, but I digress).
I disagree strongly with the point in the digression. People get a much better feel for how functions behave and what answers should look like when they've had to actually go and work them out a few times. This is important. Otherwise, when one makes a typo in your data input or the computer goes all squirrely you likely won't have enough feel for the results to notice the problem.
Is that why scientists don't get religion?
Economics is bullshit wrapped in numbers to hide the fact they don't know shit.
Unless the physicst is attempting to get a lander onto Mars, in which case we do expect him to predict when two lines will collide.
Please explain why you have to love math to be in CS? Its helpful to explain some of the theory, and that theory is useful, but I pretty much don't use any math. I business business applications though, and not some 3D graphics engine. I realize that some sections of CS might require more hands on math, but not all. Set theory is certainly important to work with databases, but again you're not required to directly use math each day, for many in the CS field.
I use a computer every day but I don't use my electronic engineering knowledge, even though computers are built from electronics.
I don't find this at all preposterous.
Everything depends on your area of expertise. You have to understand Stats to realize how they can be manipulated to say whatever you want them to say and thus how bogus they are. Statistical analysis is only relevant in the insurance industry, IMHO. Be that as it may, If you can get a hold of the text that your course will come from you will get an idea as to what you need to relearn. Then get a good PreCalc text book from the library and go over it. Then get a Calc I book and read thru it. Use the tutor sites when you can't get it yourself. Mostly, education is teaching others how to teach themselves. More than likely, because your brain has matured a lot since college, you will "Get" math in a way you didn't before and love it. Have fun!
During high school I was a swimmer / water polo player. Every day we spent 1-2 hours in the pool swimming laps or playing polo. That's it.
A friend was on the football team and one day I went to watch him during practice - the entire team was 'doing bleachers', meaning they were sprinting up and down the bleacher seats (effectively running up and down a flight of stairs.) When I asked him about it later, explaining that it looked like bullshit to me (there are no stairs on the football field, so why run up and down stairs?) he explained 'if you can't handle 'doing bleachers', you can't handle being a football player.'
It doesn't take calculus to code most of the stuff I work with today as a software engineer, but I honestly wouldn't want developers on my team that couldn't at one point in their lives handle calculus. They don't have to be able to do it today, but at one point they needed to show that they could master it (mentally). If you can master calculus (even for a brief period of time during undergrad) then you're probably the caliber of man I want tackling the difficult problems that come up coding some of the stuff we code. If not, probably not.
Glonoinha the MebiByte Slayer
An old post - but I'll still respond (I only rarely check once they move off the front page).
You misunderstand - my .5% error was when I used improper methods. His original estimate was nearly 30% off of my final answer. Nor did he understand what I had done for the one they went with - they had to find another engineer to go over it.
That is if I made what was essentially a trapezoidal solid into a true rectangle I got his numbers. If I calculated the area of the trapezoid I got nearly a 30% difference - the pit as built was *obviously* a trapezoid and thus didn't contain even 100%, let alone the extra volume required by law.
Further I *designed* a freaking containment pit for three 100k+ gallon gas tanks - the same engineering company that signed off on the a fore mentioned pit signed this one.
I do not have any real knowledge of how to design a pit to contain a liquid. Would it hold the pressure? What are the regulations with regard to containment? Does containing freaking *gasoline* have different requirements from water (I would bet so)? For the most part dunno - I have no idea if I followed them. I didn't talk to their engineers or anything either.
What I do know now for certain is that I calculated the volume correctly. I do know that the pit as designed can handle the pressures if filled with a liquid. But the rest (especially given that there are likely questions I do not even know to ask)? I have no idea.
Supposedly an engineer signed off on what I did. Supposedly it was a different engineer than they had used before (who was grossly incompetent - he really should have his license revoked). If said engineer was, well qualified then I have no reservations whatsoever. I fully documented everything and it isn't uncommon for a licensed engineer to have others design/calculate and then simply verify the design. For the most part that type of design isn't really hard as much as it is specialized knowledge that you wouldn't otherwise have.
So, in the end I still do not know how to feel about it. They were lucky in that I understood the math enough to do the right thing even in the parts I were not trained in - at least in all the areas I have since learned. Their handling of it in the past doesn't really make me feel good about it being signed off on - after all a roughly 30% error was too.
------- Sorry about the spelling, I suffer from two problems. Dyslexia makes it difficult to spell well, lazy makes it