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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.
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.
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
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.
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
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.
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.
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
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
Math is useful in general. And western society doesn't just stress about learning math. An even greater number are probably stressed about passing english tests. Society thinks language and math are important to education; your basket-weaving and sculpture not so much. I personally don't see the problem with this.
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.
Because it is the basis of all fields of science.
And quite a few fields of art.
I *HATE* math, but I use it every single day, and in the areas I'm known for, I can do the math needed...mostly in my head. I've also found that as I've tried to branch out of my areas of expertise, that I can't rely on the few areas of math that I know fluently, because I'm starting to bang my head against the ceiling.
For instance, I took a few basic undergrad courses recently (I have a masters in psychology), and I couldn't remember the damn quadratic equation...I could get the answer just fine -- if I wanted to spend 15 minutes solving it (or as I did, write a quick plot app on my laptop to show the answers figuring it out computationally as opposed to mathematically)...and it was only after one of my twenty-something classmates looked at me and said Dude, Why Don't You Just Use The Quadratic Equation that I realized how much I had forgotten (I had no use for math 20 years ago and slept through this).
It is funny how knowing the simple concepts can make your life simple. Anyone can brute force just about anything.
If you don't want to do anything science based...and this includes almost any social science even if people think these are not real...or any advanced art (I have a friend that does weavings, and to get what she wants, and for the patterns to work out in real life, not just paper, she needs to know math to get these to work)...math is the basis for all of this. Oh and the chess algs? it is all math...pretty advanced math...it isn't chess these guys were after...it was computational mathmatics to attack a human problem.
This summer, I am signing up for a 100 level math course and getting the basics back again...I wish I would have done it before...it sucks that I can get results from Mathematica or SPSS, but I can't do simple algebraic equations. You might not think it interesting or necessary, but then again, I can't tell if you are being serious or if your humor is just VERY dry...if you are serious...wow...
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...
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.......
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
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.
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
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?
Essentially because:
1) Everyone should learn logic and disciplined thought. Otherwise you'll end up with adults who can't read instruction manuals, have an attention span of 5 year olds and can't see their own mistakes and contradictions due to disorganized thought processes and hubris. Math can have a humbling effect on people.
2) Proper mathematics is used constantly by good electrical engineers, physicists and mathematicians. If you want a good engineer, you have to teach him math from childhood. And since you can't have a grade school for scientists and another one for everyone else, everyone has to learn math.
3) Math greatly contributes to keep idiots out of the sciences, med school and other important professions.
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
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.
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.
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