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.
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.
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.
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 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.
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
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.
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
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...
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.......
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.
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.
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.
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.
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.
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
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.
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
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
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
Me too. I studied at the University of Manchester University.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
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.
Slashdot: news for Apple. Stuff that Apple.
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.