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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?"
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.
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
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
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
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.
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...
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.
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.
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.
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.