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Help Me Get My Math Back?

kdawson posted about 4 years ago | from the we-can-forget-it-for-you-wholesale dept.

Math 467

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?"

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If you can't handle calculus, science isnt for you (4, Funny)

elucido (870205) | about 4 years ago | (#31720466)

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.

Re:If you can't handle calculus, science isnt for (5, Informative)

Anonymous Coward | about 4 years ago | (#31720492)


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.

Re:If you can't handle calculus, science isnt for (4, Funny)

Anonymous Coward | about 4 years ago | (#31720648)

You must be a scientist, because apparently you have no sense of humor.

Re:If you can't handle calculus, science isnt for (1)

zach_the_lizard (1317619) | about 4 years ago | (#31720668)

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.

Re:If you can't handle calculus, science isnt for (4, Funny)

Anonymous Cowar (1608865) | about 4 years ago | (#31720768)

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...

Re:If you can't handle calculus, science isnt for (0)

Anonymous Coward | about 4 years ago | (#31720840)

Yeah, bleh. All that useless stuff like discovering the causes and cures of disease.

Re:If you can't handle calculus, science isnt for (4, Insightful)

LurkerXXX (667952) | about 4 years ago | (#31720892)

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.

Re:If you can't handle calculus, science isnt for (3, Funny)

Gorobei (127755) | about 4 years ago | (#31720908)

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.

Re:If you can't handle calculus, science isnt for (5, Interesting)

Garridan (597129) | about 4 years ago | (#31720562)

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.

Re:If you can't handle calculus, science isnt for (3, Informative)

Anonymous Coward | about 4 years ago | (#31720614)

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.


Re:If you can't handle calculus, science isnt for (-1, Flamebait)

Brian Gordon (987471) | about 4 years ago | (#31720628)

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.

Re:If you can't handle calculus, science isnt for (4, Insightful)

fruitbane (454488) | about 4 years ago | (#31720734)

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.

Re:If you can't handle calculus, science isnt for (2, Insightful)

Anonymous Coward | about 4 years ago | (#31720816)

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.

Re:If you can't handle calculus, science isnt for (4, Informative)

zach_the_lizard (1317619) | about 4 years ago | (#31720690)

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.

Re:If you can't handle calculus, science isnt for (4, Interesting)

shdo (145775) | about 4 years ago | (#31720834)

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.......

Practice, practice, practice (3, Insightful)

Anonymous Coward | about 4 years ago | (#31720886)

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 [conestogac.on.ca]

BTW, Jamie Escalante, http://en.wikipedia.org/wiki/Jaime_Escalante [wikipedia.org], 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.

Re:If you can't handle calculus, science isnt for (1)

rubycodez (864176) | about 4 years ago | (#31720610)

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.

Re:If you can't handle calculus, science isnt for (2)

wonderboss (952111) | about 4 years ago | (#31720632)

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.

Re:If you can't handle calculus, science isnt for (1)

zach_the_lizard (1317619) | about 4 years ago | (#31720724)

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 [umuc.edu]. It does happen.

Re:If you can't handle calculus, science isnt for (4, Insightful)

GAATTC (870216) | about 4 years ago | (#31720636)

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.

Re:If you can't handle calculus, science isnt for (1)

vilain (127070) | about 4 years ago | (#31720864)

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.

Re:If you can't handle calculus, science isnt for (-1, Flamebait)

SlappyBastard (961143) | about 4 years ago | (#31720676)

Why do I never have mod points when I need them . . . good points all around. I mean, calculus is the core of our understanding of change. Without calculus, you might as well just things "improved" or "declined" and call it at that. 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.

Re:If you can't handle calculus, science isnt for (0)

Anonymous Coward | about 4 years ago | (#31720812)

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.

Re:If you can't handle calculus, science isnt for (4, Insightful)

Vellmont (569020) | about 4 years ago | (#31720830)

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.

Re:If you can't handle calculus, science isnt for (0)

Anonymous Coward | about 4 years ago | (#31720838)

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.

Re:If you can't handle calculus, science isnt for (1)

izomiac (815208) | about 4 years ago | (#31720878)

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).

Re:If you can't handle calculus, science isnt for (5, Insightful)

thenextstevejobs (1586847) | about 4 years ago | (#31720882)

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.

Re:If you can't handle calculus, science isnt for (0)

Anonymous Coward | about 4 years ago | (#31720904)

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.

Re:If you can't handle calculus, science isnt for (2, Interesting)

haruharaharu (443975) | about 4 years ago | (#31720916)

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.

wat??? (-1, Offtopic)

Anonymous Coward | about 4 years ago | (#31720468)


Define: "a few math courses to wrap up a degree" (4, Informative)

0100010001010011 (652467) | about 4 years ago | (#31720482)

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. [mit.edu]

Always without a calculator. (4, Funny)

elucido (870205) | about 4 years ago | (#31720504)

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.

Re:Always without a calculator. (4, Funny)

blackraven14250 (902843) | about 4 years ago | (#31720622)

If we're bombed back into the stone age, derivatives and integrals aren't going to help him tie a sharpened stone to a stick.

Re:Always without a calculator. (5, Insightful)

fm6 (162816) | about 4 years ago | (#31720744)

"Bombed back to the stone age" is best regarded as just an expression. The iron age is here to stay, no matter how much civilization declines. Even if we forget how to smelt iron ore, there would be billions of tons of refined iron lying around in abandoned machinery, buildings, and such.

Re:Always without a calculator. (3, Funny)

Anonymous Coward | about 4 years ago | (#31720814)

...Even if we forget how to smelt iron ore, there would be billions of tons of refined iron lying around in abandoned machinery, buildings, and such.

Not if they've come for our metals and women.

Re:Define: "a few math courses to wrap up a degree (4, Informative)

moteyalpha (1228680) | about 4 years ago | (#31720708)

I have gone through those at MIT, just for fun. I also found that Khan Academy [khanacademy.org] 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 [academicearth.org] was very informative. It doesn't hurt that some of the profs are also quite entertaining.OR science and magic on youtube [youtube.com]

Re:Define: "a few math courses to wrap up a degree (0)

Anonymous Coward | about 4 years ago | (#31720900)

Khan's Academy is Great. Strangs linear algebra is great. MIT's Calc III is great.

Engineering Math by Stroud (5, Informative)

smith6174 (986645) | about 4 years ago | (#31720484)

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.

Why? (4, Insightful)

pushf popf (741049) | about 4 years ago | (#31720500)

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.

Re:Why? (2, Interesting)

Darkness404 (1287218) | about 4 years ago | (#31720530)

If you haven't needed a degree or calculus in 20 years, why bother now?

In case you haven't realised it, there is a recession going on, a -lot- of people are either unemployed, their spouse is unemployed or they need a way to secure their job. Rather than doing the rational thing of looking at productivity, most businesses hire and pay based on education. If his wife lost her job and he was expecting the income, the only way he can get a raise to keep up his standard of living might be through a degree.

Most degrees are completely useless when done for a raise, but, money is money.

Re:Why? (0)

Anonymous Coward | about 4 years ago | (#31720612)

Rather than doing the rational thing of looking at productivity, most businesses hire and pay based on education.

The "Rather than doing the rational thing" makes the sentence sound anti-education up to "I didn't acquire higher education but I am financially successful".

Re:Why? (1)

Darkness404 (1287218) | about 4 years ago | (#31720758)

Ever spend some time in a company? Generally the people who are paid the most do the least amount of work. It is generally the people with a bit of college doing the bulk of the work while the people with the highest forms of education are sitting at their desks doing nothing.

Re:Why? (1)

Penguinisto (415985) | about 4 years ago | (#31720730)

Dunno - perhaps he wants to shift careers a bit, or enter academia?

Sometimes a degree is useful when you want to leave one area of his career and enter another. For instance, perhaps the guy has been doing field engineering all this time, but now wants to do design? Maybe he's sick of working/running a lab, and instead wants to create and run the projects?

Even in my own corner of the working world (IT), I find myself increasingly wishing that I'd taken more business courses as I leave behind being a server monkey (and in one previous job, code monkey). Nowadays I'm routinely running my own budgets, doing the politics dance, and overseeing both people and projects. Mind you, I have no desire to get an MBA, but having to handle vendors, routinely run RFP's of six figures (one this year approached seven), while handling/syncing various execs' ideas of project management... ? Well, more and more these days, some of the subjects in an MBA course would damned sure come in handy right about now.

Re:Why? (2, Interesting)

pushf popf (741049) | about 4 years ago | (#31720810)

Even in my own corner of the working world (IT), I find myself increasingly wishing that I'd taken more business courses as I leave behind being a server monkey (and in one previous job, code monkey). Nowadays I'm routinely running my own budgets, doing the politics dance, and overseeing both people and projects. Mind you, I have no desire to get an MBA, but having to handle vendors, routinely run RFP's of six figures (one this year approached seven), while handling/syncing various execs' ideas of project management... ? Well, more and more these days, some of the subjects in an MBA course would damned sure come in handy right about now. After 20 years, an MBA would be really useful. After 20 years of not needing them, calculus and trig are a waste unless the OP is trying to switch careers or just wants the satisfaction.

FWIW, it's much more profitable to go into consulting and do/manage whatever it is that you're good at and happy doing, than try to maintain a dead-end job as one of the "cogs." Businesses are much happier to pay someone a good rate for services that they need, when they need them, as long as the consultant will happily vanish when the need vanishes.

This site helped me (5, Informative)

Anonymous Coward | about 4 years ago | (#31720506)

This tutorial site helped me through 6 years of school. Hope it helps you too! http://tutorial.math.lamar.edu/

Some sites I've come across (5, Informative)

FlyByPC (841016) | about 4 years ago | (#31720508)

Helpful handouts [germanna.edu] 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 [mathforum.org] (full disclosure: I'm a current Drexel employee and student -- but the Math Forum strikes me as pretty cool.)
Project Euler [projecteuler.net](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 [purplemath.com]

Re:Some sites I've come across (1)

zach_the_lizard (1317619) | about 4 years ago | (#31720772)

Interestingly enough, I used to take a handful of classes at Germanna. To add to the list, I would say that Wolfram Alpha can be helpful, because it can be used to break down more complicated integrals and derivatives into steps when you don't understand them. Just don't become dependent upon them. Also, one thing that can be helpful is to go to Yahoo Answers and answer math related problems. Break everything down into steps, explain the theorems needed, and bask in the knowledge that teaching is a good way to learn. By breaking things down for people who may not have a good understanding of math, you will help build up your own understanding too. I actually used this while taking various Calc classes to help practice what I knew, and help break down how exactly I knew it and thought about it.

Hard work should do the trick (3, Insightful)

nitroamos (261075) | about 4 years ago | (#31720512)

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.

CC (1)

pieisgood (841871) | about 4 years ago | (#31720514)

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.

Re:CC (1)

Killer Orca (1373645) | about 4 years ago | (#31720586)

I second the community college courses, but you might need to sift through till you get a good instructor. I lucked out in the ones I have had so far have been able to explain things quite well and have good homework polices. $60 a class is unreal though, mine cost about $350 per class.

Re:CC (1)

h2oliu (38090) | about 4 years ago | (#31720590)

I was going back to school to become a teacher. In so doing I had to take a Trig course. I did so online from my local community college. It really refreshed my math skills (that were ~20 years old).

Keep in mind I had taken through Series and Diff Eq. in college, so I had mastered the material previously. (Don't ask why I needed trig. in spite of having had the upper level courses. Just a magic hoop to jump through).


Re:CC (1)

zach_the_lizard (1317619) | about 4 years ago | (#31720796)

Don't ask why I needed trig. in spite of having had the upper level courses. Just a magic hoop to jump through.

In high school, I had that same sort of problem. I moved from one school system where you took World History in two parts, one in 8th grade (middle school) and one in 9th grade (high school), to one where the two parts were pushed up a year. Despite having completed both classes successfully, they made me retake history part I, because they just didn't trust that I learned anything. They also made me take the standardized test for the second history class, which I passed with a perfect score on, making their theory that being taught something a year earlier isn't good look a little silly.

Krzysztof Wilczynski (4, Informative)

kwilczynski (1684804) | about 4 years ago | (#31720522)

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! (1, Informative)

Anonymous Coward | about 4 years ago | (#31720524)

cheat! and the TI-89 series makes it easy!

If you need to review "pre college" level stuff (0)

Anonymous Coward | about 4 years ago | (#31720526)

Just get review books for the New York State Regents exams.

A Bit of Advice and a Few Suggestions (5, Insightful)

eldavojohn (898314) | about 4 years ago | (#31720532)

I don't know how bad you want this but I can tell you that nothing feels better than finishing something you started even if it comes two decades later.

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 [mit.edu]:

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 [wikipedia.org]. Your codex might be Wolfram's MathWorld [wolfram.com]. 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 [amazon.com]. 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 [umn.edu] 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 [theannotatedturing.com] 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.

Let me google that for you... (0)

Anonymous Coward | about 4 years ago | (#31720542)


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.

Go to your public library (1)

aussersterne (212916) | about 4 years ago | (#31720548)

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.

Cheap, easy classes (1)

Darkness404 (1287218) | about 4 years ago | (#31720554)

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.

Khan, MIT (2, Informative)

chub_mackerel (911522) | about 4 years ago | (#31720556)

You might like:

Khan Academy http://www.khanacademy.org/ [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/ [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.

Motivation (4, Insightful)

cosm (1072588) | about 4 years ago | (#31720558)

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.

Get a real life tutor (1)

Evrion (1459047) | about 4 years ago | (#31720560)

To be honest, that is your best bet. Find someone who knows how to teach, and understands the material. Get that person to catch you up.

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.

Re:Get a real life tutor (0)

Anonymous Coward | about 4 years ago | (#31720680)

I wholeheartadly agree.
A student tutor is much more cost- and time-effective than a cram course.

Re:Get a real life tutor (1)

ctmurray (1475885) | about 4 years ago | (#31720718)

I concur. Through high school I missed out on Geometry. When I got to college and started Calculus the prof asked if anyone had not had Geometry and Trigonometry, so I raised my hand. He tutored me for a few hours and I was good to go. Much of geometry and trig is taking the time to prove the various relationships. I just had to accept that they were correct, never went through the pain of the proof process. One could argue that I missed something valuable, but it has never come up in 30 yrs of working as a scientist.

I attended a small liberal arts college and the professors were all about teaching. My prof was a very good teacher, so that may account for his skill in getting me up to speed. So try to seek out the best teachers (small colleges, maybe community colleges) and pay for a tutor, these profs can always use the cash.

I agree with an earlier post that I have used calculus rarely (and just went to the book to look up the integration/ differentiation rules). On the other hand in the last 10 years the use of statistics has really jumped in industry (I am a chemist/mauf engineer not a programmer) with Six Sigma and the like. So again you don't need to learn all the proofs behind the statistics, but you need to know how to run software for analyzing the data and what the results mean. How to run a DOE, how to plot an M&IR, how to use ANOVA to prove that a statistically significant exists/doesn't exist with data sets.

Your mileage may vary, since you might be in a vastly different arena. And of course there is the internet and various web sites where you could get help if you get in too deeply.

MIT Opencourseware? (3, Informative)

kaiidth (104315) | about 4 years ago | (#31720584)

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/ [mit.edu]

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 :)

http://yaymath.org/ is the best source (0)

Anonymous Coward | about 4 years ago | (#31720600)

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.

Sigh... (3, Insightful)

Digana (1018720) | about 4 years ago | (#31720618)

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.

Re:Sigh... (4, Informative)

Z8 (1602647) | about 4 years ago | (#31720720)

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?

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 [ets.org]. 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.

Re:Sigh... (0)

Anonymous Coward | about 4 years ago | (#31720854)

Many mathematicians have thought about the prestige of mathematics. IIRC some big name (Kolmogorov? Arnold?) was writing about how maths-fanaticism in France allowed under-10-year-olds to engage in conversations like "Q: What is 2 + 5? A: It is 5 + 2 of course."

The problem is that if you don't do this, then no maths will be learned by anyone, which is a worse outcome.

Re:Sigh... (4, Informative)

clifyt (11768) | about 4 years ago | (#31720766)

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...

Re:Sigh... (0)

Anonymous Coward | about 4 years ago | (#31720856)

... I can't tell if your humor is VERY dry or are you just boring in general.

Always been a pet peeve of mine (1)

Sycraft-fu (314770) | about 4 years ago | (#31720914)

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.

Schaum's outlines (1)

ColorTheory (897257) | about 4 years ago | (#31720652)

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 .

A Very Good Survey (3, Informative)

richg74 (650636) | about 4 years ago | (#31720694)

If what you are looking for is a way to get your mind back into "math mode", I'd suggest one book that I have used, both to refresh my memory and to read for pleasure since I was an undergrad ~40 years ago. It's called What is Mathematics?, by Richard Courant and Herbert Robbins, in the 2nd edition (which I have).

There is a new edition, edited by Ian Stewart, which Amazon has:
What is Mathematics? [amazon.com]

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.

More Effort Required On Your Part (0)

Anonymous Coward | about 4 years ago | (#31720698)

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.

Newtonian physics (2, Insightful)

oldhack (1037484) | about 4 years ago | (#31720700)

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.

Just do it! (0)

Anonymous Coward | about 4 years ago | (#31720722)

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.

ThatQuiz.org (1)

blixel (158224) | about 4 years ago | (#31720770)

I'm not sure to what extent this site would help:

www.ThatQuiz.org [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.

The Teaching Company (1)

The Hatchet (1766306) | about 4 years ago | (#31720774)

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?

Bad textbooks, bad teachers. (1)

tinylobsta (1782462) | about 4 years ago | (#31720778)

I don't know about other people, but it seems like the biggest inherent flaw is not a lack of resources for math, but rather that people generally don't know where to go.

Up until right now, I just used http://www.purplemath.com/ [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!

Calculus (1)

CODiNE (27417) | about 4 years ago | (#31720794)

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.

The Princeton Review (2, Informative)

Phaldyn (1657411) | about 4 years ago | (#31720820)

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!!!

For geometry (1)

Xamusk (702162) | about 4 years ago | (#31720870)

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.

Not enough information. (3, Informative)

wickerprints (1094741) | about 4 years ago | (#31720876)

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.

Book Suggestion (0)

Anonymous Coward | about 4 years ago | (#31720888)

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.

What is Mathematics? by Courant and Robbins (1)

Funkeriffic Toad (518830) | about 4 years ago | (#31720890)

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.

iTunes U (3, Informative)

shrtcircuit (936357) | about 4 years ago | (#31720902)

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.
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