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Learning Math

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Re: Learning Math

#21

Post by mattculbreth »

iamwil wrote: post #3

I'm in my late twenties, and even though I did comm systems as a EE undergrad (lots of math), I still don't feel like I really have a deep understanding on probability/stochastic processes, differential equations, and complex analysis. www.betterexplained.com has some good tidbits for math. I've found MIT's opencourseware to be a pretty good help: http://ocw.mit.edu/OcwWeb/web/courses/courses/index.htm#Math... Only t…

Wow, a link to Killer Cain's site at Tech. That is awesome. I had Cain's Calculus classes at 8:00 am for my first year at Tech, and that's a hell of a way to get welcomed to college. He's still one of best professors I ever had.

Re: Learning Math

#23

Post by ptn »

Try Euclid. Though difficult (which is not that much of a problem given that you are not a complete beginner), it's all there.

Re: Learning Math

#24

Post by mark-t »

The only way to learn math is to do math, and you should learn to do math the same way you learn to program: solve problems that you find interesting.

Personally, I like to do contest problems. You can find tons and tons of them on John Scholes's website: http://www.kalva.demon.co.uk/ but they tend to be on the hard side. The AIME is possibly the easiest on there, and those are the sort of problems where the average high school only has one student every decade or so that can solve any.

There are contests for junior high students and less advanced high school students, too, but I can't find the problems online. There are books, though. You might want to look at the AMC 8, 10, and 12.

Or, you know, make some up. Think of a problem you've always been curious about, and try to solve it. There are forums online that can offer guidance. For example, I work on http://math2.org/mmb/ .

Re: Learning Math

#25

Post by whacked_new »

gms wrote: post #16

The book 'Calculus' by Michael Spivak. In the same way that SICP transforms you from a high-schooler into a wise adult when it comes to programming, so too does Calculus when it comes to maths. If you find the book to be heavy going, then read whatever preliminary material you need, and go back to it. Edit: I should also stress that maths requires a fair amount of discipline (a lot more than programming), so it's rea…

Have you ever seen one of those REA problem solvers books? They are thick books full of problems and solutions (and explanations) and are organized from beginner to advanced.

Do you think this would lead to a more solid foundation (from less frustration), for self studying, than reading from a thorough but dense text? I don't know Spivak's Calculus, but some reviewers on Amazon compare it to Apostol, which I found so abstract, and so unpractical, that I promptly forgot everything. It is now on my to-read list, but like you said, I won't be starting until I can dedicate myself to studying it, and now that I have seen the REA book, I wonder if it would be better to work on that book, as a refresher and foundation builder.

Oh yeah, dwaters, if you happen to be interested in Apostol, and want a study buddy, I nominate me.

Re: Learning Math

#28

Post by rsheridan6 »

gms wrote: post #16

The book 'Calculus' by Michael Spivak. In the same way that SICP transforms you from a high-schooler into a wise adult when it comes to programming, so too does Calculus when it comes to maths. If you find the book to be heavy going, then read whatever preliminary material you need, and go back to it. Edit: I should also stress that maths requires a fair amount of discipline (a lot more than programming), so it's rea…

Seconded. Spivak is ideal for self-study because there is an answer book for it. I tried Apostol first, and, although it's a good book, I had no idea if I was doing the exercises right because I didn't know what a proof was supposed to look like.

Re: Learning Math

#29

Post by DaniFong »

The book What is Mathematics by Courant et. al. is a terrific, read, and highly recommended from generations of mathematicians. It's one of the few math books good enough to compel you to read through the whole thing.

http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-...

There's also the Princeton Companion for Mathematics, which isn't out yet but is available online. It's a wonderful book.

http://pcm.tandtproductions.com/

User: Guest Pass: PCM

Re: Learning Math

#30

Post by asdflkj »

Start with mathematical logic, set theory, abstract algebra and number theory, in that order. Do not follow the usual course of calculus, differential equations, linear algebra and so on. That is, do learn those things, but later on.

The problem with math education is that "the basics" (things that I recommend you start with) are neither easy to understand nor obviously useful in "the real world". Or at least the latter was true before computer science came along. But most educational programs were established before CS, so basic math is regarded as something you don't really need to know. But you do, if your goal is to understand math, and not to be able to design bridges as soon as possible.

Now universities are gradually fixing the situation. They still start you off with calculus and such, but before you go on to more rigorous classes like Analysis or abstact algebra, they give you a "transition course", which is essentially a survey of the basics.

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