Free Math Texts

[AuSmith]

I've been meaning for a long time to point out that there are some good math texts out there for free download. So, if you can learn by just reading a book or by asking questions on here, and have been wanting to learn calculus or some more advanced math and don't want to pay $70 for a textbook you don't even know you want... there are several sites, but Mr. Cain does a fine job of listing a bunch. And, there's always google scholar... then you just can't keep them.


http://www.math.gatech.edu/~cain/textbo ... books.html
Generatingfunctionology: Likely the most popular free download, Herbert Wilf explains the theory of generating functions, which makes sequences much easier. Highly recommended.


http://www.math.gatech.edu/~cain/textbo ... books.html
GA Tech: About 65 different downloads. I guess I would recommend graph theory, number theory, complex analysis, and probability stuffs.


Hope somebody finds these as exciting as I did. I have about 1 GB of math PDFs that took much effort. Am thinking about downloading all hundred years of the American Mathematical Monthly from JSTOR, which is an appreciable part of a million PDFs. I think a subscription is several thousand dollars a year. lol, how nerdy.

-Aaron

[Quelloquialism]

I just took a glance at Generatingfunctionology, though I'm not sure what I'll be able to get from it...I'm only half-way through Precal in high school, and my background in Calculus is lacking (put simply, I don't know what a power series is, and a working knowledge and familiarity of that seems to be a prerequisite). Still, it won't prevent me from trying, and I don't have a shortage of resources, I think.

[AuSmith]

Power series are just polynomials except you can have an infinite number of terms.

[unparseable or potentially dangerous latex formula]

This is the generating function for the sequence [unparseable or potentially dangerous latex formula]


So, the generating function for the Fibonacci sequence would be [unparseable or potentially dangerous latex formula]

Similarly, [unparseable or potentially dangerous latex formula] is the generating function for the integers.

Who knows the formula for the nth Fibonacci number?

[makashi]

It's Binet's formula.

[AuSmith]

Ok well, does 1-x-x^2 or x^2+x-1 look familiar?

[AuSmith]

Here's one way to derive Binet's formula that generatingfunctionology gives. Find the nth coefficient of the Fibonacci generating function:

Notice that the golden ratio [unparseable or potentially dangerous latex formula] and it's conjugate [unparseable or potentially dangerous latex formula] are roots of the denominator in the Fibonacci generating function [unparseable or potentially dangerous latex formula]. So we factor,

[unparseable or potentially dangerous latex formula]

and decompose

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

and, turn the rest into two geometric series.

[unparseable or potentially dangerous latex formula]

So, you can look at the coefficients to get Binet's formula

[unparseable or potentially dangerous latex formula]

[polymath25]

also on the topic of free math texts, MIT has an OCW where you can find Calculus textbooks and such for free. The only thing is that most of it is in PDF, and PDF and I have never been very good friends. you can check it out at http://ocw.mit.edu/index.html.