Re: Introductory inspiring math books

On Sun, 15 Jan 2006 22:26:15 GMT, "David Park" <djmp@xxxxxxxxxxxxx>
wrote:

>I would recommend "Numbers and Geometry" by John Stillwell. It presupposes
>only high school algebra but has real mathematics. He also has a second book
>"Mathematics and Its History" that is more advanced but doable.
>
>Also, if possible, I would suggest you get Mathematica and try to learn its
>'functional programming' and 'rule base programming', which are a very
>mathematical way of thinking. A good CAS can be very useful provided you use
>it as a mathematician and push computer science into the background. It
>would go well with "Numbers and Geometry".

I have experience with purely functional programming languages
(Haskell) and some of the theory behind (eg. currying, lambda calculus
etc), as well as a few other functional languages that allow side
effects (Scheme etc). I can't say I use these languages for real world
purposes, but I don't regret learning them. Scheme is the most
beautiful language I know of. I have never used Mathematica though,
but the rule based programming seems interesting ("A language that
doesn't affect the way you think about programming, is not worth
knowing" --Alan Perlis).

I think I belong in some grey zone. I barely remember the trigonometry
relationships from high school, or the calculus. On the other hand
(unlike most high school students), I have picked up loads of bits and
pieces from programming (contests). I know more about practical graph
theory than my friends who study computer science for example. I have
coded a radix-2 FFT using inline assembly. I know that you can make
Miller-Rabins primality test non-random if you use the bases 2, 7 and
61, if you are only interested in testing numbers smaller than 32 bit.
I have used Eulers totient function. And I often read mathworld just
to find interesting things to code. I don't tell you this to sound
impressive, but rather because I am really lost here and I'm looking
for books at the right level. Most people learn math before
programming, not the other way around.

Many people have recommended I should read Knuth's Concrete
Mathematics, and it's on my to-buy list, but I think it's a better
idea to read/study something more general about mathematics first,
rather than a math book especially for programmers (which will
probably give me some wrong ideas about what math is about).

I will check out the "Numbers and Geometry", thanks for the
suggestion! "The Mathematical Experience", "Concepts of Modern
Mathematics", and "What Is Mathematics?" seems like other interesting
books too!

Thanks!
B
.

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