Stan: Teach her about integer computations mod p, mod q, etc., and then the Chinese Remainder Theorem. She can use single precision integer math (except for the CRT part) to do matrix math _exactly_, without any roundoff error. Teach her some of the Babylonian & Egyptian diophantine equations. I got a summer course in number theory while a high school student (courtesy of the National Science Foundation) and we studied "Number Theory and its History" by Oystein Ore, and I fell in love. I had the same problem as she did, but I eventually got over it -- once you see how cool number theory is, who cares if it is useful or not! (Oystein Ore, Dover Publications, ISBN #0-486-65620-9 -- i.e., _cheap_, if you can find it.) If she is a really good student, whisper "Knuth" into her ear. His 3-part tome is the best source of cool math applied to useful things that has ever been written. It is expensive, it is very dense, and it will take her the rest of her professional life to grok it, but it will provide her with more interest & satisfaction than any 500 other books. See also: "The Unreasonable Effectiveness of Number Theory" http://www.amazon.com/gp/product/0821855018/ref=nosim/104-1699250-7817501?n=... At 05:13 PM 4/12/2006, Stan E. Isaacs wrote:
I had a student in my computer class ask me a mathematics question: she asked what was the use of prime numbers? She knew there were lots of work done on primes, but what she wanted to know was, what *good* are they, besides being a fascination to math people. It caught me unawares, I mumbled something about that there are theorems where it is easier to prove them for primes, and then extend the proof to all numbers, but I couldn't think of an example. I looked around a little, but most of the things I see, off-hand, talk about all the things you can prove about primes themselves, not what use they might be elsewhere. I could probably mention mods, since you need mod p to be prime, to allow division. But what I really want is some examples where they might be of use in "everyday life", or at least in some mathematics that would apply to more everyday things. Anyone have ideas of what to tell her? Or references of places I could look?
Thanks,
-- Stan -- Stan Isaacs 210 East Meadow Drive Palo Alto, CA 94306 stan@isaacs.com