Re: [seul-edu] Programming Mathematics

[lp <prevettl@cochise.cc.az.us>]

Roger Dingledine wrote:
> 
> I'll answer some of these in perl, as sparetime fun programming things.
> But remember that the motto of perl is 'there's more than one way to
> do it'. So only post optimizations if they are substantially better
> (faster and more readable) than my code. ;) (And I reserve the right to
> kill this thread if it gets too pedantic.)
> (I didn't deal with some end-cases. So these snippets aren't as robust
> as they could be.)
....
> hope this helps. only expmod, is_prime, and print_factors are remotely
> publishable... the rest is just glue.
> --roger

Thanks, Roger, I'll add these to my growing list. Besides the posts
here, I've had luck going to programming and math books. One of my 
favorite books is "Number Theory" by George E. Andrews, a professor 
at Penn. State. There is a small section on "The Use of Computers 
in Number Theory" with some good suggestions for programming projects.

Speaking of being pedantic, one of the projects is to find all of 
the "perfect numbers" between 2 and 500. A number is "perfect" if 
the sum of all the divisors of the number (not including 
the number itself) add up to the number. So 6 is a perfect number 
since 1 + 2 + 3 = 6. 28 is perfect since 1 + 2 + 4 + 7 + 14 = 28.
Once you find the list of perfect numbers then you go looking for 
patterns in the numbers that might predict the nth perfect number.
A curious property of perfect numbers is that the sum of the 
reciprocals of the divisors of a perfect number add up to 2. Odd.
1 + 1/2 + 1/3 + 1/6 = 2. Sorry! I just couldn't help mentioning 
it!

The classic books by Donald Knuth on the "Art of Programming" have
a lot of other interesting examples. Another interesting book I have
found is "Number Theory in Science and Communication", by M.R.
Schroeder. This book is great. It describes "noble" numbers as numbers
whose continued fraction expansions end in infinitely many 1's and 
relates them to the rings of Saturn. (You'll be gone for days 
thinking about that one.) The mathematics journals put out by the 
MAA and the AMA are also providing some good examples.

If you are into this topic as a hobby or because you can't help it,
you can get these books and journals at the library or go down to
Borders Books - a truly enlightened bookstore. They carry Linux 
software, books, and give teachers a 20% discount.

lp