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ImperialCollegeLondon / xena-UROP-2018

A place to put our 2018 Xena project UROP thoughts and programs.
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Elementary Number Theory #6

Open kbuzzard opened 6 years ago

kbuzzard commented 6 years ago

A suggested source is Silverman's "A friendly introduction to number theory" ,which is probably in Imperial's library. We could also work on digitising Prof Gee's M3P14 example sheets. Note: even if you're only a first or second year -- M3P14 doesn't need much background, it mostly develops basic properties of the integers without using too much machinery, so probably most people can contribute.

gml16 commented 6 years ago

Could someone point me to where I can find Prof Gee's M3P14 example sheets? Or maybe put them in this repository? Thanks

Edit: they are here https://github.com/kbuzzard/xena/tree/master/P14

kbuzzard commented 6 years ago

We now have gcd's of integers -- M3P14 sheet 1 is mostly formalised! We need -- sums over general sets (e.g. sums over divisors of n of ...). finset.sum does sum over a finite set -- maybe this helps for this situation?

kbuzzard commented 6 years ago

This stuff seems to be going really well. What helps is that there is a very solid API for naturals an integers. A lofty goal here would be to prove the law of quadratic reciprocity. Several people (@gml16 @ClaraList @sj2816 and others too) have started formalising questions and solutions on the example sheets -- my only worry is that we'll get different people working on the same thing.