M3P14: Elementary Number Theory

Tue 11-12 in Huxley 340, Thu 12-1 in Huxley 139, Fri 12-1 in Huxley 340
Dr. David Helm
672 Huxley
dhelm@imperial.ac.uk
Office Hours: Tue 1-3

Course description

This course is an introduction to elementary number theory. We will study topics including factorization, the distribution of primes, and modular arithmetic, as well as some simple diophantine equations.

Suggested References

T. Apostol, Introduction to analytic number theory
K. Rosen, Elementary number theory and its applications (this suffers from unfortunate "edition bloat"; earlier editions are generally preferable)
K. Ireland and M. Rosen, A classical introduction to modern number theory (this is somewhat more advanced than the first two)

Lecture Notes

I am grateful to Robert Rouse for making his lecture notes available online. They are now complete and up to date as of 13/03/2015.

Problems

Example Sheets will be posted here every two weeks. They will not be assessed work, but they will be collected, two weeks after being assigned, and marked. This is purely optional if you want feedback on the assignments.
Example Sheet 1 (Due Friday 31 October) Solutions
Example Sheet 2 (Due Friday 14 November) Solutions
Example Sheet 3 (Due Friday 28 November) Solutions
Example Sheet 4 (Due Friday 12 December) Solutions

Mastery Material

The mastery material for fourth-year students in this course is about the ring of p-adic integers and Hensel's Lemma, and is based on these notes. These notes contain many exercises; they will not be assessed, but they are essential to understanding the subject. Most of the exercises are straightforward; the one that is not is marked as optional and will not be examinable material. I will be happy to answer questions (within reason) about the material (in particular, if you think you have found a mistake or typo, please let me know.)