Mat 410 - Topics in Number
Theory
Fall 2016: Syllabus Outlines
- Integrates learning
advanced topics in Number Theory (e.g. Gauss and
Jacobi sums) and research on Weil zeros, using SAGE
as math software for computations and explorations,
a uniform approach using Fourier Analysis on Finite
Abelian Groups.
- Textbook: A classical introduction to modern
number theory by K. Ireland and M. Rosen
Fall 2015: Syllabus
Outlines
- Integrates learning advanced topics in Number
Theory (e.g. Gauss and Jacobi sums) and research on Weil
zeros, using SAGE as math software for computations and
explorations.
- Textbook: A classical introduction to modern number
theory by K. Ireland and M. Rosen
Fall 2012:
Syllabus
Outlines: Ch.1-5
Ch.6-end
(Pythagorean Thesis: "Numbers
Rule the Univers")
- The first week will be devoted to a review of
elementary topics of Number Theory; further lacking background
will be remediated as we go
- Textbook: Introduction to
Analitic Number Theory by Tom Apostol
... Enjoy!
Spring
2011:
1) Before we start ...
The 1st week will be a "clinic" on basic number theory; but
please do not wait, and review the following topics, as much as
you can:
- Theory and congruences in Z (integers);
- Basics of abalian groups Z (integers & factorization into
primes), Zn (integers modulo n);
Read for instance the first three chapters of "Elementary Number
Theory" by G.A. Jones & J. M. Jones (textbook).
Additional
topics
will be reviewed in class, the first week or so:
Syllabus and
Some outlines:
Updated 8/20/2012