Mathematics 6110 Introduction to Number Theory Fall 2012
A 200x200 grid on which the primes have been mapped in a spiral.
Official description: Examines divisibility properties of integers, congruencies, diophantine equations, arithmetic functions, quadratic residues, distribution of primes, and algebraic number fields. Prereq., MATH 3140. Undergraduates must have approval of the instructor.
Topics that will definitely be included: Unique factorization and principal ideal domains, arithmetic functions, congruences, primitive roots, quadratic reciprocity, Gauss sums, finite fields, quadratic fields, quadratic forms, Pell equations.
Grading breakdown: Homework 50%, Takehome Midterm 20%, Takehome Final 30%.
Optional alternative grading: Homework 40%, Project 15%, Takehome Midterm 20%, Takehome Final 25%. In this alternative, you can skip one homework of your choice in order to do the project instead that week. The project can be an exposition on a topic of special interest to you, or an implementation of some number theoretical algorithms on the computer, together with some background info. This is a little bit more work than one homework assignment, but more fun.
Textbook: Kenneth Ireland, Michael Rosen, A Classical Introduction to Modern Number Theory, Second Edition (Springer GTM 84).