Mathematics 6110 Introduction to Number Theory Fall 2012
A 200x200 grid on which the primes have been mapped in a spiral.
Course Description
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).
Due Wednesday, August 29th: Please read Ireland and Rosen, Sections 1.1 and 1.2. Also, please read the course notes, Section 2 "Problems in Number Theory" which covers a bit more than I did in class.
Due Friday, September 7th: Your first homework assignment is here, and solutions are here.
Due Friday, September 14th: Your second homework assignment is here and solutions are here.
Due Friday, September 28th: Your third homework assignment is here and solutions are here.
Due Friday, October 5th: Your fourth homework assignment is here and solutions are here.
Takehome Midterm Due Monday, October 29th:Now up and solutions.
Due Friday, November 16th: Your fifth homework assignment is here and solutions are here.
Due Friday, December 7th: Your sixth homework assignment is here and solutions are here.
The Final Takehome Will be available on December 12th and Due on December 17th at noon. It is now available here and solutions.