Course page for Math 6110, Fall 2019


Course meets MWF from 11-11:50 pm in MATH 220

Instructor: Professor David Grant.
Office hours: M 2:30-3:30, W 12:30-2:30, or by appointment in MATH 303.
Syllabus for course  

Text: K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory (Springer, 2nd edition)


Daily Schedule, Readings, and Homeworks


Date Section and Topic Read before class Homework
August 26 Organization and introduction
August 28 Unique Factorization in the integers Chapter 1; Sections 1, 2 HW 1 Due on September 9
August 30 Unique factorization in k[x] Chapter 1; Sections 2, 3 Chpt 1: 7, 9, 18, 21, 23, 25, 26, 35-38.
September 4 Unique Factorization in PIDs, Euclidean Domains Chapter 1; Sections 3, 4
September 6 Gaussian and Eisenstein Integers Chpt1; Sect 4. Chpt 2, Sect 1
September 9 Infinitude of Primes Chpt 2; Sections 1, 3 HW 2 due September 18
September 11 Arithmetic Functions Chpt 2, Section 2 Chpt 2; 1, 2, 6, 7, 8, 9, 10, 12, 15, 21, 26, 27
September 13 Growth of π(x) Chpt 2; Section 4
September 16 Congruences Chpt 3; Sections 1, 2
September 18 Chinese Remainder Theorem Chpt 3; Section 3, 4 HW 3 due Sept 30: Chpt 3; 1, 3, 5, 16, 18-21; Chpt 4: 1, 6, 8, 11, 12
September 20 Primitive Roots Chpt 4; Section 1
September 23 nth-power residues Chpt 4; Section 2
September 25 Quadratic residues Chpt 5; Section 1
September 27 Quadratic reciprocity Chpt 5; Section 2
September 30 Proof of quadratic reciprocity Chpt 5; Section 3
October 2 Algebraic numbers and algebraic integers Chpt 6, Section 1 HW 4 due Oct 14; Chpt 5: 1, 3, 16; Chpt 6: 2, 8, 11, 13.
October 4 The quadratic character of 2 Chpt 6, Section 2
October 7 The quadratic Gauss sum Chpt 6, Section 3
October 9 Sign of the quadratic Gauss sum, a la Schur Handout
October 11 Sign of the quadratic Gauss sum, a la Kronecker Chpt 6, Sect 4
October 14 Introduction to Finite Fields Chpt 7, Sect 1
October 16 More on finite fields Chpt 7, Sect 2 Take home midterm due Oct 28
October 18 Quadratic reciprocity via finite fields Chpt 7, Sect 3
October 21 Multiplicative characters Chpt 8, Sect 1
October 23 Gauss Sums Chpt 8, Sect 2
October 25 Jacobi Sums Chpt 8, Sect 3
October 28 More on Jacobi sums, Fermat equation Chpt 8, Sect 4, 5
October 30 More on Jacobi sums Chpt 8, Sect 6
Nov 1 Points on diagonal hypersurfaces Chpt 8, Sect 7 HW5 due Nov 11; Chpt 9, 19-25
Nov 4 Arithmetic of Eisenstein integers Chpt 9, Sect 1, 2
Nov 6 Cubic residues Chpt 9, Sect 3
Nov 8 Proof of cubic reciprocity Chpt 9, Sect 4
Nov 11 Intro to p-adic integers B&S: 1.3.1, 1.3.2
Nov 13 p-adic integers and p-adic numbers 1.3.2, 1.3.3
Nov 15 Convergence of p-adic numbers 1.3.4