Syllabus (including office hours and section information)

A note on homework assignments: reading the text of the sections from which the homework is assigned is implicitly part of the assignment.

**Homework 1, due Apr 13, 2017.**

__Chapter 5 exercises__

Section 1 (Direct Products): #4, 11, 12.

Section 2 (Fundamental Theorem of Finitely Generated Abelian Groups): #1, 8, 12, 14.

Section 3 (Table of Groups of Small Order): #1.

**Homework 2, due Apr 20, 2017.**

Section 4 (Recognizing Direct Products): #5, 8, 9, 13, 15.

Section 5 (Semidirect Products): #2, 5, 12.

**Homework 3, due Apr 27, 2017.**

__Chapter 7 exercises__

Section 1 (Basic Definitions and Examples): #7, 14, 25, 29, 30.

Section 2 (Polynomial Rings, Matrix Rings, and Group Rings): #2, 7, 12, 13.

**Homework 4, due May 9, 2017.**

__Chapter 7 exercises__

Section 3 (Ring Homomorphisms and Quotient Rings): #5, 12, 21, 29.

Section 4 (Properties of Ideals): #7, 9, 11, 29.

**Homework 5, due May 11, 2017.**

__Chapter 7 exercises__

Section 5 (Rings of Fractions): #3, 4, 5.

Solve: Let R = Q[x,y]/(y^2 - x^3). (a) Prove that R is an integral domain. (b) Prove that the fraction field of R is isomorphic to Q(t), the field of rational functions in one variable. [Hint: t = y/x.]

**Homework 6, due May 18, 2017.**

__Chapter 7 exercises__

Section 6 (Chinese Remainder Theorem): #1, 5, 6, 7.

__Chapter 8 exercises__

Section 1 (Euclidean Domains): #3, 6.

**Homework 7, due May 25, 2017.**

__Chapter 8 exercises__

Section 1 (Euclidean Domains): #8, 9, 10, 11.

Section 2 (Principal Ideal Domains): #1, 2.

**Homework 8, due June 1, 2017.**

__Chapter 8 exercises__

Section 2 (Principal Ideal Domains): #3, 5.

Section 3 (Unique Factorization Domains): #2, 5, 8.

__Chapter 9 exercises__

Section 1 (Polynomial Rings): #5, 7. 8.

**Homework 9, due June 8, 2017.**

__Chapter 9 exercises__

Section 2 (Polynomial Rings over Fields I): #1, 12.

Section 3 (Unique Factorization Domains): #1, 4.

Section 4 (Irreducibility Criteria): #3.

Final Exam

Errata for the textbook can be downloaded from Foote's web page.