Math 111B, Spring 2017

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