University of Wisconsin-Madison
Mathematics Department

Math 542
Modern Algebra
A second course in abstract Algebra
Lecturer: Andrei Caldararu

Fall 2018

About the course:

Math 542 is the second course in abstract algebra. The core topics are ring and module theory, and some elements of Galois theory. Along with Math 521 and Math 551 this course is a necessity for students considering going on to graduate school in mathematics.

Special goal: One of the goals of this course is to reinforce what you have learned in Math 541 about how to construct and write proofs.

Lectures: There will be two 75 minute lectures per week:

TR 2:30-3:45 in B119 Van Vleck

Text: The textbook for the course is

Abstract Algebra, by David Dummit and Richard Foote, Third Edition, John Wiley and Sons, Inc., 2004.

Office hours: Tuesdays 1:30-2:30 in Van Vleck 605 and by appointment.

Grading: The term grade will be based on homework and the exams as follows: Homework: 30% Midterm: 30% Final Exam: 40%. Final grades are computed by totalling the points from the homework, the midterms and the final. Grade letters will be assigned with the following curve as a guideline: 20% A's, 30% B's, 30% C's, 20% D's and F's.

Homework: Homework will be due a week after it is assigned, during lecture. All claims that you make in your homework MUST BE PROVED in order to receive credit.

Homework assignments:

Homework assignment 1, due 9/13: §7.1: 3, 5, 8, 11, 14, 21, 23

Homework assignment 2, due 9/27: §7.2: 2, 3, 7, 10; §7.3: 2, 3, 13, 18, 19

Homework assignment 3, due 10/4: §7.4: 4, 7, 9, 12, 13, 15, 17, 26

Homework assignment 4, due 10/11: §7.4: 27, 30, 36, 37; §7.5: 2, 3

Homework assignment 5, due 10/18: §7.6: 1, 4, 7; §10.1: 3, 5, 6, 8, 9

Homework assignment 6, due 11/13: §10.1: 13, 15; §10.2: 3, 4, 10, §10.3: 1, 4, 5, 6, 7, 9

Homework assignment 7, due 11/20: § 10.3: 11, 13, 15, 23, 27; §10.4: 3, 4, 6, 7, 9, 11, 17, 18, 24

Homework assignment 8, due 12/11: §10.4: 12, 16; §12.1: 1, 2, 3, 5; §12.2: 1, 2, 3, 4, 9

Exams: There will be one 75 minute in-class midterm on Thursday October 25. There will be a 2 hour final exam on Tuesday, December 18, 10:05-12:05 in room Psychology 103. The exams will be a random selection of problems similar to homework problems from the homework assignments. The final exam will be cumulative.

Syllabus: It is available here.