Course: MA 542, Modern Algebra II
Instructor: Jared Weinstein
Lectures: MWF 1:25 pm - 2:15 pm in FLR 123
Discussion Sections: M 12:20 pm - 1:10 pm in FLR 123
Office Hours: F 10:00 am - 11:00 am in MCS 238

Course Overview

This course is the second half of the abstract algebra sequence. MA 541 dealt with groups, whereas MA 542 deals with rings. Rings are algebraic structures which have two operations: addition and multiplication. Examples include the integers, the rational numbers, the real numbers, the complex numbers, and polynomial rings. The theory of rings (and especially fields) is used to answer the question of how to solve polynomial equations. This will lead us to the final topic, Galois theory, which establishes a relationship between solutions of a polynomial equation and properties of a group associated to that equation.

Text

John B. Fraleigh, A First Course in Abstract Algebra, 7th ed., Addison-Wesley.

Resources relevant to this course can be found here.

Assignments and Exams

In order to gain mastery of the concepts it is crucial to do many exercises. I will be assigning problem sets every week which will usually be due on Wednesdays. You are allowed and encouraged to work together on homework assignments, but you must hand in solutions which are written in your own words. Select problems from each problem set will be graded and returned to you the following week.

The midterm and final exams will be take-home. You are not allowed to work together on the exams. The first midterm will be due on Wednesday, March 25, and the final will be due Wednesday, May 6.

HW Assignment Due
#1 §18: 1, 5, 7-13, 14, 15, 20, 27, 37, 46, 55.
§19: 1,2, 14, 29.
§20: 1, 6, 27.
Jan. 29
#2 §21: 1, 2.
§22: 2, 3, 6, 11, 12, 13, 22, 25.
§23: 5,7, 9, 34, 36.
Feb. 5
#3 §24: 4, 6, 9, 10, 12.
§26: 1, 3, 9, 12, 13, 14, 20, 24, 30.
Feb. 12
#4 §26: 34, 35, 36.
§27: 5, 15, 16, 24, 28, 37.
§29: 1, 2, 14, 16, 17, 25.
Feb. 19
#5 §29: 29, 30, 31, 32, 34.
§30: 4, 6, 21, 23.
Feb. 26
#6 §31: 7, 10, 13, 24, 33, 35, 37.
§32: 3, 4, 8.
Mar. 4
#7 §33: 8, 9, 10, 11, 12, 13, 14. Mar. 18
#8 §48: 1, 7, 8, 36, 39.
§49: 7.
§50: 1, 2, 5, 7, 8, 9, 10.
Mar. 25
#9 §50: 18, 23, 24.
§51: 1, 2, 3, 11, 14a, 15.
Apr. 1
#10 §51: 16, 17.
§53: 2-11.
Apr. 8
#11 §53: 12, 13, 14, 15, 17, 22. Apr. 15
#12 §54: 1, 4, 6, 7, 8, 11, 12. Apr. 22
#13 §55: 2, 6, 10, 11.
§56: 1, 2, 3, 4, 8.
Apr. 29