MA 542 — Spring 2019
Modern Algebra II

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.

Instructor

Name: Robert Pollack
Office: MCS 271
Office hours: Monday 3-4, Friday 10-11
E-mail: rpollack@math.bu.edu

Lectures

MWF 1:25-2:15, CAS 324

Text

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

Course website:

All homework sets and solutions plus occasional announcments will be posted at our course website:
http://math.bu.edu/people/rpollack/Teach/542spring2019.html

Exams

Midterm: Friday, March 8 in class
Final exam: Saturday, May 11 in TBA, 12:30-2:30

Recent Announcements:

Homework (an essential part of the course!)

Problem sets will be assigned each Wednesday and are due at the start of class on Wednesday of following week.
Late homeworks will not be accepted, but your bottom two homework grades will be dropped.
You are encourage to work together on problem sets. However, each student must write-up their own problem sets in their own words, notation, etc.

Course grading Your final grade will be computed using the following breakdown:

Homework: 25%
Midterm: 30%
Final: 40%
Lecturer discretion: 5%

Outside help:

You are very much encouraged to attend my office hours as posted above.
In MCS B24 at most times during working hours, there are math graduate students on duty to answer questions from any class. This is a fantastic resource that is available all week long.
Professor Wayne Snyder will supervise "Math Help Night" in the Cinema Room of Rich Hall on West Campus on Tuesdays, 7-10 pm. You do not need to live on West Campus to take advantage of this opportunity.

Miscellaneous Items of Interest:

Late homeworks are not accepted.
Make-up exams are only given in the case of serious illness.
Incompletes are rarely given and only for extreme situations.

Date of assignment	Due date	Homework Assignment	Solutions to select questions
1. Jan 23	Jan 30	§18: 2, 6, 8, 10, 11, 12, 13, 16, 18, 27, 33, 37, 44, 55 §19: 3, 14, 17, 29	Solutions for HW1
2. Jan 30	Feb 6	§20: 2, 3, 4, 6, 8, 10, 23, 24, 27 §21: 1, 2, 4, 5, 8, 10 §22: 2, 6, 14, 24	Solutions for HW2
3. Feb 6	Feb 13	§22: 17, 23, 25 §23: 2, 6, 7, 9, 12, 14, 16, 18, 20, 25, 26, 28, 30, 34, 37c	Solutions for HW3
4. Feb 13	Feb 20	§26: 1, 3, 4, 10, 12, 13, 14, 16, 17, 24, 26, 27, 30, 31, 32	Solutions for HW4
5. Feb 20	Feb 27	§27: 5, 6, 8, 14, 15, 16, 17, 18, 24, 30, 32, 34, 35	Solutions for HW5
6. Feb 27	Mar20	§29: 2, 4, 6 (check irred), 12, 16, 18, 23, 25, 30, 31, 32, 35 §30: 1, 3, 4, 6, 15, 16, 22, 24	Solutions for HW6
7. Mar 22	Mar 27	§31: 1,2,4,6,8,12,19,23,27,29	Solutions for HW7
8. Mar 27	Apr 3	§31: 20, 21, 24, 28, 31, 33, 36	Solutions for HW8
9. Mar 27	Apr 10	§48: 2, 4, 8, 10, 12, 14, 16, 18, 22(a,b), 34, 36(a,b), 39	Solutions for HW9
10. Apr 10	Apr 24	Click here for HW10	Solutions for HW10
11. Apr 24	May 1	Click here for HW11	Solutions for HW11

MA 542 — Spring 2019 Modern Algebra II

MA 542 — Spring 2019
Modern Algebra II