# Abstract Algebra Mathematics 451 — Fall 2023

### Prof. Weibel (640:451)

Rigorous study of abstract algebraic systems including groups, rings, and fields. For students preparing for graduate study in the mathematical sciences.

• Lectures: T2F2 (10:20-11:40PM) in Beck 119 (Livingston)
• Text: Algebra (2nd ed.), by M. Artin Prentice-Hall, 2011 (560 pp.); (ISBN: 0-13-241377-9; ISBN13: 9780132413770)
• Weibel's Office hours: (Hill 218) Monday and Tuesday 1:40-3:00 PM

• Homework: Homework problems are listed in the schedule of lectures below.
They should be turned in on Canvas by the following Tuesday.
I will be happy to answer homework-related questions anytime.

#### Tentative Course Syllabus

Week Lecture dates Sections HW (due Tuesdays) Suggested Problems
1 9/5, 8 3.1-3.7 Ch.3 #2.1, 2.3, 2.4(p=5,7 only), 3.22.11,4.3
2 9/12,15 3.5-7, 4.1-3 Ch.3 #4.8,5.2(a,b),6.1; Ch.4#1.1,1.3,2.13.6.3,4.2.3,4.3.4
3 9/19,22 4.5-7 Ch.5 #1.2,2.3,3.2,3.3(a,b); Ch.6#3.6(a)5.1.2,5.2.3
4 9/26,29 2.1-5 Ch.2 #2.6,4.9,6.1,6.4,7.1,8.1,8.12,9.74.5,5.1,6.3,8.4
5 10/3,6 2.6-12 Ch.2 #8.3,8.10,9.4,10.5,11.5,12.28.4,9.1,11.1,11.6,12.4
6 10/10,13 Review and Midtermcumulative
7 10/17,20 7.7 (Sylow Theorems) Ch.7 #7.3, 7.5, 7.6, 7.7, 7.8, 7.9
8 10/24,27 11.1-11.8 (Rings) Ch.11 #1.1,1.8; 2.2; 3.2,3.6,3.12; 4.1; 5.6; 6.1 #1.6, 3.3, 3.9, 5.7
9 10/31,11/311.5-11.9 (Rings) Ch.11 #6.7, 7.1, 7.2, 8.1, 8.4, 9.1, 9.5 #7.5, 8.3, 9.2, 9.6
10 11/7,10 14.1-14.6 (Modules) Ch.14 #1.4, 2.1,2.3, 4.1(a),4.6, 6.1, 7.1,7.2, 9.1(a) #1.2,3.4,4.5,4.7,6.2,7.5,9.3
11 11/14,1714.7-8 (Applications) : finite abelian groups and Jordan CF 7.2, 7.4, 7.9, 8.1, 8.2, 8.6
11+ 11/22(Fri.sched) Midtermcumulative
12 11/28,12/112.1-3 (Integer Polynomials) Ch.12 #1.5, 2.2,2.10, 3.1,3.2, 4.1 1.3, 2.4, 2.8, 3.4, 3.6
13 12/5,812.4-5 (Gauss Integers) Ch.12 #4.3,4.6,4.7, 5.1,5.3,5.5 4.4,4.12, 5.4,5.6,5.7
14 12/12 Review for Final Exam
Dec 15, 2023 Math 451 Final Exam (8:00 AM-11:00 AM in Beck 119)

Self-Reporting Absence Website: Students are expected to attend all classes; if you expect to miss one or two classes, please use the University's absence reporting website to indicate the date and reason for your absence. An email is automatically sent to me.
Academic integrity policy: All students in the course are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously.
Disabilities policy: Rutgers is fully committed to compliance with the Americans with Disabilities Act; see policies and procedures.