Abstract Algebra II
Mathematics 452 — Spring 2013
Prof. Weibel (640:351)
-
Rigorous study of abstract algebraic systems including groups, rings, and
fields. For students preparing for graduate study
in the mathematical sciences.
- Lectures: MW6 (5:00-6:20PM) in ARC 108
- Text: Michael Artin; Algebra (second edition); Prentice-Hall, 2011 (560 pp.); (ISBN: 0-13-241377-9; ISBN13: 9780132413770)
- Weibel's Office hours
- Homework: Suggested homework problems are listed in the
schedule of lectures below. One homework problem (marked *)
will be collected each week.
I will be happy to answer homework-related questions anytime.
Tentative Course Syllabus
| Week | Lecture dates | Sections | Suggested HW |
|---|---|---|---|
| 1 | 1/23 | 3.1-3.4 | Ch.3 #2.1,2.3,3.2,4.2, *3.4.18* |
| 2 | 1/28, 30 | 3.5-7, 4.1-3 | Ch.4 #1.2,1.4, *2.4*, 3.1,3.3,3.4 |
| 3 | 2/4, 6 | 4.4-5-6-7 | Ch.4 #4.1,4.2,4.6, 5.1(b), 6.3, *6.5(a)*, 6.9, 7.4,7.7 |
| 4 | 2/11, 13 | 11.1-11.4 | Ch.11 #1.3,1.7,2.1,3.3, 3.5(b), *3.9*, 3.13 |
| 5 | 2/18, 20 | 11.4-5-6 | Ch.11 #4.3(a,b,c), 5.1,5.3,5.5, 6.2,6.5, 6.8(CRT)
*Find all ideals in R={p/q∈Q:q odd}* |
| 6 | 2/25, 27 | 11.7-8-9 | Ch.11 #7.1,7.3,8.1, *8.4*, 9.1,9.6,9.9 |
| 7 | 3/4, 6 | 11.8-9, 12.1-3 | Ch.11 #9.4,9.9, *9.11*, 9.12, Ch.12 #1.4(b), 2.1,2.2,2.5,2.9 |
| 8 | 3/11, 13 | 12.3-4-5 | Ch.3 #2.8; Ch.11 #1.8,3.4,4.4,6.4,8.3,9.8; Ch.4 #7.3; Ch.12 #2.4,2.7,3.1,3.6 |
| 9 | 3/25, 27 | Review and Midterm | cumulative |
| 10 | 4/1, 3 | 15.1-4, 15.6 | Ch.15 #1.1,2.1,2.3,3.1,3.4,3.9, 4.2,6.3,7.2,7.9 |
| 11 | 4/8, 10 | 15.5-15.8 | Ch.15 #5.1,5.2a,5.4, 6.1,7.5,7.7,7.14, 8.1, *8.2* *It is impossible to construct a regular 7-gon* |
| 12 | 4/15, 17 | 16.1-4 | Ch.16 #1.1(b,e),3.1,3.2,3.3, *4.1* |
| 13 | 4/22, 24 | 16.5-7 | Ch.16 # 5.1(a,c,d), *5.2*, 6.2, 6.3, 7.1, 7.4 |
| 13+ | 4/26 (Friday) | Optional Midterm | 15.1 through 16.4 |
| 14 | 4/29, 5/1, 5/6 | 16.7-10 | Ch.16 #7.2,7.4,7.7, *7.11*, *8.1*, 8.4, 10.3,10.7 |
| 17 | May 10 (Friday) | 4-7 PM | Final Exam (cumulative) |
Charles Weibel / weibel@math.rutgers.edu / Spring 2013