| Prerequisites: |
Math 5285 or its equivalent: exposure to some abstract group theory and linear algebra, along with the ability to write and read mathematical proofs. |
| Instructor: | Victor Reiner (You can call me "Vic"). |
| Office: Vincent Hall 256 Telephone (with voice mail): 625-6682 E-mail: reiner@math.umn.edu |
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| Classes: | Mon-Wed-Fri 10:10-11:00am, Vincent Hall 207. |
| Office hours: | Monday 12:20pm, Tuesday 3:35pm, Friday 11:15am; also by appointment. |
| Course content: |
This is the second semester of a course in the basic algebra of
groups, ring, fields, vector spaces, and perhaps modules over rings. Roughly speaking, the Fall semester (Math 5285) covered vector spaces, linear algebra, group theory and symmetry, doing a lot of Chapters 1-6 of the course text by Artin, touching lightly upon Chapters 7 and 9. In this second semester, we will study more seriously rings, fields, and perhaps modules over rings, covering some portion of Chapters 10-14 of Artin's text; see below for what portion more specifically. To give some feeling for the topics, rings and fields are the keys to understanding why it is that...
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| Required text: | Algebra, by Michael Artin, Prentice-Hall, 1991.
We expect to cover much of Chapters 10-14, in this order: Ch. 10 (skip Sec. 7,8) Ch. 11 (skip Sec. 5-12) Ch. 13 (skip Sec. 7,8,9) Ch. 14 (skip Sec. 6) Ch. 12 (skip Sec. 8) |
| Level | Title | Author(s), Publ. info | Location |
|---|---|---|---|
| Lower | A concrete introduction to higher algebra |
Childs, Springer-Verlag 1995 | On reserve in math library |
| Lower | Contemporary abstract algebra | Gallian, Houghton-Mifflin 1998 | On reserve in math library |
| Same | Topics in algebra | Herstein, Wiley & Sons 1999 | On reserve in math library |
| Higher | Abstract algebra | Dummit and Foote, Wiley & Sons 2004 | On reserve in math library |
| Homework, exams, grading: |
As with the Fall semester, there will be 5 homework assignments due usually every other week, but
I encourage collaboration on the homework, as long as each person understands the solutions, writes them up in their own words, and indicates on the homework page their collaborators. The take-home midterms and final exam are open-book, open-library, open-web, but in contrast to the homework on exams, no collaboration or consultation of human sources is allowed. Late homework will not be accepted. Early homework is fine, and can be left in my mailbox in the School of Math mailroom near Vincent Hall 105. Homework solutions should be well-explained-- the grader is told not to give credit for an unsupported answer. Complaints about the grading should be brought to me. |
| Final course grade basis : |
|
| Assignment or Exam | Due date | Problems from Artin, unless otherwise specified |
|---|---|---|
| Homework 1 | 2/13 |
10.1: 4,5,6,8,12 10.2: 7 10.3: 7,8,9,15,17,24 10.4: 3(b) (removed 2) 10.5: 1,12 (removed 3,10; moved 5 to HW2) |
| Homework 2 | 2/27 |
10.5: 5,14,15 10.6: 2,3,5 Chap. 10 Misc. Probs.: 2 11.1: 1,4,8,15 (removed 12) 11.2: 5,8,13 11.3: 4 11.4: 3,4,8 |
| Exam 1 | 3/5 | Midterm exam 1 in PostScript, PDF. |
| Homework 3 | 3/26 |
13.2: 3(a,b),4,5 13.3: 1,3(a,b,c),8,14 13.4: 1,5,6 13.6: 10 (moved 3,5,8,9,11 to HW4) Chap. 13 Misc. Probs.: 2 |
| Homework 4 | 4/9 |
13.5: 2 13.6: 3,5,8,9,11 14.1: 7, 8(a), 9, 12, 13 14.5: 2 |
| Exam 2 | 4/16 | Midterm exam 2 in PostScript, PDF. |
| Homework 5 | 4/30 |
14.1: 1,15,17 (problem 20 removed from HW) 14.5: 11 (problem 4 removed from HW) 14.9: 8 12.1: 1, 6, 7 12.2: 3,4,5 |
| Final Exam | (Friday!) 5/9 | Final exam in PostScript, PDF. |