| Prerequisites: | Theoretical background on groups, and vector spaces over a field, including understanding of change-of-basis, eigenvectors, etc. One should either have 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 113. |
| Office hours: | Monday and Friday 9:05-9:55am, Tuesday 12:20-1:10pm, and by appointment. |
| Course content: |
This is the second semester in a 2-semester sequence on
the algebra of groups, ring, fields, and vector spaces. In the fall we dealt with group theory, as well as vector spaces over fields, while the second semester should be about rings, modules, and field theory Some goals are understanding the following:
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| Required text: | Algebra, 2nd edition, by Michael Artin, Prentice-Hall, 2017.
We plan to cover some (but not all) of Chapters 11,12,14,15,16 |
| Level | Title | Author(s), Publ. info | Location |
|---|---|---|---|
| Lower (like Math 4281) |
Algebra: abstract and concrete | Goodman | author's download page |
| Same | Judson | Abstract algebra: theory and applications | author's download page |
| Topics in algebra | Herstein, Wiley & Sons | In Math Library (QA155.H4 1975b) | |
| Higher (like Math 8201) |
Abstract algebra | Dummit and Foote, Wiley & Sons | On reserve in math library |
| Algebra | Lang, Springer/Nature | On reserve in math library | |
| Proof writing and reading |
How to read and do proofs | Solow, Wiley & Sons | In Math Library (QA9.54.S65 2014) |
| How to prove it | Velleman | In Math Library (QA9.V38 1994) |
| Homework, exams, grading: |
There will be 5 homework assignments due Wednesdays,
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. Forming study groups is a great idea. Here is a guide from Duke University on how to form a successful study group 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 (Wednesdays, except HW 1) |
Problems from Artin, unless otherwise specified |
Lecture notes |
|---|---|---|---|
| Homework 1 | 2/11 (Mon, not Wed!) |
11.1: 2,3,7 11.2: 1 11.3: 2,3(a,b,d),5 11.4: 3(b),4 (removed 3(c,e)) 11.5: 1,5 (removed 3) 11.6: 1,5 Note: Feel free to use (without proof) a fact which comes up a couple of times: the real numbers 1, √ 2 , √ 3 , √ 6 , are linearly independent over the rational numbers. |
Jan 23 Jan 25 Jan 28 Feb 1 Feb 4 Feb 6 Feb 8 |
| Homework 2 | 2/27 |
11.5: 3 11.7: 1,3 11.8: 1,3 12.1: 1,5 12.2: 1,4,6(b) 12.3: 4,6 12.4: 1,6,7,9,13 |
Feb 11 Feb 13 Feb 15 Feb 18 Feb 20 Feb 22 Feb 25 |
| Exam 1 | 3/6 | Midterm 1 | |
| Homework 3 | 3/27 |
15.1: 1,2 15.2: 1,2,3 15.3: 1,2,3,6,7(a),10 15.4: 1 15.5: 3,4 |
Feb 27 Mar 1 Mar 4 Mar 6 Mar 8 Mar 11 Mar 13 Mar 15 |
| Homework 4 | 4/10 |
15.6: 1 15.7: 3,4,7,11 15.8: 1,2 Chap. 15 Misc. Problems: M.1, M.4 16.3: 1,2(b,c),3 16.4: 1 |
Mar 25 Mar 27 Mar 29 Apr 1 Apr 3 Apr 5 Apr 8 Apr 10 |
| Exam 2 | 4/17 | Midterm 2 | |
| Homework 5 | 5/1 |
16.6: 2 16.7: 3,4,6,10 16.8: 1,2(b,c,d) 16.9: 1 16.10: 3 16.11: 1 16.12: 1,5,8 Chap. 16 Misc. Problems: M.5 |
Apr 12 Apr 15 Apr 17 Apr 19 Apr 22 Apr 24 Apr 26 |
| Final Exam | 5/8 (during finals week) |
Final exam |
Apr 29 May 1 May 3 May 6 |