| Prerequisites: |
Some previous exposure to linear algebra (vectors, matrices,
determinants) would help. One should either have the ability to write and read mathematical proofs, or have the desire and drive to learn how. |
| Instructor: | Victor Reiner (You can call me "Vic"). |
| Office: Vincent Hall 256 Telephone (with voice mail): 625-6682 E-mail: reiner@math.umn.edu |
|
| Classes: | Mon-Wed-Fri 10:10-11:00am, Vincent Hall 311. |
| Office hours: | Mon and Fri at 11:15am, Tues at 3:35pm; also by appointment. |
| Course content: |
This is the first semester of a course in the
basic algebra of groups, ring, fields, and vector spaces. Roughly speaking the Fall and Spring semesters should divide the topics as follows: Fall-- Vector spaces, linear algebra, group theory and symmetry Spring-- Rings, modules, and field theory To give a feeling for the Fall subject matter, group theory can be thought of as the study of symmetry. Some nice examples of finite groups are the symmetries of regular polyhedra (like the Platonic solids). You can get a feel for these symmetries by playing with some manipulable regular polyhedra on the web site of my colleague Joel Roberts. |
| Required text: | Algebra, by Michael Artin, Prentice-Hall, 1991.
The (very) tentative plan for proceeding through Artin's book goes like this: Fall-- some (but not all) of Chapters 1-7 Spring-- some (but not all) of Chapters 10,11,13,14 |
| 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: |
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 | 9/19 |
1.1: 6,7,10,16,19,20 1.2: 2,12,13,14,15,16 1.3: 1,8,11 1.4: 1,2,4 1.5: 1,3 Chap 1 Misc Probs: 3 |
| Homework 2 | 10/3 |
2.1: 4,10 2.2: 1,3,4,11(hint: do 2.3.2 first),17,19,21 2.3: 2,3,8,10,12,14 2.4: 6,7,12,16,22 |
| Exam 1 | 10/10 | Midterm exam 1 in PostScript, PDF. |
| Homework 3 | 10/24 |
5.5: 5 5.7: 2 5.8: 2 2.5: 10 2.6: 3,5,7(a),10 2.7: 1,5 2.8: 4,9,10 2.9: 4,5 2.10: 1,5,10 |
| Homework 4 | 11/7 |
5.9: 4 6.1: 3,6,8(d),14 6.2: 6 6.3: 9,13 6.4: 1,2,5(a,b),13 Chap 6 Misc Probs: 7 |
| Exam 2 | 11/14 | Midterm exam 2 in PostScript, PDF. |
| Homework 5 | 12/5 |
3.1: 1 3.2: 11,16 3.3: 5,7,15 3.4: 5,11 Chap 3 Misc Probs: 5,6 4.1: 4 4.2: 1,2,8 |
| Final Exam | 12/12 | Final exam in PostScript, PDF. |