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 09:05-09:55am, Vincent Hall 313. |
Office hours: | Mon 3:35pm - 5pm Wed 11:15am-12:05pm |
Course content: | This is the first semester of a theoretical 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: Vector spaces, linear algebra, and group theory in the Fall; rings, modules, and field theory in the Spring. |
Required text: | Algebra, by Michael Artin, Prentice-Hall, 1991. |
With regard to the book, the (very) tentative plan goes like this. We hope to do most of Chapters 1-6 and some of Chapter 7 in the Fall. Then we'll skip over a lot of Chapter 7, and skip all of Chapters 8,9. In the Spring. we should do most of Chapters 10-13 and some of Chapter 14. | |
Other useful texts: |
Topics in algebra, by I. N. Herstein, Xerox College Publishing, 1975. Contemporary abstract algebra, by Joseph Gallian,Houghton Mifflin, 1998. |
Homework: | There will be homework assignments due every two weeks in class on Fridays during the semester, starting with Friday September 17 (see table below). There should be a total of 6-7 assignments, which will count for 40% of the course grade. The assignments will mainly be exercises from the book. Late homework will not be accepted. 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 with whom they have collaborated. |
Exams: | There will be two take-home midquarter exams to be handed out on dates to be announced later, each contributing 15% to the grade. There will be a take-home final exam worth 30% of the grade given during exam period. In contrast to the homework, there is to be no collaboration allowed with other humans allowed on any of the take-home midquarter or final exams. |
Assignment | Due date | Problems |
---|---|---|
1 (shortened on 9/13/99) | 9/17 |
1.1 # 6,7,10,13,16,19 1.2 # 2,7,12,14,15 1.3 # 2,4,8,11,12 |
2 | 10/1 |
1.4 # 1,2,4,5 1.5 # 1,3 2.1 # 3,5,7,8,9,10 |
3 | 10/22 |
2.3 # 4,7,10,14 2.4 # 6,7,11,12,16,19,22 2.6 # 3,5,7,8,10,12 2.9 # 2,4,5,6 |
4 | 11/5 |
2.7 # 1,7 2.8 # 4,7,8 2.10 # 1,5,6,8 Chap. 2 Misc. Probs # 4 3.1 # 1 3.2 # 1,8,10,11,12,15 |
5 | 11/19 |
3.3 # 2,5,7,12 3.4 # 1,10 3.6 # 1,2 Chap. 3 Misc. Probs # 4,6,8 |
6 | 12/10 |
4.5 # 1,4(b),5,8 4.6 # 1,3,7 5.2 # 3,4,13,15 5.3 # 1,2,4 |
Exam | Due date | Problems |
---|---|---|
Midterm 1 | 10/8 |
Chap.1 Misc. Problems # 3,7 (and #8 for extra credit) 2.2 # 2,9,11,12,17 Some problems not from the book: 1. Say an n-by-n matrix A is orthogonal if A^{T} A = I. (a) Prove that an orthogonal matrix A has det(A)=+1 or -1. (b) Prove that the set of orthogonal n-by-n matrices forms a group under matrix multiplication. 2. Say an n-by-n matrix A is skew-symmetric if A^{T} =-A. Prove that when n is odd, skew-symmetric n-by-n matrices are never invertible. |
Midterm 2 | 11/29 |
4.1 # 2,8 4.2 # 8 4.3 # 5,6,9,10 4.4 # 2,9 (Problem 5 was removed) |
Final Exam | (Thursday) 12/16 |
5.4 #9 5.5 #1,5,8,10 Chapter 2 Misc. Problems #1 Chapter 3 Misc. Problems #7 Chapter 4 Misc. Problems #1,6,18 |