Modern Algebra.
Fall 2005
Math 631 16824 LEC001

Dr. Willenbring

1  Course Description

Math 631 is the first semester of a year long algebra sequence. In the past, the year has focused on Group theory, including normal subgroups, quotients, permutation groups, Sylow's theorems, Abelian groups; field theory; linear algebra over general fields, Ring theory, including ideals, quotient rings, Euclidean rings, polynomial rings, unique factorization; modules, including vector spaces, linear transformations, canonical forms; bilinear forms. Math 631 is often taken by both graduate students and undergraduate students. See the Undergraduate or Graduate Bulletin where the above information has been taken from. Note that Math 631 is designed to follow Math 531, and the material in Math 632 is designed to precede the Math 731-732 sequence.
Often the course uses the book by Artin. This book was chosen as our textbook this year, in part, because of the emphasis on linear algebra and matrices, which is a cornerstone in any mathematician's education. For the first semester, we will aim at the first 5 or 6 chapters. The author suggests the following: Chapter 1, Chapter 2, Chapter 3: 1-4, Chapter 4, Chapter 5: 1-7, Chapter 6: 1,2.

2  Course Details

Class time
2:00pm-3:15pm Tuesday and Thursday in EMS E495A
Textbook
Algebra by: Michael Artin.
Published by Prentice Hall 1991
Upper Saddle River, New Jersey 07458
ISBN: 0-13-004763-5
Examinations
Exams will be in class. No make-up exams, except in severe situations such as illness. Students will be allowed to complete examinations or other requirements that are missed because of a religious observance.
Midterm
October 20 (Thursday) 2:00pm-3:15pm in EMS E495A
Counts for 35% of your course grade.
Final
December 22 (Thursday) 10:00am-12:00 Noon location EMS E495A
Counts for 35% of your course grade.
Homework
Homework will be assigned throughout the course and will constitute 30% of your course grade.
First Homework
We will cover the first chapter, Matrix Operations, as quickly as possible. Take a look at exercises: 1.5, 1.6, 1.7, 1.11, 1.16, 1.20; 2.13, 2.14, 2.15, 2.16, 2.18; 3.9, 3.10, 3.11, 3.12; 4.2, 4.4, 4.5, 4.6; 5.3. Also, turn in problems 2 and 3 (to be graded) from the Miscellaneous Problems section on page 36. These two problems will be due on September 20. (Note: Some of the "more difficult" problems are marked with an asterisk. If these problems are not assigned, you may turn them in for extra credit.)
Second Homework
For Chapter 2, take a look at exercises: 1.2; 2.3, 2.20; 3.10; 4.6, 4.12; 5.2, 5.3; 6.8, 6.12; 7.8; 8.7; 9.8; 10.8, 10.10; Misc. Problems: 1,2,4,7,10. Turn in problems 9 and 12 from the Misc. Problems section (on page 77) for extra credit by Oct. 11. Also, turn in Misc. problems 3 and 4 by Oct. 13.
Third Homework
For Chapter 3, take a look at exercises: 1.1; 2.14, 2.15; 3.6, 3.10, 3.11; 4.9, 4.10, 4.11, 4.12; 5.5; 6.2. Turn in Misc. problems: 3 and 7. These problems are due on Oct. 25.
Fourth Homework
For Chapter 4, take a look at exercises: 1.4, 1.8; 2.1, 2.4, 2.8; 3.4, 3.8, 3.9; 4.3, 4.4, 4.11, 4.12; 5.4, 5.5; 6.1, 6.7, 6.10; 7.6, 7.8; 8.5, 8.6, 8.19; Misc: 2,3,11,15,18. Turn in Misc. problems: 2 and 3. These two are due on Nov 15.
Fifth Homework
For Chapter 5, take a look at exercises: 1.4; 2.15; 3.2, 3.3; 4.3; 5.8, 5.9, 5.10; 6.1, 6.7; 7.4; 8.2, 8.4, 8.7; 9.5, 9.6, 9.7; Misc.: 3,7; Turn in Misc. Problem 9.
Sixth Homework
For Chapter 6, take a look at exercises: 1.9; 2.7, 2.9; 3.9, 3.10; 4.6, 4.9.
Contact Information
 
Web Page:
http://www.uwm.edu/~jw/
email:
j w a t u w m d o t e d u
Phone:
(414) 229-4936
Office:
EMS E494
Office Hours:

4:00pm-5:00pm Tuesday;
12:30pm-1:30pm, 4:00pm-5:00pm Thursday
Prerequisites
Prereq: jr st, Math 531(P) or consent of instructor, or graduate standing. In general, students should be advised that in Math 631 we assume that you know what a mathematical proof is and how to read and write one.
Disabilities
If you have any disability, please feel free to contact me for any help or accommodation which you may need.
Honesty
The university has a responsibility to promote academic honesty and integrity and to develop procedures to deal effectively with instances of academic dishonesty. Students are responsible for the honest completion and representation of their work, for the appropriate citation of sources, and for respect of others' academic endeavors. Further information can be found at:
http://www.uwm.edu/Dept/Acad_Aff/policy/academicmisconduct.html


File translated from TEX by TTH, version 3.61.
On 08 Dec 2005, 13:50.