Modern Algebra.
Spring 2006
Math 632

Dr. Willenbring

1  Course Description

Math 632 is the second 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 632 is designed to follow Math 631 (which in turn follows 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 second semester, we will first finish some odds and ends that we left out in Math 631 (Fall 2005). We will then move onto the core material in Chapters 10, 11 and 12. An application of these three chapters to canonical forms of matrices will follow from the structure theory of finitely generated modules over a principal ideal domain. If time permits, we will either backtrack to Chapters 7 (Bilinear Forms) and 8 (Linear Groups), or continue onto Chapters 13 (Fields) and 14 (Galois theory). The choice of these two options will depend on a class vote.

2  Course Details

Class time
2:00pm-3:15pm Tuesday and Thursday in EMS W109
Textbook
Algebra by: Michael Artin.
Published by Prentice Hall 1991
Upper Saddle River, New Jersey 07458
ISBN: 0-13-004763-5
Examinations
Your grade in Math 632 will be determined by two exams. The first (March 14) will be in class and will constitute 50% of your grade. The second exam will serve as a cumulative take-home final. A portion of the problems will be taken directly from problems assigned 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
March 14 (Tuesday) 2:00pm-3:15pm in EMS W109 (In Class Exam)
Counts for 50% of your course grade.
Final
Due Thursday May 18 12:30pm (Take Home Exam)
Counts for 50% of your course grade.
http://www.uwm.edu/schedule/examsSpring2006.pdf
Homework
Homework will be assigned throughout the course, but will not be graded.
Homework 0
Classify all groups of order less than 16.
Homework 1
10.1: 12; 10.2: 6; 10.3: 24, 32.
Homework 2
10.4: 7, 8; 10.5: 4, 13; 10.6: 2, 5.
Homework 3
10.6: 9; 10.7: 7, 11, 12; 10.8: 4.
Homework 4
11.1: 5,11; 11.2: 5,12; 11.3: 1,5,8. 11.4: 8, 13.
Homework 5
12.1: 1, 6, 7, 9, 11, 12;
Homework 6
12.2: 1,3,6; 12.3: 4; 12.4: 7,10; 12.5: 2,3,4;
Homework 7
12.6: 2, 4; 12.7: 1,5,6,12;
Homework 8
12.7: 16, 17, 18, 19, 21, 24; Misc: 4,7,8,9,10.
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:
3:15pm-3:45pm Tuesday and Thursday
12:00pm-2:00pm Wednesday
Important Dates
January 24
First class
February 3
Last day to add or change from a graded basis to audit or credit/no credit status.
February 17
Last day to drop or withdraw without a "W" on record
March 14
Midterm Exam
March 17
Last day to drop
March 19-26
Spring break
May 11
Last day of class
Prerequisites
Math 631 or consent of instructor. In general, students should be advised that in Math 632 we assume that you know what a mathematical proof is and how to read and write one.
Attendance
Attendance is required, and will be occasionally monitored. Absences due to illness require a medical excuse on Physician's letterhead, signed by the physician.
Disabilities
If you have any disability, please feel free to contact me for any help or accommodation which you may need.
Statement of Sexual Harassment
Sexual harassment is reprehensible and will not be tolerated by the University. It subverts the mission of the University and threatens the careers, educational experience, and well being of students, faculty, and staff. The University will not tolerate behavior between or among members of the University community which creates and unacceptable working environment. The draft policy on discriminatory conduct, including sexual harassment, can be found at
http://www.uwm.edu/Dept/uc/briefings/S-47-Mar05rev.pdf
Statement of Academic Misconduct
The university has a responsibility to promote academic honesty and integrity and to develop procedures to deal effectively with instances of academic dishonestly. 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.
Posted room changes
or class cancelations will be on Official Department Letterhead
Course Evaluation Policies
are posted here:
http://www.uwm.edu/Dept/SecU/acad%2Badmin_policies/S52.5.htm




File translated from TEX by TTH, version 3.61.
On 12 Apr 2006, 13:36.