Modern Algebra.
Math 531 Section 001-31051 (Spring 2005)

Dr. Willenbring

1  Course Description

Modern algebra is a core course within the undergraduate math major curriculum. This is indeed true at every university and so it is important to have a proper first exposure. This fact is especially true of students who will go on to graduate school in mathematics, or become high school teachers.
Many student are surprised to see the word algebra being used to describe the content of this course. Indeed, students that I have talked to have indicated that the word symmetry probably describes the course better than algebra. However, among mathematicians the word algebra refers to a body of ideas containing the material in Math 531. More specifically, the course will closely follow the description of Math 531 in the UWM Undergraduate Bulletin located at:

During most of the semester, we will discuss group theory. This subject is, in part, a mathematical description of symmetry at a fundamental level. I am hopeful that we spend at least one month on other algebraic structures such as rings (and maybe fields and vector spaces). Once students have mastered these algebraic structures they will be ready to see how the material may be used to understand algebraic equations.
The content of the course will be related to Math 431, which some of you may have taken. The difference between Math 431 and Math 531 is that the former emphasizes applications (especially to computer science), while the latter emphasizes theory and proofs. With this said, I would like to add that Math 531 will also discuss applications. (For starters, take a look at chapter zero of our textbook!)

2  Course Details

Class time
12:30pm-1:45pm Tuesday and Thursday in EMS E160
Contemporary Abstract Algebra by: Joseph A. Gallian.
Published by Houghton Mifflin Company; 5th edition. 2001.
I highly recommend looking at the author's web page for supplementary material related to the book:
Exams will have both an in class and a take home component. 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.

March 17 (Thursday) 12:30pm-1:45pm in EMS E160
Counts for 40% of your course grade

May 19 (Thursday) 10:00am-12:00pm location PHYSICS 135
Counts for 40% of your course grade.

Homework will be assigned throughout the course and will constitute 20% of your course grade.

First Homework
Much of Chapter 0 reviews the material that you probably learned in Math 341. Read this chapter. Note that we will not formally cover this material. There are some interesting exercises concerning the mathematics behind assigning driver's license number, check digits for the identification of money orders, ISBN numbers etc.
For your first (graded) homework assignment write up problems: 14, 25, 46, and 50 from the exercises at the end of Chapter 0. These four problems will be due on February 8, 2005.

Contact Information
Web Page:
j w a t u w m d o t e d u
(414) 229-4936
EMS E494
Office Hours:
1:45pm- 3:15pm Tuesday and 4:00pm- 5:30pm Thursday and by appointment.
Math 234(P) & 341(241)(P). Of the listed prerequisites, Math 341 is the most important. In general, students should be advised that in Math 531 we assume that you know what a mathematical proof is and how to read and write one. If you have not taken Math 341 please talk to me!
If you have any disability, please feel free to contact me for any help or accommodation which you may need.
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:

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On 26 Jan 2005, 15:58.