  University of Wisconsin-Madison
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Math 541 |
Fall 2007
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About the course: Math 541 is the first course in abstract algebra. The core topics are groups, rings, and fields. Math 541 is particularly useful for future K-12 math teachers since one of the main points of this course is to explain where addition, subtraction, multiplication and division come from, why they do what they do, and how they can be sensibly modified. If you are going to be teaching math, then you will need to explain these things to your students. Along with Math 521 and Math 551 this course is a necessity for students considering going on to graduate school in mathematics.
In order to do well in this course it will help to have (1) a good study ethic and (2) some experience with matrix algebra, such as that obtained in Math 340 or Math 320 (or any one of several other math, engineering or economics or statistics courses).
Special goal: One of the goals of this course is to teach everybody how to construct and write proofs.
Lectures:
TTh 11:00-12:15 in B235 Van Vleck
Text: The textbook for the course is
I also recommend the following books:
I strongly recommend you get one or all of these books (read them, study them, do problems from them, look things up in them, absorb them, osmose them, sleep with them under your pillow, and carry them with you everywhere you go).
Course Notes:
How to do proofs: postscript file
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pdf file
Sets and functions: postscript file
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pdf file
Groups and Group actions: postscript file
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pdf file
Groups and Group actions, the proofs: postscript file
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pdf file
A list of small groups: postscript file
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pdf file
Cyclic groups: postscript file
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pdf file
Dihedral groups: postscript file
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pdf file
Symmetric groups: postscript file
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pdf file
Alternating groups: postscript file
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pdf file
Group examples: postscript file
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pdf file
Rings and Modules: postscript file
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pdf file
Rings and Modules, the proofs: postscript file
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pdf file
Fields and Vector spaces: postscript file
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pdf file
Fields and Vector spaces, the proofs: postscript file
or
pdf file
Vocabulary quizzes: One of the challenges when one is first starting to learn proof oriented mathematics, is to remember the rules of the game (the definitions). This EXTREMELY IMPORTANT part of doing proofs is easy since it is just regurgitation. We will negotiate some form of vocabulary assessment on the first day of class.
Learning examples: Besides vocabulary, the other BIG part of learning proof oriented mathematics is the examples. I have arranged for a Wiki to help us learn definitions and discuss examples. This Wiki is housed at https://chatter.lss.wisc.edu/moodle/ They've turned on the TeX editing capability. Try it out.
Vocabulary lists:
Vocabulary list 1Office hours: TTh 12:15-1:15pm in B235 Van Vleck and MWF 9:45-10:45 in Van Vleck 711. If you are having any problems, questions or concerns please come talk about it. If you do not keep me informed I cannot help.
Grading: The term grade will be based on homework and the exams as follows: Homework: 15% Each midterm: 20% Final Exam: 25%. Final grades are computed by totalling the points from the homework, the midterms and the final. Grade letters will be assigned with the following curve as a guideline: 20% A's, 30% B's, 30% C's, 20% D's and F's.
Homework: Homework will be weekly, due by 9am on Wednesdays. Turn in your homework to my mailbox, on floor 2 of Van Vleck Hall. All claims that you make in your homework MUST BE PROVED in order to receive credit.
Homework assignments:
Homework assignment 1: DUE September 12, 2007 pdf file solutions updated 3 October 2007
Homework assignment 2: DUE September 19, 2007 pdf file solutions updated 3 October 2007 Homework assignment 3: DUE September 26, 2007 pdf file solutions Homework assignment 4: DUE October 3, 2007 pdf file 
Midterm Exam I: Thursday October 4, 2007 Homework assignment 5: DUE October 10, 2007 pdf file Homework assignment 6: DUE October 17, 2007 pdf file Homework assignment 7: DUE October 24, 2007 pdf file Homework assignment 8: DUE November 1, 2007 pdf file Midterm Exam II : Thursday November 1, 2007 Homework assignment 9: DUE November 8, 2007 pdf file Homework assignment 10: DUE November 15, 2007 pdf file Homework assignment 11: DUE (Wednesday) November 21, 2007 pdf file Homework assignment 12: DUE November 29, 2007 pdf file Midterm Exam III : Thursday November 29, 2007 Homework assignment 13: DUE Never Homework assignment 14: DUE December 13, 2007 pdf file Final Exam III: 10:05am Thursday December 20, 2007 in Ingraham 120 Exams: There will be three 65 minute in-class midterms: October 4, November 1 and November 29. There will be a 2 hour final exam at 10:05am Thursday December 20 in Ingraham 120. The final exam will be cumulative. Please note the following change: The exams will not be a random selection of homework problems from the homework assignments. The exams will be made according to the schematic discussed in class.
Syllabus: The following is my general plan for the topics to be covered and the ordering which I have in my mind at the moment.