Math 541, Modern Algebra - Spring 2015
Nigel Boston
Contact Information
303 Van Vleck
Telephone: 263-4753.
E-mail: boston@math.wisc.edu
Homepage
Office Hours: M 3-4:30 (303 VV) and W 1:30-3 (3619 EH), or by appointment.
Text
Abstract Algebra by Herstein (3rd edition).
Prerequisites
Math 320 or 340, or consent of instructor.
Alternatives
Math 441 is a less theoretical version of Math 541.
Subsequent Courses
Math 542.
Background and Goals
This is the first semester of an introduction to basic abstract algebra. It is recomended for math majors and it is essential for students preparing for graduate studies in mathematics and in some related fields.
Sections
- Main Lecture: MWF 8:50-9:40, B231 Van Vleck.
Course Description
- How to do proofs; Sets and functions: unions, intersections, products, injections, surjections, bijections, inverse functions, equivalence relations
- Groups: subgroups, normal subgroups, homomorphisms and quotients
- Rings: subrings, ideals, homomorphisms, and quotients
- Commutative rings: fields, integral domains, prime ideals, maximal ideals, PIDs and Euclidean domains
Homework Assignments and Grading Policy
Homework will be set most Wednesdays and due the following Wednesday. You are encouraged to discuss
the exercises with your classmates but the work you hand in should be your own. You will be
expected to read the sections of the notes to be covered in advance of class.
It is planned that there will be two midterms and the final. Dates of
the midterms will be during class on TBA. There will be no make-up exams.
The HW will be worth 10%, each midterm 20%, and the final 50%, of your grade.
- HW1, due Feb 4: Chapter 1, Section 2 - 6, 13, 21; Section 3 - 1(a)(c), 3, 17; Section 4 - 2, 15, 21.
- HW2, due Feb 11: Chapter 1, Section 5 - 1(c),(d), 4, 13(b), 14(b); Chapter 2, Section 1 - 1(d),(e),(f), 8, 17, 26.
- HW3, due Feb 18: Chapter 2, Section 3 - 1, 2, 3, 9, 14, 16; Section 4 - 2, 6, 19.
- HW4, due Feb 25: Chapter 2, Section 5 - 1(b)(c), 2, 7, 12, 14; Section 6 - 1 , 2, 7, 15.
- HW5, due Mar 11: Chapter 2, Section 6 - 12, 18; Section 7 - 3, 4, 5; Section 8 - 2; Chapter 3, Section 1 - 2, 3, 4.
- HW6, due Mar 18: Chapter 3, Section 2 - 3(a)(c)(e), 6, 11, 12; Section 3 - 2, 3; Chapter 4, Section 1 - 1, 9, 19.
- HW7, due Mar 25: Chapter 4, Section 1 - 4, 11, 22, 30; Section 2 - 1, 9; Section 3 - 1, 2, 4.
- HW8, due Apr 15: Chapter 4, Section 3 - 5, 19; Section 4 - 6, 7, 9; Section 5 - 1, 2, 6, 13.
- HW9, due Apr 29: Chapter 4, Section 5 - 3(a)(d), 10(e)(f), 14(a); Section 6 - 3, 5, 12; Section 7 - 3,4.
- HW10, due May 6: HW 10
Honors
If you are taking this course for an honors credit, you must hand in a report (at least 5 pages long) at or before the last class. This report will be on a topic related to the course subject matter but going beyond the course. It does not need to be original but must be presented in your own words. Come see me if you need suggestions for topics.
Midterms
Final Exam