# Math 541, Modern Algebra - Fall 2011

# Nigel Boston

## Contact Information

303 Van Vleck
Telephone: 263-4753.

E-mail: *boston@math.wisc.edu*

Homepage

Office Hours: Tuesday 2:30 to 3:30 in 303 VV, Wednesday 2 to 3 in 3619 EH, Thursday 10 to 11 in 303 VV, 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: TR 11:00-12:15, B203 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 Thursdays and due the following Thursday. 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 (worth 25% each) and the final (worth 35%). Dates of
the midterms will be during class on October 11 and on November 10. There will be no make-up exams.
- HW1, due Sep 22: Chapter 1, Section 2 - 6, 13, 21; Section 3 - 1(a)(c), 3, 17; Section 4 - 2, 15, 21.
- HW2, due Sep 29: 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 Oct 6: Chapter 2, Section 3 - 1, 2, 3, 9, 14, 16; Section 4 - 2, 6, 19.
- HW4, due Oct 20: Chapter 2, Section 5 - 1(b)(c), 2, 7, 12, 14; Section 6 - 1
, 2, 7, 15.
- HW5, due Oct 27: Chapter 2, Section 6 - 12, 18; Section 7 - 3, 4, 5; Section 8 - 2; Chapter 3, Section 1 - 2, 3, 4.
- HW6, due Nov 3: Chapter 3, Section 2 - 3(a)(c)(e), 6, 11, 12; Section 3 - 2, 3; Chapter 4, Section 1 - 1, 9, 19.
- HW7, due Nov 17: Chapter 4, Section 1 - 4, 11, 22, 30; Section 2 - 1, 9; Section 3 - 1, 2, 4.
- HW8, due Dec 1: Chapter 4, Section 3 - 5, 19; Section 4 - 6, 7, 9; Section 5 - 1, 2, 6, 13.
- HW9, due Dec 8: Chapter 4, Section 5 - 3(a)(d), 10(e)(f), 14(a); Section 6 - 3, 5, 12; Section 7 - 3,4.
- HW 10, due Dec 15

## Final Exam

2:45pm, Saturday, December 17, B239 Van Vleck.