Math 330/MthT 435

Abstract Algebra

Fall 2002

MWF 1:00 LC E2

Instructor David Marker

Office: 411 SEO
Office Phone: (312) 996-3069
Office Hours: M 9-11, W 12-1 and by appointment
Fax: (312) 996-1491
e-mail: marker@math.uic.edu
web page: http://www.math.uic.edu/~marker
course web page: http://www.math.uic.edu/~marker/math330

Text

J. Gallian, Contemporary Abstract Algebra, Fifth Edition, Houghton Mifflin Company, Boston 2002.

Prerequisites

Grade of C or better in Math 215 Introduction to Advanced Mathematics and a grade of C or better in Math 320 Linear Algebra I. I will assumethat you are comfortable and competent writing proofs. In particular I expect you to already be familiar with the material in Chapter 0 of the text.

Description

This is a first course in Abstract Algebra. We will study the basic properties of groups, rings and fields. We will hopefully cover most of Chapters 2--23 of the text.

Here is a list of exactly the material that will be covered.

Grading

There will be one midterm and a final exam. The midterm willcount for 30% of the final grade. The final will count for 50% of thefinal grade. Homework will count for 20% of the final grade.
The midterm exam is scheduled for Friday October 18. The midterm will cover Chapters 1-10 of the text.
The final exam will be on Friday December 13 1:00-3:00.

Software

The author's website http://www.d.umn.edu/~jgallian/msproject/project_xukai.html
has useful software for doing instrutive computations.

Handouts

A summary of the material you are responsible for in the text.
The dihedral group D3 (pdf file)
An example nonAbelian group where the squares are not a subgroup (pdf file)
A sketch of the classification of groups of order six (pdf file)
Study Guide for 10/18 midterm
Sample midterm (pdf file) and partial solutions (pdf file)
midterm exam with solutions
Summary of important material on factorization in polynomial rings. (pdf file)
Sample final and study guide (pdf file)

Practice Problems

I will assign practice problems for all sections. While practice problems will not be collected or graded they will usually have answers or hints in the back of thebook for you to check. Doing problems is the way to learn mathematics.So while the practice problems will not effect your grade, you should not consider them "optional".

Chapter 0: # 3, 7, 13, 21, 27, 47
Chapter 1: # 1, 3, 5, 7, 9, 21
Chapter 2: # 1, 3, 5, 9-19(odd),29,33
Chapter 3: # 1, 9, 11 , 13, 15, 17, 21, 29, 33, 49
Chapter 4: # 1-9 (odd), 15, 17, 19 ,21, 27
Suplementary Problems (pg 89-90): # 1, 5, 7, 9, 11
Chapter 5: # 1, 3, 5, 7, 9, 19, 23, 25, 33
Chapter 6: # 1, 3, 5, 7, 13, 15, 17, 23, 25, 27
Chapter 7: # 1, 7, 9, 11, 13, 15, 19, 21, 23, 25
Chapter 8: #1-17 odd
Chapter 9: #1-17 odd
Chapter 10: # 1-23 odd
Chapter 11: # 1-21 odd
Chapter 12: # 1,3 9, 11, 15-25 odd
Chapter 13: # 3-21 odd
Chapter 14: # 1-23 odd

Homework

Homework assignments will be collected and graded.Almost all homework assignments will be writing proofs.The homework will count for 20% of your final grade.I will drop one homework grade. Late homework will be accepted up untilthe begining of the next class period, but will be penalized.

You may discuss homework problems with other students, but you must writeup your solution independently. All proofs should be written neatly with complete gramatical sentences.

Problem Set 1: (Due Friday August 30)
- Chapter 0: # 27, 48
- solutions (pdf file)
Problem Set 2: (Due Friday September 6)
- Chapter 1: # 10
- Chapter 2: # 6, 18, 34
- solutions (pdf file)
Problem Set 3: (Due Friday September 13)
- Chapter 3: # 14, 30, 42
- Supplementary Problems (pg 89): # 2
- solutions (pdf file)
Problem Set 4: (Due Friday September 20)
- Chapter 4: # 14, 30, 48
- Chapter 5: # 6, 18
- solutions (pdf file)
Probelm Set 5: (Due Friday September 27)
- Chapter 5: # 36, 42
- Chapter 6: # 22, 26, 30
- solutions (pdf file)
Problem Set 6: (Due Friday October 4)
- Chapter 7: # 8, 14, 26, 30, 38 (bonus problem 28)
- solutions (pdf file)
Problem Set 7: (Due Friday October 11)
- Chapter 8: # 22, 26
- Chapter 9: # 10, 22, 47
- solutions (pdf file)
Problem Set 8: (Due Friday October 25)
- Chapter 10: # 16, 20, 22
- Chapter 11: # 10, 12
- solutions (pdf file)
Problem Set 9: (Due Friday November 1 )
- Chapter 12: # 22, 40
- Chapter 13: # 22, 34, 38
- solutions (pdf file)
Problem Set 10: (Due Friday November 8)
- Chapter 14: # 10, 24, 38, 45
- solutions (pdf file)
Problem Set 11 (Due Friday November 15) (gif file)
- solutions (pdf file)
Problem Set 12: (Due Friday November 22)
- Chapter 16: 12, 20, 30,
- Chapter 17: 14, 22
- solutions (pdf file)
Problem Set 13: (Due Wednesday December 3)
- Chapter 18: 4, 30
- Chapter 20: 4, 8, 10
- solutions (pdf file)

Last revised: 12/9/02