This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Modern Algebra I -- Fall 2011

### From Mathematics Is A Science

**MTH 450 - 3 - Modern Algebra.** Structure of the abstract mathematical systems: fields, rings, groups, with illustrations and applications from number theory. (PR: MTH 230 ; REC: MTH 300)

- Time and Place: 5:00 - 6:15 pm TR at 513 Smith Hall.
- Instructor: Peter Saveliev (call me Peter)
- Office: 742D Smith Hall
- Office Hours: MW 5:00 - 6:15, T 3:30 - 4:30, or by appointment
- Office Phone: x4639
- E-mail: saveliev@marshall.edu
- Class Web-Page: math01.com
- Prerequisites: the ability to understand and write proofs.
- Text: Contemporary Abstract Algebra by Gallian
- Goals: good familiarity with groups, ability to work in the definition-theorem-proof format, some "mathematical maturity".
- Evaluation: 2 tests, final exam, weekly homework, quizzes.
- Grade Breakdown:
- homework + quizzes: 40%
- 2 exams: 15% each
- final exam: 30%

- Letter Grades: A: 90-100, B: 80-89, C: 70-79, D: 60-69, F: <60

See also Course policy.

## Contents

## 1 Chapter 0

Review Linear algebra: course

- Lectures: Chapter 0
- Practice exercises: 7,9-11,13,14,18-21,46-49
- Problems to be submitted: 10,20

## 2 Chapter 1

- Lectures: Chapter 1
- Practice exercises: 1-6,14-17,22
- Problems to be submitted: 16

## 3 Chapter 2

- Lectures: Chapter 2
- Practice exercises: 1-5,9,11,14,15,17,18,20
- Problems to be submitted: 14,18

- Practice exercises: 22-26,29,30,33-36
- Problems to be submitted: For #16 Sec. 1, quantitatively describe a symmetry of the strip.

## 4 Chapter 3

- Lectures: Chapter 3
- Practice exercises: 1,2,4,6,7,10,14,16,17,19,21-23,29,30,31,33,35,45,46-49,52,53 10
- Problems to be submitted:

## 5 Chapter 4

- Lectures: Chapter 4
- Practice exercises: 1,4-7,11-14,17-19,22,23,30-36 30
- Problems to be submitted: 30 and 33

## 6 Test 1

- Chapters 0-4
- Sample: Group theory: test 1

## 7 Chapter 5

- Lectures: Chapter 5
- Practice exercises: 1-18 10
- Problems to be submitted: in a finite group, |ab|=|ba|.

- Practice exercises: 24-26,34,35,38-40,46,54,55 46
- Problems to be submitted: 40 and 46

## 8 Chapter 6

- Lectures: Chapter 6
- Practice exercises: 1-7
- Problems to be submitted: 4

- Practice exercises: 10,22-25,27,28,30,37 10
- Problems to be submitted:

## 9 Chapter 7

- Lectures: Chapter 7
- Practice exercises: 1-3,7,8,12-15,18-22 22
- Problems to be submitted:

- Practice exercises: 24-31,33,38 28
- Problems to be submitted:

## 10 Chapter 8

- Lectures: Chapter 8
- Practice exercises: 1-17,23-26,31,32 32
- Problems to be submitted:

## 11 Chapter 9

- Lectures: Chapter 9
- Practice exercises: 1-13,18,20,21 18
- Problems to be submitted:

- Practice exercises: 26,27,30-34,44-48,57,59 30
- Problems to be submitted:

## 12 Chapter 10

- Lectures: Chapter 10
- Practice exercises: 5-19,24-27 24
- Problems to be submitted:

- Practice exercises: 34,35,37-39,44-46,52,53 44
- Problems to be submitted:

## 13 Test 2

- Chapters 5-8
- Sample: Group theory: test 2

## 14 Chapter 11

- Lectures: Chapter 11
- Practice exercises: 1-17,21,24,25,28-31
- Problems to be submitted:

## 15 Chapter 12

- Lectures: Chapter 12
- Practice exercises: 1-18,43-50
- Problems to be submitted:

## 16 Final exam

Thursday, Dec. 8, 4:30-6:30 same room.

Sample: Group theory: final exam

The transcribed lectures will appear here: Group theory: course.