Introduction to Abstract Algebra

Instructor: Vera Serganova
Email address: serganov@math

webpage:/~serganov

Phone Number: 642-2150

Office hours: Tu 1:00-2:00, W 3:00-4:00 in 709 Evans

Text: T.W. Hungerford, Abstract Algebra, an Introduction

Homework: Each Thursday problems will be posted on this webpage. Homework will be due the following Thursday

Exams: There will be one midterm on Thursday, October 6 during usual class hours. Usually we will have one quiz every second week

Final Exam is on Wednesday, December 14, 8:00-11:00 .

Grading policy: Your grade will be computed according to the following rule: 10% for your homework, 30% for quizzes, 20% for the midterm and 40% for the final.

Course outline

Arithmetic in Z, Euclidean algorithm

Modular Arithmetics

Definition and examples of rings, homomorphism

The ring of polynomials F[x]

Ideals and quotient rings

Groups, definition and examples, homomorphism

Normal subgroups and quotients

The symmetric group

Action, orbits and counting formula

Sylow theorems

Field extensions

Finite fields

Ruler and compass constructions

Homework assignments

Homework 1 (due 9/1). Section 1.1 #2,9, Section 1.2 #1(g),13,20,32,36, Section 1.3 #12,13,22, Section 1.4 #11.

Homework 2 (due 9/8). Section 2.1 #12,14,30, Section 2.2 #8,11, Section 2.3 #1,7,13, , Section 13.1 #14,19.

Quiz #1 September 8, covers Chapters 1,2 and Section 13.1.

Homework 3 (due 9/15). Section 3.1 #6,9,20,24,25, Section 3.2 #2,5,21,22,30, Section 3.3 #17,23,33,40

Quiz #2 September 20, covers Chapter 3.

Homework 4 (due 9/22). Section 4.1 #3,5,12,16,17,18, Section 4.2 #10, Section 4.3 #14,21,22,23.

Homework 5 (due 9/29). Section 4.4 #8,18,27,28,29, Section 4.5 #1(c,e),3,5,6,12,13,Section 4.6 #1,3

Homework 6 (due 10/6). Section 5.1, #11,13, Section 5.2 #14,15, Section 5.3 #1(b,c),7,8.

Homework 7 (due 10/18) (Deadline postponed). Section 6.1 #4,10,15,34, Section 6.2, #20,22,24,32.

Homework 8 (due 10/20). Section 6.1 #39,40,43, Section 6.2 #5,13,18,28,29,31, Section 13.3 # 3,4.

Homework 9 (due 10/27). Section 7.1 #13,19,21,31, Section 7.2 # 18, 30, 32, 36, Section 7.3 #3,12,25,35

Quiz #3 10/20, covers Chapter 5, Sections 6.1, 6.2 and 13.3.

Homework 10 (due 11/3). Section 7.4 #14,18,21,25,27, Section 7.5 #12,18,22,24, Section 7.6 #7,16,17,18,21

Quiz #4 11/8, covers Sections 7.1--7.6

Homework 11 (due 11/10). Section 7.7 #13,21,22,23,24,26, Section 7.8 #8,10,11,17,21

Homework 12 (due 11/17). Section 7.9 #1,3,14,19, Section 7.10 #6,10, Section 8.1 #6,28, Section 8.2 #3,5,8,20

Quiz #5 11/17, covers Chapter 7.

Homework 13 (due 12/1). Section 8.2 #12,17, Section 8.3 #6,7,13,14, Section 8.4 #5,8,9,10, Section 8.5 #7,15.

Quiz #6 12/1, covers Chapter 8.

Review session 12/6, 11-12:30 usual room.

Solutions for selected problems