# Math 103A Fall 2006

### Instructors

#### Professor:

Name Office E-mail Phone Office Hours Lecture Time Lecture Place
Prof. Daniel Rogalski AP&M 5131 drogalsk@math.ucsd.edu 534-4421 W 11am-12pm and by appointment MWF 10-10:50am CNTR 205

#### Teaching Assistant:

Name Office E-mail Office Hours Section Times Section Place
Amanda Beeson AP&M 6452 ambeeson@math.ucsd.edu T 11-12:30, Th 12:30-1:30 T 10-10:50am CNTR 207

### General Course Information

Textbook: Contemporary Abstract Algebra, 6th Edition, by Joseph Gallian.

The main topic of this course is group theory. We plan to cover most of chapters 0-11 of Gallian, plus possibly some other special topics if we have time.

There will be 2 in-class midterms on Wed. 10/18 and Wed. 11/8, and a final exam on Monday 12/4 from 8-11am. No makeup exams will be given.

Homework assignments will be due weekly on Fridays.

The final grade will be determined as follows: Homework 25%, Midterms 25%, Final Exam 50%.

More detailed descriptions, including a tentative syllabus, may be found in the first day course handout here: Course syllabus
Check below for more up-to-date information about the schedule of homework and lectures.

### Schedule of Lectures:

9/22/06 Introduction. Chap 0: Arithmetic. Review of Induction.
9/25/06 Chap 0: Review of Equivalence relations. Integers modulo n.
9/27/06 Chap 2: Definition of a group. First examples.
9/29/06 Chap 2: More examples of groups. Basic properties of groups.
10/2/06 Chap 1: Dihedral groups.
10/4/06 Chap 3: Subgroups
10/6/06 Chap 3: Centers, Centralizers, cyclic groups
10/9/06 Chap 4: Basics on cyclic groups (read only the first half of chapter 4 for now; do not read "classification of subgroups of cyclic groups")
10/11/06 Chap 7: Cosets and their basic properties
10/13/06 Chap 7: Lagrange`s Theorem and corollaries (read only the first half of chapter 7, up through the Corollaries of Lagrange`s Theorem.)
10/16/06 Chap 9: Normal Subgroups.
10/18/06 EXAM I
10/20/06 Chap 9: Factor Groups (read only up to p. 184)
10/23/06 Chap 10: Homomorphisms. Basic Definitions and properties.
10/25/06 Chap 10: Homomorphisms II: Properties of kernels. Isomorphisms. 1st isomorphisms theorem.
10/27/06 Chap 10: Proof of 1st isomorphism theorem. Structure of cyclic groups.
10/29/06 Chap 4: More on cyclic groups.
11/1/06 Chap 5: Permutation Groups
11/3/06 Chap 5: Even and Odd permutations; the alternating group.
11/6/06 Applications of Permutations.
11/8/06 EXAM II
11/10/06 NO CLASS
11/13/06 Chap 8: Direct products of groups. Orders of elements in a direct product.
11/15/06 Chap 6: Isomorphisms (brief review). Chap 8: Decomposing a cyclic group as a direct product.
11/17/06 Chap 8: Decomposing U(n) as a direct product.
11/20/06 Chap 8: Application: A brief introduction to RSA cryptography.
11/27/06 Chap 11: Fundamental theorem of Finite Abelian Groups.
11/29/06 Chap 24: Conjugacy classes and the class equation. Groups of order p^2.
12/1/06 Introduction to Math 103b. Review.

### Homework Assignments:

Homework #1, due 9/29/06

Homework #2, due 10/6/06

Homework #3, due 10/13/06

Homework #4 plus exam review sheet, due 10/20/06

Exam 1 with solutions.

Homework #5, due 10/27/06

Homework #6, due 11/3/06

Homework #7 plus exam 2 review sheet, due 11/17/06

Exam 2 with solutions.

Homework #8, due 12/1/06

Exam Review Sheet