Math 103A Fall 2005

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 3-5pm MWF 2-2:50pm CNTR 222

Teaching Assistant:

Name Office E-mail Office Hours Section Times Section Place
Cayley Pendergrass AP&M 5018 cpenderg@math.ucsd.edu F 10am-12pm W 5-5:50pm or 6-6:50pm WLH 2115

Announcements:

11/7/05: Office hours this week are changed from their usual times. Cayley Pendergrass will have her office hours Monday 11/7 from 12-2pm. D. Rogalski will have his office hours Monday 11/7 from 4-6pm.

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 Fri. 10/14 and Wed. 11/9, and a final exam on Fri. 12/9 from 3-6pm. No makeup exams will be given.

Homework assignments will be due weekly on Mondays.

The final grade will be determined as follows: Homework 20%, Midterms 30%, 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:

9/23/05 Chap 0: Division Algorithm, GCD is a linear combination.
9/26/05 Chap 0: Euclidean Algorithm. Proofs by Induction. Modular Arithmetic.
9/28/05 Chap 0: Equivalence Relations. Functions. Binary operations.
9/30/05 Chap 2: Definition of a group. Examples.
10/3/05 Chap 1: Groups of functions. Symmetry Groups. Dihedral groups.
10/5/05 Chap 2: Basic properties of groups. Chap 3: Definitions of order of elements. Definitions of subgroups.
10/7/05 Chap 3: Examples of Subgroups. Centers and Centralizers. Matrices over F_p.
10/10/05 Chap 4: Proof that center and centralizers are subgroups. Basic properties of cyclic groups.
10/12/05 Chap 4: Fundamental theorem on subgroups of cyclic groups. Euler Phi function.
10/14/05 Exam 1.
10/17/05 Chap 5: Introduction to permutations and the symmetric group. Cycles and cycle notation. Order of a permutation.
10/19/05 Chap 5: Theorem on the order of a permutation (finish). Card shuffles. Even and odd permutations.
10/21/05 Chap 5: The alternating group. Dihedral groups as permutation groups. Chap 6: isomorphisms of groups.
10/24/05 Chap 6: Isomorphisms of groups. Examples. Properties of isomorphisms. Cayley`s Theorem.
10/26/05 Chap 7: Cosets. Lagrange`s Theorem.
10/28/05 Chap 7: Consequences of Lagrange`s Theorem. Fermat`s Little Theorem. Primality testing. Groups of order 2p.
10/31/05 Chap 8: Direct Products. Orders of elements in a direct product.
11/2/05 Chap 8: When direct products are cyclic. Decomposing Z_n and U(n) into direct products.
11/4/05 Chap 8: Applications of direct products: RSA cryptosystems. Chap 9: Introduction to normal subgroups. Examples.
11/7/05 Chap 9: Factor groups. Examples.
11/9/05 Exam 2.
11/11/05 NO CLASS
11/14/05 Chap 9: Applications of factor groups. The G/Z theorem. Cauchys theorem for Abelian groups.
11/16/05 Chap 9: Internal Direct Products. ]
11/18/05 Chap 10: Homomorphisms. Examples. Properties of the Kernel.
11/21/05 Chap 10: The 1st isomorphism theorem. Properties of subgroups under a homomorphism.
11/23/05 Chap 10: Problem Session.
11/25/05 NO CLASS
11/28/05 Chap 11: Fundamental theorem of abelian groups. Examples.
11/30/05 Chap 11: Proof of the fundamental theorem.
12/2/05 Review of the course + a brief introduction to 103B.
12/9/05 FINAL EXAM

Homework Assignments and Exam review sheets:


Homework #1, due 10/3/05

Homework #2, due 10/10/05

Homework #3, due 10/17/05 (plus review sheet for exam 1)

Exam #1

Homework #4, due 10/24/05

Homework #5, due 10/31/05

Homework #6, due 11/7/05

Review Sheet for Exam 2

Exam #2

Homework #7, due 11/21/05

Homework #8, due Friday 12/02/05