3510.001,  Fall 2003
Introduction to Abstract Algebra
Conley

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INSTRUCTOR: Charles Conley, GAB 419, (940) 565-3326

OFFICE HOURS: MW 12:30-2:00, F 12:30-1:30

CLASS MEETS: MWF 11:00-11:50, GAB 206

EXAMS, HOMEWORK, AND GRADING: There will be two 100 point midterms, on Wednesday, Sept. 24 and Wednesday, Oct. 29, and a comprehensive 180 point final, on Friday, Dec. 12, 10:30-12:30.  There will be thirteen homeworks, due at the beginning of the last day of class each week.  They will be worth 10 points each, excepting those due the first week and the week of Thanksgiving, which will be worth 5 points each.  There will be no make-up exams except for emergencies, and late homework will be worth half-credit.

TEXT AND PREREQUISITES: The text is A first course in Abstract Algebra, 6th edition, by J. Fraleigh.  The prerequisite is Math 2510-20, the analysis sequence.

TOPICS:   We will cover two main topics, groups and rings.  The section of the course on groups will be an introduction to their structure, with an emphasis on examples such as the cyclic and dihedral groups, the groups of symmetries of the Platonic solids, and the symmetric groups.  The section on rings will begin with arithmetic in the integers, the unique factorization theorem, and modular arithmetic.  Then we will discuss more general rings, emphasizing the particular case of polynomial rings and their quotients, which lead to field theory.  Prior experience with analytic proofs will be assumed; here you will be introduced to algebraic proofs.

It is the responsibility of students with certified disabilities to provide the instructor with appropriate documentation from the Dean of Students Office.

FINAL EXAM: Friday, Dec.12, 10:30-12:30

HOMEWORK 13, due Friday, December 5

Section 5.3: 1-10, 24-28
Extra Problems:
(A) Find an isomorphism from the additive group Z_{16}to the multiplicative group Z_{17}^*.
(B) Find all generators of Z_{17}^*
(C) Find 1/6 in Z_{17}
(D) Find all square roots of 2 in Z_{17}
(E) Find all square roots of 6 in Z_{17}

HOMEWORK 12, due Wednesday, November 26  (This homework is worth only 5 points, not the usual 10)

Section 5.2: 2-4, 8-10, 12, 27

HOMEWORK 11, due Friday, November 21

Section 5.1: 2, 4, 6, 12, 14-16, 19, 28, 32, 38, 40, 49, 52, 55

HOMEWORK 10, due Friday, November 14

Section 3.1: 25, 28, 29, 33-38, 41, 42, 49
Section 3.2: 31, 34*

EXTRA PROBLEMS:

In problems (A)-(D), prove that no surjective homomorphism exists from

(A) S_3 to Z_3,  (B) A_4 to Z_2,  (C) A_4 to any 4 element group, (D) S_4 to any 8 element group.

In problems (E)-(H), argue geometrically that surjective homomorphisms exist and compute their kernels:

(E) S_3 to Z_2, (F) A_4 to Z_3, (G) S_4 to S_3, (H) S_4 to S_2.

HOMEWORK 9, due Friday, November 7

Section 2.4: 1-5, 9, 11, 15-20
Section 3.1: 4, 5, 16-21, 44, 45, 47
Extra problems: These are postponed until next week.

EXAM 2:   Wednesday, October 29

HOMEWORK 8, due Friday, October 24

Section 0.2: 34-36
Section 2.3: 1-4, 6-12, 16, 26-30, 33, 35, 38, 39

HOMEWORK 7, due Friday, October 17

Section 2.1: 18-20, 23-26, 42-44
Section 2.2: 1-3, 7-18, 24ab, 31

HOMEWORK 6, due Friday, October 10

Section 1.5: 16-20, 34-39, 52-54, 64, 65a
Section 2.1: 1-9, 11-13, 16-17

HOMEWORK 5, due Friday, October 3

Section 1.4: 36, 41, 42, 46, 47, 49, 55
Section 1.5: 7, 9, 11, 12-15, 21, 22, 26-33

EXAM 1:   Wednesday, September 24

HOMEWORK 4, due Friday, September 19

Section 1.3: 20a, 26, 27, 29, 30, 32, 33, 34, 35, 40
Section 1.4: 5, 7, 20, 27, 28

HOMEWORK 3, due Friday, September 12

Section 1.2: 16, 17, 25, 26, 29, 30, 31
Section 1.3: 1-6, 10

HOMEWORK 2, due Friday, September 5

Section 1.1: 1-7
Section 1.2: 2-7, 10

HOMEWORK 1, due Friday, August 29:

Section 0.1: 29, 30
Section 0.2: 3
Section 0.3: 1, 3, 4, 5, 8b