**3510.001, Fall 2002**

**Introduction to Abstract Algebra**

**Conley**

the University of North Texas. |

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

**OFFICE HOURS:** Monday and Wednesday, 12-1, Tuesday and
Thursday, 11-12

**CLASS MEETS:** Monday, Wednesday, and Friday, 11:00-11:50, GAB
206

**EXAMS, HOMEWORK, AND GRADING:** There will be two 100 point
midterms, on Wednesday, Sept. 25 and Wednesday, Oct. 30, and a
comprehensive 180 point
final, on Monday, Dec.9, 10:30-12:30. There will also be twelve
10
point homeworks, due Fridays at the beginning of class. There
will
be no make-up exams except for emergencies, and late homework will be
worth
half-credit.

**TEXT, PREREQUISITES, AND OTHER REFERENCES: **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.

FINAL EXAM: Monday, Dec.9, 10:30-12:30

HOMEWORK 12, due Friday, Dec. 6:

Section 5.3: 3-10, 27, 28

HOMEWORK 11, due Friday, Nov. 22:

Section 5.1: 32, 39, 40, 43, 49, 52, 55

Section 5.2: 1, 2, 4, 8-10, 12, 27

HOMEWORK 10, due Friday, Nov. 15:

Section 5.1: 2, 4, 6, 8, 10, 12, 14, 15, 16, 19, 28, 38

HOMEWORK 9, due Monday, Nov. 11 (note the change in the due date):

Section 2.4: 1, 2, 4

Section 3.1: 4, 5, 16, 18, 44, 45, 47

Five handwritten problems (see your copy of Exam II)

EXAM 2: Wednesday, October 30

HOMEWORK 8, due Friday, Oct. 25:

Section 2.2: 24a, 31

Section 2.3: 1-4, 6-11, 15, 26, 27

HOMEWORK 7, due Friday, Oct. 18:

Section 2.1: 11-13, 16, 18-20, 23-26, 42, 43

Section 2.2: 1-3, 7-14, 16, 17

HOMEWORK 6, due Friday, Oct. 11:

Section 1.5: 13, 20, 21, 31, 33, 34, 36-38, 52-54, 64,
65a

Section 2.1: 1-9

HOMEWORK 5, due Friday, Oct. 4:

Section 1.4: 4, 5, 6, 7 for 4-6, 20, 27, 28, 41, 42,
43, 46,
51, 55

Section 1.5: 14, 15, 18, 19, 22, 26, 27, 28, 32

EXAM 1: Wednesday, September 25

HOMEWORK 4, due Friday, September 20:

Section 1.3: 1, 3, 7, 10, 20, 26, 27, 29, 30, 33, 40,
5, 6,
7, 20, 27

HOMEWORK 3, due Friday, September 13:

Section 1.1: 1-11, 23

Section 1.2: 2-8, 10, 16, 17

HOMEWORK 2, due Monday, September 9:

Section 0.2: 1, 2, 9, 10, 11, 12, 16, 18, 19, 25, 26,
31, 32, 33, 34, 35b

HOMEWORK 1, due Friday, August 30:

Section 0.1: 9, 10, 13, 18, 19, 26, 28, 29, 30

Section 0.3: 1, 3, 4, 5, 8b