**3510.001, Fall 2005**

**Introduction to Abstract Algebra**

**Conley**

the University of North Texas. |

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

**OFFICE HOURS:** MW 12:00-1:00, TR 11:00-12:00

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

**EXAMS, HOMEWORK, AND GRADING:** There will be two 100 point
midterms, on Wednesday, Sept. 28 and Wednesday, Nov. 2, and a
comprehensive 180 point final, on Monday, 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, and
late homework will not be accepted.

**TEXT AND PREREQUISITES: **The text is *A first course in
Abstract Algebra,* 7th 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.12, 10:30-12:30

HOMEWORK 13, due Friday, Dec. 9:

Section 18: 23-24, 32, 37-38, 40, 44, 52, 55

Section 20: 1-10, 27, 29

HOMEWORK 12, due Friday, Dec. 2:

Section 14: 6, 10, 12, 30, 31 (Optional:
Problem 43 of Section 13)

Section 18: 2, 4, 6, 12, 14-16, 19, 28

HOMEWORK 11, due Wednesday, Nov. 23:

Section 13: 17-21, 33, 38, 41-42, 44-45, 47

HOMEWORK 10, due Friday, Nov. 18:

Section 11: 1-6, 8-12, 15, 17, 46-49, 53

Section 13: 4-6, 16, 49

HOMEWORK 9, due Friday, Nov. 11:

Section 10: 1, 3-12, 14-16, 27, 30-35, 39, 40

HOMEWORK 8, due Friday, Oct. 28:

Section 9: 1-3, 7-18, 27ab, 34HOMEWORK 7, due Friday, Oct. 21:

Section 8: 1-9, 11-13, 16-20, 23-36, 44-46HOMEWORK 6, due Friday, Oct. 14:

Section 6: 7, 9, 11, 13-16, 18, 22-24, 28-29, 44, 47, 49, 51Optional problems (these are tricky and will not be graded, but feel free to ask me about them): Section 6: 46, 48, 50, 56

HOMEWORK 5, due Friday, Oct. 7 (NOTE: We have gotten a little behind so I have modified this assignment. I recommend that you turn in the optional extra problems in Section 5 as practice with proofs, but they will not be graded.)

Section 5: 36, 41-42, 46-47, 49, 55 Optional extra problems: 50, 51, 54, 57.The following problems are postponed until Homework 6: Section 6: 7, 9, 11, 13-16, 18, 22-24, 28-29

EXAM 1: Wednesday, September 24

HOMEWORK 4, due Friday, Sept. 23:

Section 4: 7-8, 20, 28-29, 31-34, 40-41 (NOTE: For part (b) of 20, replace U_4 by Z_4. You can skip part (c) entirely.)Section 5: 20, 27-28

HOMEWORK 3, due Friday, Sept. 16:

Section 2: 36, 37Section 3: 2, 4, 6, 10, 16, 26, 27, 31, 32

Section 4: 3-5, 10

HOMEWORK 2, due Friday, Sept. 9:

Section 1: 22, 23, 29, 31-34

Section 2: 2, 4, 6, 8, 13, 28

HOMEWORK 1, due Friday, Sept. 2:

Section 0: 3, 4, 26, 32, 34-36