3510.001,  Fall 2005
Introduction to Abstract Algebra
Conley


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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.


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

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

EXAM 2:   Wednesday, Nov. 2

HOMEWORK 8, due Friday, Oct. 28:

   Section 9:  1-3, 7-18, 27ab, 34

HOMEWORK 7, due Friday, Oct. 21:

   Section 8:  1-9, 11-13, 16-20, 23-36, 44-46

HOMEWORK 6, due Friday, Oct. 14:

   Section 6:  7, 9, 11, 13-16, 18, 22-24, 28-29, 44, 47, 49, 51
   Optional 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, 37
   Section 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