M301A: Abstract Algebra

Mathematics 301A: Abstract Algebra

Instructor: Jonathan Smith, 496 Carver, 4-8172 (voice mail)

e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)

Office Hours: Mon. 11am, 2:10 pm, 5:30pm; Wed. 11am, 2:10pm (subject to change)

Special Finals Week office hours: Tue. 12/12, 1 - 5pm.

Grading: 10% for each of three graded homework assignments, 20% for each of two in-class tests, and 30% for the final (Wed. 12/13, 9:45-11:45am, Carver 132).
Click here for information about special accommodations.

Textbook: J.A. Gallian, Contemporary Abstract Algebra, 6th ed., Houghton Mifflin, ISBN 0-618-51461-6

Study Plan: reserve 1 - 2 hours for homework between each pair of classes. Successful performance in the class depends critically on completion of the homework assignments.

Communication devices must remain switched off during the class periods and final.

Syllabus: Groups and rings, selected topics from Parts 1, 2, 3.

Homework Assignments

Click here for Practice Final

12/1 for 12/4: pp.315-6, Ex. 6, 7, 8.

11/29 for 12/1: p.316, Ex. 12.

Third graded homework due 11/27: Three questions from pp.254-6, Ex. 4, 6, 18, 26, 38.

11/13 for 11/15: pp.298-9, Ex. 1, 6.

Click here for Practice Test #2

11/3 for 11/6: p.241, Ex. 8, 12, 13.

Second graded homework due 10/30: Three questions from p.148, Ex. 14; p.194, Ex. 50, 52; p.213, Ex. 44, 52.

10/23 for 10/25: pp.82-3, Ex. 4, 8, 10, 11, 17.

10/20 for 10/23: p.212, Ex. 29.

10/18 for 10/20: p.191, Ex. 7; pp.213, Ex. 49.

10/16 for 10/18: p.191, Ex. 1, 5; pp.210-1, Ex. 4, 7.

Click here for Practice Test #1

10/4 for 10/6: pp.68-70, Ex. 20, 46.

10/2 for 10/4: pp.23-5, Ex. 11, 48.

9/22 for 9/25: p.55, Ex. 25.

First graded homework due 9/27: Three questions from pp.54-5, Ex. 14, 26, 28; pp.112-3, Ex. 9, 22.

Challenge Problem 3: Can you give a geometrical or combinatorial rule to determine which pairs of 3-cycles in A₄ multiply to a 3-cycle, and which multiply to an element of V₄?

9/18 for 9/20: p.113, Ex. 18(b), 15, 12.

9/15 for 9/18: p.55, Ex. 16 (first proof only), 18, 20.

9/13 for 9/15: p.56, Ex. 37; p.114, Ex. 40.

9/11 for 9/13: pp.113-4, Ex. 18(a), 30.

9/8 for 9/11: p.26, Ex. 53.

Practice "graded" homework due 9/1: pp.23-4, Ex. 4, 10, 14, 18, 19.

Challenge Problem 2: In how many ways can 1 be expressed as a linear combination

1 = s 5 + t 7

with integer coefficients s and t ? (The challenge is to prove that your claim is correct.)

8/25 for 8/28: p.23, Ex. 12.

8/23 for 8/25: p.23, Ex. 1, 2.

Challenge Problem 1: Prove the Well-Ordering Principle.

8/21 for 8/23: p.23, Ex. 5, 6.