Course: MA541, Modern Algebra I
Instructor: Jared Weinstein
Lectures: TR 3:30 pm - 5:00 pm in PSY B39
Office Hours: M 10:00 am - 12:00 pm and Th 2:00 pm - 3:00 pm in MCS 227

Course Overview

This course is an introduction to abstract algebra, with an emphasis on groups. A group is an algebraic structure which was invented to capture the notion of symmetry. Groups appear in almost every field of mathematics, so it is important to master them. Topics include permutation groups, Lagrange's theorem, homomorphisms, the isomorphism theorems, and the Sylow theorems.

Text

John B. Fraleigh, A First Course in Abstract Algebra, 7th ed., Addison-Wesley.

Assignments and Exams

In order to gain mastery of the concepts it is crucial to do many exercises. I will be assigning problem sets every week which will usually be due on Tuesdays. You are allowed and encouraged to work together on homework assignments, but you must hand in solutions which are written in your own words. Select problems from each problem set will be graded and returned to you the following week.

On Tuesday, October 16, I will hand out a take-home midterm, which will be due on Tuesday, October 23. Here are the solutions. You are not allowed to work together on the midterm.

HW Assignment Due
#1 § 0: 1, 2, 9, 10, 11, 12, 14, 15, 17, 18, 19, 29, 30, 36 Sept. 11
#2 § 1: 1-4, 16-18, 22-27, 33, 34, 37. § 2: 1-9, 26 Sept. 18
#3 § 3: 6,7,16,33. § 4: 8, 19, 20, 28, 29, 32, 34, 35 Sept. 25
#4 § 5: 8, 10, 13, 26, 30, 40, 43, 49, 53. § 6: 53 Oct. 2
#5 § 8: 1, 2, 18b, 35, 51b. § 9: 1, 4, 5, 7, 10, 13, 17, 34, 35. Oct. 11
#6 § 12: 6, 8, 10, 16. § 13: 17, 20, 27, 44, 47, 50. Nov. 1
#7 § 14: 4, 6, 8, 30, 33. § 15: 4, 9, 13, 23, 25, 37. Nov. 8
#8 § 16: 13b, 13c. § 17: 1, 4, 7. § 34: 2, 7, 9. Nov. 20
#9 § 35: 8, 9, 22. § 36: 1, 2, 3, 5, 13, 19, 20. Dec. 6
#10 § 37: 4, 6, 8. § 38: 2, 4. § 39: 12c, 13c. Dec. 13

The final will be given on Tuesday, December 18, 3:00 pm - 5:00 pm, in PSY B39. You must take the final to receive a passing grade.