Math 541: Modern Algebra

Math 541 Section 002, Spring 2019

Lectures: MWF 1:20 - 2:10 pm, VV B123

Instructor: Daniel Corey, VV 321, dcorey[at]math.wisc.edu

Office Hours: Wednesdays 2:20-3:50 pm, Thursdays 12:50-2:20 pm VV 321, or by appointment.

Textbook: Abstract Algebra, by Dummit and Foote, Third Edition, 2004. The plan is to cover the following sections: 1.1-1.7, 2.1-2.4, 3.1-3.3, 3.5, 4.1-4.3, 5.1, 5.2, 7.1-7.4.

Syllabus

Homework: Homeworks will be due in class, typically on Fridays. All references to problems are from Dummit and Foote.

  • Problem Set 1: 0.1 7; 0.2 1a, 3, 4; 0.3 4, 6, 9, 12, 13, 14; Due Feb 1.
  • Problem Set 2: 1.1 6, 11, 20, 25, 31, 32; 1.4 8, 10ab, 11abde (take F to be the real numbers R); Due Feb 8.
  • Problem Set 3: 1.1 24; 1.2 3, 14 (for 14, find a finite set of generators); 1.3 2, 3, 10, 12, 15; 1.5 1; Due Feb 15.
  • Problem Set 4: 1.6 1, 2, 6, 23; 2.1 1, 6, 7, 15; 2.3 4, 14; Due Feb 22.
  • Problem Set 5: 2.4 6, 14, 19; 3.1 3, 7, 24, 36; 3.2: 4, 8, 16; Due March 8.
  • Problem Set 6: 3.2 9; 3.3 3, 4, 9; 3.5 2, 3, 9; Due March 15.
  • Problem Set 7: 1.7 14; 2.2 12; 4.1 1, 6; 4.2 4, 7b; Due March 29.
  • Problem Set 8: 4.3 2bc, 5, 8, 11, 29; 5.1 5, 14; Due April 5.
  • Problem Set 9: 5.2 4, 5, 9 (only compute the number of elements of order 2); 7.1 3, 4, 5, 7, 13ab, 14. Due April 19.
  • Problem Set 10: 7.2 3, 10, 12; 7.3 2, 10, 17, 18, 24. Due April 26.
  • Problem Set 11: 7.3 29, 31; 7.4 4, 7, 8, 11, 13, 19, 37. Due May 3.

Honors Problem Set: If you are signed up to take this class with Honors, please complete the following assignment. Read section 4.5 in the book and complete exercises 16, 22, 23, 28 (may omit proof that G is abelian), 30, 45. Instead of turning in this assignment, we will meet one-on-one sometime in late April. I will ask you to present solutions to two problems of my choosing on the blackboard. The meeting should take no more than 30 min. Whether or not you earn honors credit will depend on the extent to which you demonstrate to me during this meeting that you have understood these problems and their solutions.

Midterm exam 1: Friday March 1 in class. Will cover everything up to and including lecture on Feb 20. In the text, this is sections 0.1-0.3, 1.1-1.6, 2.1-2.4 (excluding material on group actions), 3.2.

Midterm exam 2: Wednesday April 10 in class. Will cover everything since exam 1 up to an including the lecture on April 3. In the text, this is sections 1.7, 2.2, 3.1, 3.3, 3.5, 4.1-4.3, 5.1, 5.2.

Final Exam: Friday May 10, 7:45-9:45 am. Location SOC SCI 6240.