Math 541: Modern Algebra

Math 541 Section 001, Fall 2018

Lectures: MWF 9:55 - 10:45 am, VV B123

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

Office Hours: Mondays 1-2:30 pm, Wednesdays 2:30 - 4 pm VV 321, or by appointment.

Course Assistant: Dadong Peng, Office Hours: Wednesdays 4-7 pm, VV B205.

Textbook: Abstract Algebra, by Dummit and Foote, Third Edition, 2004.

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 7; 0.3 6, 12, 13, 14; 1.1 9, 20, 22, 25, 31 Due: Sept. 14.
• Problem Set 2: 1.2 7; 1.3 7, 12, 15; 1.4 11 (all parts except c); 1.5 2; 1.6 2, 4, 6, 20, 23 Due: Sept. 21.
• Problem Set 3: 2.1 6 (Hint: see page 64), 7, 15; 2.2 # 10, 14 (assume F =R the real numbers); 2.3: 4, 14, 19, 26 Due: Sept 28.
• Problem Set 4: 2.4 6, 14, 19; 3.1 3, 24, 36; 3.2 4, 8, 16 Due Oct. 5.
• Problem Set 5: 3.1 7, 9, 10; 3.2 11; 3.3 3, 4, 7 Due Oct. 12.
• Problem Set 6: 2.2 12; 3.5 9 (V_4 is just Z/2Z x Z/2Z); 4.1 1, 6; 4.2 4, 11 Due Oct. 26.
• Problem Set 7: 4.3 5, 11, 13, 27, 29; 5.1 5, 14 Due Nov. 2.
• Problem Set 8: 5.2 4, 5, 9, 16; 5.4 1, 7, 20 Due Nov. 9.
• Problem Set 9: 7.1 5, 7, 13ab, 14, 24, 26, 27; 7.2 3, 5 Due Nov. 21. (Note that this is a Wednesday).
• Problem Set 10: 7.2 6, 7, 10, 12; 7.3 2, 10, 17, 18, 19, 20 Due Nov. 30.
• Problem Set 11: 7.3 24, 29, 31; 7.4: 2, 8, 14abcd, 15, 37, 38 Due Dec. 7.
• Problem Set 12: 7.4: 13, 18, 19, 31, 39, 41; 7.6: 1, 4, 5. Do not turn in.

Honors assignment: 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 23, 27, 30, 45. Instead of turning in this assignment, we will meet one-on-one sometime during the first week in December. 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: Wednesday Oct. 17 in class. It will cover the following sections in the text: 0.1-0.3, 1.1-1.6, 2.1-2.4 (except for material on group actions), 3.1-3.3, and 3.5.

Midterm exam 2: Wednesday Nov. 14 in class. It will cover the following sections in the text: 1.7, 2.2, 4.1-4.3, 5.1, 5.2, and 5.4.

Final Exam: Monday Dec. 17 5:05-7:05pm in VV B119. Roughly half of the exam will be material since Exam 2 (in the text, this is 7.1-7.4, 7.6), and the other half will be material from exams 1 and 2.