Spring 2019: Math 453, Abstract Algebra 1

Class: Math 453, Algebra 1

Day/Time: MWF, 1030-1120 and 1130-1220

Location: REC 122

Office Hours: Monday 1230-200 PM, Tuesday 1200-200 PM, Wednesday 830-1030 AM

About the class:

Our focus in this class will be on the concepts of groups and rings. There is no required textbook for this class. There are several good books on the subject of abstract algebra. There are also many good online sources (e.g. wikipedia and class notes from similar classes taught at other universities).

The class will have weekly problem sets and 2-3 exams. The problem sets will be posted here in .pdf format.

Some Popular Books/Notes:

• Abstract Algebra by Dummit and Foote
• Algebra by Artin
• Algebra by Lang
• Basic Algebra (volumes 1-3) by Jacobson
• Modern Algebra (volumes 1-2) by Van Der Waerden
• Topics in algebra by Herstein
• Theory of groups by Hall
• The theory of groups by Zassenhaus
• Permutation groups by Dixon and Mortimer
• An introduction to the theory of groups by Rotman

Class News (Newest first/irrelevant removed):

• 4-10: The review problems for Midterm 2 have been posted. The exam will come directly from this set of problems. These review problems also replace Problem set 7. Turn in your solutions to the review problems on April 19.
• 4-8: Office hours this week will be Wednesday 830-1030, Th 1200-200, F 830-1030.
• 4-8: Office hours for the week of Midterm 2 will be W 1230-200, Th 1200-200, F 830-1030. Midterm 2 will be in-class on April 19.

Class Lectures (non-existent lectures removed):

• Monday, January 7: Class overview.
• Wednesday, January 9: Sets and Functions.
• Friday, January 11: Sets and Functions.
• Monday, January 14: Binary operations on sets.
• Wednesday, January 16: Review of linear algebra.
• Friday, January 18: Groups associated to matrices.
• Wednesday, January 23: Groups associated to matrices.
• Monday, January 28: More matrix groups.
• Friday, February 1: Reflection/review/relax day.
• Monday, February 4: Modular arithmetic.
• Friday, February 8: Cosets and quotients.
• Monday, February 11: Cosets and quotients.
• Wednesday, February 13: Game day.
• Friday, February 15: First Isomorphism Theorem.
• Monday, February 18: Review for Midterm 1.
• Wednesday, February 20: Review for Midterm 1. NO PSET due.
• Friday, February 22: Midterm 1.
• Wednesday, February 27: Hand back Midterm 1 and go over the exam.
• Friday, March 1: Isomorphism Theorems. Pset 5 due.
• Monday, March 4: Rng, Rings, and more.
• Wednesday, March 6: Rings, homomorphisms, and ideals
• Friday, March 8: Ideals. Pset 6 due.
• Monday, March 18: Quotient ideals.
• Wednesday, March 20: Isomorphism theorems.
• Friday, March 22: Integers and Polynomial rings, I.
• Monday, March 25: Integers and Polynomial rings, II.
• Wednesday, March 27: Integers and Polynomial rings, III.
• Friday, March 29: Integers and Polynomial rings, IV.
• Monday, April 8: Review rings.
• Wednesday, April 10: Review rings.
• Friday, April 12: Review rings.
• Monday, April 15: Review rings
• Wednesday, April 17: Review rings.
• Friday, April 19: Midterm 2.
• Monday, April 22: Handback Midterm 2.

Class Files: