Objectives
This course is the second half of the abstract algebra sequence. MA 541 dealt with groups, whereas MA 542 deals with rings. Rings are algebraic structures which have two operations: addition and multiplication. Examples include the integers, the rational numbers, the real numbers, the complex numbers, and polynomial rings. The theory of rings (and especially fields) is used to answer the question of how to solve polynomial equations. This will lead us to the final topic, Galois theory, which establishes a relationship between solutions of a polynomial equation and properties of a group associated to that equation.
Times and Places
Lectures will take place MWF 1:25 pm - 2:15 pm in PSY B45.
Office hours will take place Mondays 2:30 pm - 3:30 pm in CDS 543.
Class is cancelled for Monday, April 8.
Textbook
A First Course in Abstract Algebra, by John Fraleigh.
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 be due on Wednesdays. You will submit assignments using Gradescope. Select problems from each problem set will be graded and returned to you the following week.
The midterm and final exam will be take-home. You are not allowed to work together on the exams. The midterm will be due on Wednesday, March 27, and the final will be due Wednesday, May 8.
Grades
The grading rubric is: 60% Assignments, 20% Midterm, 20% Final Exam.
If you experience an emergency which prevents you from turning in an assignment, you may skip it without penalty. You don't need to explain to me what the emergency is. If you turn in every assignment, I will drop the lowest one. Late assignments will not be accepted.
Academic Integrity
It is fine to check the textbook for answers to the odd-numbered questions, as long as you have put some effort into solving the problems unaided.
You are allowed and encouraged to work together on homework assignments, but you must hand in solutions which are written in your own words. The work on the exams must be yours alone.
Please try to solve the problems unaided before you seek the back of the book or online forums. If you learned how to solve a problem this way, that's fine and you will still receive credit, but please cite where you found the solution, and write the solution in your own words.
Representing another person's work as your own is academic dishonesty, and will be reported as such. This includes using AI, as AI is based on the writing of people.