Math 200 A: Algebra I

Fall 2013

 Lectures: M-W-F 10:00 PM--10:50 PM APM 5402 Office Hour: M-F 2:00 PM--3:00 PM APM 7230 W 1:00 PM--2:00 PM APM 7230 TA information: NONE

Book

• D. S. Dummit and R. M. Foote, Abstract algebra. (The main textbook)
• I. M. Isaacs, Algebra.
• J. J. Rotman, An introduction to the theory of groups. (For the group theory part of the course).
• D. Hungerford, Algebra.

Description

This course is an introduction to group theory and ring theory. In the group theory part, finite groups will be discussed mainly, e.g. Sylow theorems, symmetric groups, p-groups, etc. In the ring theory part, we cover even less. We introduce and prove basic properties of a PID, a UFD, etc.

Prerequisite: one undergraduate course in group theory and ring theory and a solid background in linear algebra. Students with little or no prior background in algebra should consider taking Math 100 instead.

Math 200 courses and the qualifying exam: The algebra qualifying exam which will be given in May 2014 (and September 2014) will be based on the topics that are covered in the Math 200A, B and C. In Math 200B, you will learn about module theory, field theory, etc. In Math 200C, commutative algebra will be discussed (we go through the book written by Atiyah and Macdonald). And only the first three chapters will be needed for the algebra qualifying exam.

Homework (30%), Midterm (30%), Final (40%).

• Please make sure that you have understood the discussed materials. It is important that you would be able to solve all the assigned weekly problems.
• Do not hesitate to come to me or your TA and chat about:
• what is covered in the class;
• an assigned problem;
• a problem (reasonably related to the course) that you have encountered in a book or a previous qualifying exam.
• If you want to take the qualifying exam on May, I would suggest that you take a look at the previous years exams and try to see if you can do the group theory portion of the exams.
Schedule

• Lecture 1 (9/27/13)
• Lecture 2 (9/30/13)
• Lecture 3 (10/2/13)
• Lecture 4 (10/4/13)
• Lecture 5 (10/7/13)
• Lecture 6 (10/9/13)
• Lecture 7 (10/11/13)
• Lecture 8 (10/14/13)
• Lecture 9 (10/16/13)
• Lecture 10 (10/18/13)
• Lecture 11 (10/21/13)
• Lecture 12 (10/23/13)
• Lecture 13 (10/25/13)
• Lecture 14 (10/28/13)
• Lecture 15 (10/30/13)
• Lecture 16 (11/1/13)
• Lecture 17 (11/4/13)
• Lecture 18 (11/6/13)Midterm
• Lecture 19 (11/8/13)
• Veterans day (11/11/13)
• Lecture 20 (11/13/13)
• Lecture 21 (11/15/13)
• Lecture 22 (11/18/13)
• Lecture 23 (11/21/13)
• Lecture 24 (11/23/13)
• Lecture 25 (11/25/13)
• Lecture 26 (11/27/13)
• Thanksgiving holiday (11/29/13)
• Lecture 27 (12/2/13)
• Lecture 28 (12/4/13)
• Lecture 29 (12/6/13)

Assignments.

All the assignments are due at 4:00pm on Fridays. You can put your solutions in my mail box or drop-by my office and give them to me.

There are 6 problem sets. Your cumulative homework grade will be based on the best 5 of the 6.

• HW1, Due 10/18: here is the first set of problems. I will grade only a selected set of problems.
• HW2, Due 10/25: here is the second set of problems. I will grade only a selected set of problems.
• HW3, Due 11/01: here is the third set of problems. I will grade only a selected set of problems.
• HW4 and HW5, Due 12/02: here is the forth set of problems. I will grade only a selected set of problems.
• HW6, Due 12/06:

Exams.

There will be an in-class midterm on November 6. The final exam is 8:00am-11:00am December 13. Exams will be posted here.

Here is the midterm.

Here is the final exam of the course.