Math 600 -- Abstract Algebra I

Instructor: Harry Tamvakis

Lectures: TuTh 2:00-3:15, MTH 0411

Office: 4419 Mathematics Building
Office hours: By appointment
Telephone: (301)-405-5120
E-mail: harryt@math.umd.edu

Course guide:

Text: D. S. Dummit and R. M. Foote, Abstract Algebra, Third edition, John Wiley and Sons, 2004.

Content:
This is the first semester of a year long graduate course in abstract algebra, which also serves as preparation for the Mathematics Department's qualifying exam in algebra. We will cover the basic theory of vector spaces, groups, rings, modules, fields, some homological and multilinear algebra, and category theory. The second semester will feature a treatment of Galois theory and the representation theory of finite groups. Additional topics will be included with a view toward applications in algebraic geometry and number theory, as time permits. Over the course of the year we plan to cover all of the sections in the textbook except possibly sections 3.4, 5.3, 6.2, 14.9, 15.4, 15.5, 16.1, 16.2, 16.3, 17.2, 17.3, 17.4, 19.2, and 19.3.

Homework:
The best and only way to learn mathematics is to do mathematics! Your weekly homework assignments are therefore the most important part of this course. Homework will be assigned on Thursday and is due in class on the Thursday of the following week. I urge you to hand in all of your assignments on time - however my policy is to allow up to TWO late homework assignments per student (any further late assignments will not be graded). You may discuss the problems with others and work in groups if you wish, but whatever you turn in should be written up on your own. There will be three types of homework problems: A, B, and C. While the A problems are fairly standard exercises, the B problems will be more substantial and sometimes quite difficult. The extra credit C problems are optional - they can improve your grade, but you do not need to solve them to do well in the course. People looking for a challenge are encouraged to attempt them! Our homework grader is Qihang Li, and his email is mathlqh@terpmail.umd.edu. He has office hours on Mondays, 3:00 - 4:00 pm, in 2109 Toll Physics Building. Please contact him with any questions you may have about the homework grading and solutions to the problems.

Exams:
We will have two exams during the course, a midterm and a final exam. The midterm will be held in class from 2:00 - 3:15 on Tuesday, November 2. The final exam has been scheduled for Saturday, December 18, 10:30 - 12:30. Make-up exams will only be given for compelling and documented reasons.

Grading Policy:
The course grade will be determined by adding your midterm score (25%) to your final exam score (40%) and your homework total (35%). Participating in class and working on extra credit problems is encouraged and will help to improve your grade.

READ THIS:
University of Maryland course related policies. Includes a discussion of academic integrity, the honor pledge, and accomodations for students with disabilities.

Note on masks in class:
Face coverings over the nose and mouth are required while you are indoors at all times. There are no exceptions. Students not wearing a mask will be given a warning and asked to wear one, or will be asked to leave the classroom immediately. Students who have additional issues with the mask expectation after a first warning will be referred to the Office of Student Conduct for failure to comply with a directive of University officials.

Office Hours:
Feel free to come by my office and talk at any time, either by chance or by appointment.


HOMEWORK

Assignment 1 (Due 9/9/21): ps, pdf, tex

Assignment 2 (Due 9/16/21): ps, pdf, tex

Assignment 3 (Due 9/23/21): ps, pdf, tex