Math 601 -- Abstract Algebra II

Course guide:

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

Content:

This is the second 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 link to the web page for Abstract Algebra I is here. 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 and arithmetic geometry, 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 TBA, and his email is TBA. He has office hours on TBA. 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 9:30 - 10:45 on Tuesday, March 24. The final exam has been scheduled for Tuesday, May 12, 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 (30%) to your final exam score (40%) and your homework total (30%). 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 accommodations for students with disabilities. If you have any issues with accessibility and course materials - please inform the course instructor, so that these issues can be addressed.

Office Hours:

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