Math 404 -- Field Theory

Course guide:

Text: John M. Howie, Fields and Galois Theory, Springer-Verlag, 2006.

Content:

This is a second course in abstract algebra, and assumes familiarity with groups, rings, and some linear algebra (the prerequisites are typically covered in Math 403). Our main goal is to study the theory of fields and some of their most important applications. The course will include the fundamental insights of Galois about the subject, specifically on the problem of solving polynomial equations by formulas which employ radicals. There will be many proofs done in class, and you will also need to prove results on your own in the homework and provide (simpler) proofs on exams. I plan to cover most of the textbook, and include some additional topics, time permitting.

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 after 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, which should be turned in at most two weeks after their due date. Any further late assignments will not be graded. You may discuss the problems with others if you wish, but whatever you turn in should be written up on your own. The extra credit 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 Oscar Coppola, and his email is ocoppola@umd.edu. 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 12:30 - 1:45, on Thursday, March 13. The final exam has been scheduled for Tuesday, May 20, 4:00 - 6:00 pm. Make-up exams will only be given for compelling and documented reasons.

Grading Policy:

The course grade will be determined by adding your midterm test 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. This includes a discussion of academic integrity, the honor pledge, and accomodations for students with disabilities. If you have a documented disability and wish to discuss academic accommodations with me, please contact me as soon as possible.

Electronic devices:

No electronic devices are required for this course, and they will not be allowed in class during exams.

Office Hours:

I will available at these times specifically to help you: Tuesdays 2:00 - 3:00 in my office and Wednesdays 10:00 - 11:00 (on Zoom). Feel free to come by my office and talk at any time, either by chance or by appointment.

Resources:

The testbank archive of past exams has examples of tests from past years, and is a good source of problems.