Prerequisites: MATH 300 and MATH 310. It is expected that you are thoroughly familiar with the material from these courses, including: elementary set theory, modular arithmetic, counting, direct proof, contrapositive proof, proof by contradiction, if-and-only-if proof, proof by induction (both regular and strong), existence proof, counterexamples, relations, equivalence relations, partitions, integers modulo n, functions, matrix multiplication and inverses, determinants, vector spaces, subspaces, etc.
Text: Abstract Algebra: Theory and Applications, By Thomas J. Judson (ISBN 978-0-9824062-2-9)
Abstract Algebra deals with the structure of algebraic systems. The familiar algebraic operations on numbers are distilled into mathematical entities called groups, rings and fields. This greatly widens the scope, utility and generality of algebra. The course is designed to expose you to some key algebraic ideas used in advanced mathematics, as well as to sharpen your abstract reasoning and theorem-proving skills.
Although abstract algebra has many applications, our approach is primarily theoretical. You will write lots of proofs. You may have to think about things in new and challenging ways. This can require lots of time, hard work, deep thought and imagination.
The course covers material selected from the first 20 chapters of the text. Your grade is determined by homework assignments, participation, two tests and a final exam. Details follow.
Participation: Participation means that you in some way demonstrate intellectual involvement in the course. It does not necessarily mean that you ask questions or volunteer answers. Active participation may include your working lots of exercises, taking advantage of office hours, and displaying preparedness, dedication and intellectual curiosity. Things that could cause you to lose participation points include sleeping in class, leaving your cell phone on, missing too much class, and rude behavior. (Not that I expect you would do any of these things!)
Final Exam: The final exam is comprehensive, covering all material discussed in class. It is closed-book and closed-notes. It is scheduled for 1:00–3:50 PM on Tuesday December 14. In writing the final exam, I will assume that you have been studying the material at least 6 hours per week outside of class, throughout the entire semester.
Attendance: I do not take attendance, but I do notice if you are not attending class. If your grades are high, I do not mind if you miss class occasionally; otherwise excessive absences may result in a reduced participation score.
As a matter of courtesy, you should arrive punctually and stay for the entire duration of each class you attend. Please inform me ahead of time if you must leave early.
Internet: Information about this course is posted on my web page (not on Blackboard). Go to http://www.people.vcu.edu/~rhammack/ and click on "Math 501." There you will find the syllabus, a calendar, homework assignments, copies of old tests, and other materials. Solutions for all graded work (homework and tests) will be posted after the due dates.
Cell Phones: Please be sure that all cell phones and other electronic devices (including iPods, BlackBerries and laptops) are turned off and stowed away for the entire duration of each class. Leaving such devices on may lower your participation score.
Office: Please feel free to stop by my office whenever you have a question,
or if you just want to chat. If my posted hours are inconvenient, I will be
happy to schedule an appointment.
Tell me if you are having trouble. Catching up can be very difficult once
you get behind, so let me know as soon as you think there is a problem.