Introduction to Abstract Algebra
MATH 501

Fall 2010
TR 2:003:15
Harris Hall 4145

Instructor: Richard Hammack
Office hours:
Office: Harris Hall 4105
Tuesday 9:30–10:30 & 12:30–1:30
Work: 828-6237
Thursday 9:30–10:30
Home: 353-8572
and by appointment
E-mail: rhammack @ vcu . edu

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.

Homework: Assignments are collected, graded and returned. Assignments are announced in class, and also posted on the course calendar (on the web page).
  • Papers are collected at the beginning of class on appointed days.
  • Papers submitted after the beginning of class are not graded.
  • If you must miss class when homework is due, give me your homework early or have a classmate turn it in for you.
  • You may email your homework to me, but it must arrive in my inbox no later than the beginning of class on the date it is due. I often do not print emailed homework, so it may not get any written feedback from me.
  • Exceptionally sloppy work is not graded.
  • I expect compete sentences (where appropriate) and good English usage on all homework papers.
  • I encourage you to work together on homework, though the work you turn in must be your own.
  • In addition to the work you hand in, you should work lots of extra problems for practice.
  • Some homework problems are intended to make you think about ideas not discussed in class.
Tests: There will be two tests. Each is in-class and closed-book. Use of calculators is not allowed during tests. In writing the tests, I assume that you have been studying the material at least 6 hours per week outside of class. Test dates are listed on the course calendar (found on the web page).

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.

The 10-point grading scale is used:
A: 90100
B: 8089
C: 7079
D: 6069
F: 059

Your final average will be computed as follows:

Homework: 30%
Highest Test Grade: 35%
Participation: 5%
Final Exam: 30%


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.

Make-up Work:
Except in extreme circumstances, I do not make a distinction between excused and unexcused absences. An absence of any type can impact your performance. I do not give makeup tests, nor do I grade late homework. I will drop your lowest test grade and some low homework grades. If you miss one test, then that counts as the dropped grade. If you miss the final exam for a legitimate reason (i.e. a documented illness or emergency) then I can give you a grade of Incomplete (I) for the course, and you will need to make up the missed exam by the deadline set by the University.

Internet: Information about this course is posted on my web page (not on Blackboard). Go to 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.

Email: Any email correspondence concerning this course should be through your official VCU email address. University policy prevents me from discussing many aspects of the course through other email addresses. I may send email messages either to the whole class or individuals in the class. It is your responsibility to check your VCU email regularly.

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.

Exercises: For each chapter we cover, you should work as many of the exercises as possible for practice. Answers or hints for many exercises can be found at the end of the text. Many of these problems will be used for the tests and final exam. Keep in mind that there can be many correct approaches for some proof-oriented questions, so the fact that your solution does not match a given solution does not necessarily mean it is wrong. Ask me if you are ever unsure about the validity of your solution.

Accommodations: Any student eligible for and needing academic adjustments or accommodations because of a disability should contact me within the first week of class.