Virginia Commonwealth University
Algebraic Structures and Functions
MATH 504
Spring 2014
Tues. Thurs. 9:3010:45
Harris 4145

Office: Harris Hall 4105
  Richard Hammack
Office hours:
  Work: 804-828-6237
Tuesday 1:30–2:30
  Home: 804-355-3963
Wednesday 12:00–1:30
Thursday 12:30–2:30
  Course web page:
and by appointment

MATH 200-201 and MATH 300. It is expected that you are familiar with the material MATH 300, including: elementary set theory, 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 and functions. Although we may review a few of these topics briefly, our main purpose is to build upon them. If you need a review, here is a link to a free textbook.

TEXT: A First Course in Abstract Algebra, by John Fraleigh, Seventh edition

This is a course in Abstract Algebra, a subject that 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, for the things that get added or multiplied in these structures are not necessarily numbers. It also can lead to a deeper understanding and appreciation of the ordinary algebra of real numbers. This course is designed to expose you to some key algebraic ideas used in advanced mathematics, to sharpen your abstract reasoning and theorem-proving skills, and to deepen your understanding of the foundations of material that you may one day teach.

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.

Material from Chapters 1, 2, 3, 4, 5 and 6 is covered.

Your grade is determined by homework assignments, three tests (one in-class and one take-home) and a final exam. Details follow.

Homework: Frequent homework assignments are collected, graded and returned.
  • Papers are collected at the beginning of class on appointed days.
  • I usually do not grade late homework.
  • I do not guarantee that I will grade messy or illegible work.
  • I am attentive to how well you communicate your ideas. Points may be deducted for bad style.
  • I encourage you to work together on homework, though the work you turn in must be your own.
  • Do not search the Internet for solutions. Many are wrong anyway.
  • Two or more of your lowest homework grades are dropped.
  • In addition to the work you hand in, you should work lots of extra problems for practice. Many odd-numbered problems have answers or hints in the back of the text.
  • Some homework problems are intended to make you think about ideas not discussed in class.

There are three tests and a final exam, scheduled as follows:
Test #1 (in-class) Sections 0–5 Tuesday, February 11
Test #2 (in-class) Sections TBA Thursday, March 6
Test #3 (in-class) Sections TBA Tuesday April 8
Final Exam Comprehensive Thursday, May 1
No computing technology may be used on the in-class test and final exam.

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:

Highest test grade
Second-highest test grade 25%
Final exam:

  • Attendance: Attendance is not taken. You are responsible for all material covered in class.
  • Etiquette: Please arrive promptly. Late arrivals are disruptive. Except in the event of emergency, do not leave class until it is officially over. Do not pack up before class is over.
  • Phones: Turn off and put away all phones for the entire duration of class. Do not text in class or leave to take a call.
  • Devices: You are expected to be connected with the course and course material. All devices not related to coursework (iPods, laptops, etc.) are to be turned off and put away for the entire duration of class.
  • Make-up work: Under normal circumstances I do not give makeup tests. I will drop your lowest test grade. If you miss one test, then that test grade will be dropped. The final exam cannot be given early. Please be sure that your travel plans do not conflict with the exam schedule. If you miss the final exam due to a documented illness or emergency, then I can give you a grade of incomplete (I) and you will have to make up the final by the deadline set by the University.
  • Honor System: You can collaborate on homework, but not on tests and exams. Any instance of cheating is considered an honor offence and is dealt with according to University policy.
  • In addition to the required homework assignments, you are expected to work lots of extra problems for practice.
  • Last Day to Withdraw: March 21. (Withdrawing means your transcript lists a "W" for the course, and you do not get credit for it.)
Read the VCU policies on the course web page. They apply to all students in this course.