Syllabus Virginia Commonwealth University Algebraic Structures and Functions MATH 504 SECTION 001 Spring 2014 Tues. Thurs. 9:30–10:45 Harris 4145

 INSTRUCTOR: 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 E-mail: rhammack@vcu.edu Thursday 12:30–2:30 Course web page: www.people.vcu.edu/~rhammack/Math504/ and by appointment

PREREQUISITES:
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.
• 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.

Tests:
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.