MODERN ALGEBRA
MAT 2031, Fall 2008
Instructor: Dr. Leslie Hayes
Office: 237 Barbelin
Office Hours: Tue. & Wed. 10:30-11:30, Fri. 10:30-12:00
(and by appointment)
Office Phone: (610) 660–1504
E-mail: [email protected]
Course web-page: http://www.sju.edu/~lhayes/algebra
About this Course : “Modern” or “abstract” algebra bears little resemblance to high school algebra. In
this course we will study algebraic structures known as groups, rings, and fields (sets together with an
operation or two and some nice properties). These basic structures are fundamental to almost all branches
of mathematics and to many other diverse fields of study (physics, chemistry, computer science, etc.). This
course will also focus on understanding and writing proofs.
Course Objectives:
1. To become familiar with the important examples of groups, rings, and fields.
2. To be able to state definitions precisely and to construct clear, rigorous proofs of fundamental
properties of groups, rings, and fields.
3. To understand the concept of homomorphisms as structure-preserving maps and to be able to use
such maps to show when two algebraic structures are in fact isomorphic.
Text: Contemporary Abstract Algebra, Sixth Edition, by Joseph A. Gallian, Houghton Mifflin, 2006. To
survive this course you must read the textbook. The good news is that I think you’ll find this book a
pleasure to read. You should read the appropriate portion of the text – pencil in hand - before each lecture.
Make notes in it. Mark where you have questions and be sure to ask me about them, in class or in office
hours.
Homework: There will be weekly homework assignments. To obtain full credit please:
DO NOT TURN IN A FIRST DRAFT! Rewrite each problem (perhaps several times!) after
discovering how to do it.
WRITE EACH PROBLEM UP BY YOURSELF (see section on academic honesty below)
Write on one side of the page only.
Skip at least two lines between each problem.
Staple it all together and cut off any jagged edges.
Please see me in office hours when you need help with the homework. Homework problems will typically
be graded on a four-point scale as follows:
A=4 Clearly written and perfect or possibly a minor error only.
B=3 Only minor errors.
C=2 Some essential ideas, but significant pieces missing.
D=1 A start, but essential ideas are missing; poorly written.
F=0 Blank or nothing worth credit.
Proof Writing: It takes a long time to learn to write mathematics well. This semester we will take time to
look at each other’s writing and talk about ways to improve it. When I grade your homework, I will
indicate places where you need to improve your mathematical writing. Initially, you will not lose points for
