Mathematics 471-2, 671-2
Abstract Algebra I, II  
(3 credit hours each)

Teacher:
Dr. Caldwell, office 429 Holt Humanities, phone 7336.  Department office 7360.  Email: caldwell@utm.edu.
Comments:
This course and the course text are intentionally difficult. Mathematics 461-2, 471-2 and 481-2 are the capstone courses for our undergraduate major and are important transition courses for those students continuing on to graduate school.  Plan to work hard, and in return, to mature mathematically.  Suggestions: (1) Do the homework!  (2) Study with a friend (make a new friend if necessary).  (3) Use other text books as references.  (4) Stay ahead of the class in the text (we will move through it sequentially, skipping some of the optional sections but we will not "hop around").  (5) Come by my office (make appointments as necessary).  I want you to succeed and will gladly help you.  (6) Do the homework!  To help you learn (and to motivate you to keep up) we will try to do a lot of board work (student proofs in class on the board).
Prerequisites:
Discrete Mathematics (Math 314) and Linear Algebra (Math 310)
Catalog Description:
Equivalence relations and partitions. Properties of the integers. Elementary theory of groups, rings; polynomial rings, integral domains,.divisibility, unique factorization domains, fields, vector spaces and linear transformations. Students are required to submit written work and make an oral presentation.
Grade:
The course grade will be a weighted average of the homework, tests, final, board-work and, for the 671-2 students, a research project. 

BRIBES (of the student, the teacher is unbribable):
    1%  for each solution on the Virginia Tech. Competition
    1%  for attempting each half of the Putnam Competition.
    3%  for each apparently correct solution on the Putnam.

Homework:
Homework will be assigned and collected daily (at the beginning of the following class period).  No late homework will be accepted.  Much of the homework will be from the text, but we will augment the text wherever necessary.   If you will miss a day, ask ahead of time what the homework will be.
Departmental
Objectives:
The student will:
  1. Understand and apply knowledge of basic set theory, mappings, properties of integers, and mathematical induction.
  2. State and apply Lagrange's theorem, Cauchy's theorem, and the homomorphism theorems.
  3. Distinguish the similarities and differences among various types of groups.
  4. Identify and compare the properties of rings, ideals, quotient rings, integral domains, principal ideal domains, unique factorization domains, and fields.
  5. Investigate various properties of factor groups and direct products.
  6. Understand the relationships among polynomial rings, roots of polynomials, and field extensions.
Text:
Contemporary Abstract Algebra, by Joseph A. Gallian, Sixth Edition, published by Houghton-Mifflin