MAT 463 -- Abstract Algebra I 
Course Information

Professor: D. Bradley

Website: http://www.umemat.maine.edu/faculty/bradley/index.html

The roots of modern abstract algebra can be traced back to the straight-edge and compass constructions studied by the Greeks in the 5th century B.C. Solutions to the problems of doubling a cube, trisecting an arbitrary angle, and squaring a circle using a straight-edge and compass awaited the arrival of the concept of a field extension, which came about 2200 years later. On the other hand, we owe the concept of a group to increasingly sophisticated attempts to solve polynomial equations in one variable, another problem with a fascinating history going back to the ancient Babylonians. Galois theory arose from ideas in the theory of groups and fields to tackle the problem of expressing the roots of a polynomial in terms of radicals.

In this course, the concrete classical problems (ruler and compass constructions, solving equations) will be the main unifying focus, from which the development of related results in abstract algebra will flow. I intend to work through a good portion of the text over the course of the semester. Grades will be based on regular attendance, in-class presentations, and written assignments related to the material discussed in the lectures. MAT 464 will follow in a similar spirit, with more emphasis on set theory and rings as opposed to groups and fields.

Text:

Charles Robert Hadlock, Field Theory and its Classical Problems, Carus Mathematical Monographs number 19, Mathematical Association of America, 1978. ISBN 0-88385-020-6

References:

• Robert H. Redfield, Abstract Algebra: A Concrete Introduction, Addison-Wesley, Boston, 2001.
• William J. Gilbert, Modern Algebra with Applications, John Wiley & Sons, New York, 1976.