Math 462, Abstract Algebra II

Spring Semester, 2005

Icosahedron Projection
Instructor:
Erol Barbut
Office:
 
Neill 301 (WSU)
Phone: 
509-335-4122
e-mail: 
ebarbut@uidaho.edu
Office Hours:
TuTh 10:30-11:30, 3:00 -4:00
(Pacific time)

Phone: (509) 335-4122 or 1-800-824-2889, press 0, and then 335-4122
FAX: (208) 885-6165 or (208) 885-5843 (math department)

Address:    Mathematics
                 PO Box 441103
                 Moscow, ID 83844 -1103


Text: John B. Fraleigh, Abstract Algebra, Sixth edition. 
Addison Wesley, Publishers, 1999
ISBN 0-201-33596-4

Prerequisites:  Math 461 and at least one of
the following: Math 215, 286, 330, 390. For description of these courses, please follow the link to The University of Idaho Catalog.

Goals of the course: Our main goal is to learn about the power of mathematical abstraction, as applied to the study of rings of polynomials, fields and their applications. In this context we will solve some age-old problems that have challenged many keen minds for hundreds of years, namely we will prove that it is impossible to trisect an arbitrary angle using only a straight-edge and compass, and that it is impossible to give a formula to find the roots of a general polynomial of degree 5.


Grading:   10 homework assignments:                 100 pts 
                    3 hour exams:                                300 pts 
                    Final exam:                                    200 pts 

Homework assignment #N will be due on lecture day marked HW#N. 

We will cover chapters 5, 6, 8 and 9 of the text. Our principal objects of study are rings and fields, with the goal of solving the ancient problem of  ruler and compass constructions and  to introduce  Galois Theory, which addresses the problem of  finding roots of polynomials by radicals. What is meant by this will be made clearer during the course. I look forward to having fun and showing some great mathematics in the process. 

For an interesting account of the history of solving for roots of polynomial equations, click here.

This link is to a page of a popular Web site on the history of mathematics.

This link contains an interesting account of squaring the circle and angle trisection using Archimedes' Spiral.

Another interesting site is http://mathworld.wolfram.com. In this site you will find the definitions of many of the concepts we have seen plus a rich set of additional information well worth exploring.

 


Daily Syllabus and Homework Assignments