Math 81
Winter 2005

Galois Theory and related topics
Last updated May 31 2008 12:24:47

## Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

Lectures Sections in Text Brief Description
1/5 Ch 7 - 9 Introduction, quotient rings and ideals
1/7 13.1 Prime and maximal ideals and quotients
1/8   No special day of classes
1/10 13.1 Characteristic, prime fields, finite extensions
1/12 13.1, 13.2 Finite extensions; simple extensions
1/14 13.2 Algebraic Extensions
1/17   No Class: Martin Luther King Day
1/19 13.2 Algebraic Extensions
1/20 (x-hour) 13.2 Algebraic Extensions
1/21 13.3 Compass and Straightedge constructions
1/24 13.4, 13.6 Splitting Fields, cyclotomic polynomials
1/26 13.4, 13.6 Algebraic Closures and uniqueness
1/28 13.4. 13.6 Algebraic Closures and uniqueness
1/31 13.5 Separable and Inseparable Extensions
2/2 13.5 Automorphism groups of fields
2/2   Midterm Exam distributed (due 2/9)
2/4 14.1 Fixed fields and automorphism groups
2/7 14.1 Fixed fields and automorphism groups
2/9 14.2 Fundamental Theorem of Galois Theory
2/10 (x-hour) 14.2 Fundamental Theorem of Galois Theory
2/11 14.2 Carnival Holiday
2/14 14.2 Fundamental Theorem of Galois Theory
2/16 14.2 Fundamental Theorem of Galois Theory
2/18 14.2 Fundamental Theorem of Galois Theory
2/21 14.3, 14.4 Finite Fields, Composite Extensions
2/23 14.4 Composite and Simple extensions
2/25 14.5 Cyclotomic and abelian extensions
2/28 14.5 Finite abelian groups are galois groups
3/2 14.6 Galois groups of polynomials
3/4 14.7 Galois groups of polynomials
3/7 14.6 Galois groups of polynomials: degrees 2, 3, 4
3/9 14.8 Wrap it up

Thomas R. Shemanske
Last updated May 31 2008 12:24:47