Math 81
Galois Theory and related topics
Last updated May 31, 2008 12:24:47 EDT

## 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
1/6   Introduction
1/9 (x-hour) 7.5, 15.4 Localization and field of fractions
1/10 13.1 Localization, characteristic, prime fields
1/13 13.1, 13.2 Finite extensions; simple extensions
1/15 13.2 Algebraic Extensions
1/17 13.2 Algebraic Extensions
1/20   No Class: Martin Luther King Day
1/22 13.2, 13.3 Compass and Straightedge constructions
1/23 (x-hour) 13.3, 13.4 Splitting Fields
1/24 13.4, 13.6 Splitting Fields, cyclotomic polynomials
1/27 13.4, 13.6 Algebraic Closures and uniqueness
1/29 13.5 Separable and Inseparable Extensions
1/31 13.5 Separable and Inseparable Extensions
2/3 14.1 Automorphism groups of fields
2/3   Approximate Date of Midterm Exam
2/5 14.1 Fixed fields and automorphism groups
2/6 (x-hour) 14.1 Fixed fields and automorphism groups
2/10 14.2 Fundamental Theorem of Galois Theory
2/12 14.2 Fundamental Theorem of Galois Theory
2/14 14.2 Fundamental Theorem of Galois Theory
2/17 14.2 Fundamental Theorem of Galois Theory
2/19 14.2 Fundamental Theorem of Galois Theory
2/21 14.3, 14.4 Finite Fields, Composite Extensions
2/24 14.4 Composite and Simple extensions
2/26 14.5 Cyclotomic and abelian extensions
2/28 14.5 Finite abelian groups are galois groups
3/3 14.6 Galois groups of polynomials
3/5 14.6 Galois groups of polynomials
3/7 14.6 Galois groups of polynomials: degrees 2, 3, 4

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