galoistheory

Galois Theory (IISER,Pune)

MTH321 January-April 2009

Topics covered:

    1. Introduction to Rings

    2. Field Extensions

    3. Finite Extension and Algebraic Extension

    4. Separable and Inseparable Extensions

    5. Splitting Field and Normal Extension

    6. Galois Extensions

    7. Main Theorem of Galois Theory

    8. Applications (mainly projects done by students)

This is a course offered during the semester January-April 2009 at IISER, Pune.

Instructor : Anupam Singh

Time : 3 hours a week

Grading Method : 3 exams and a project

References :

    1. Algebra : Lang

    2. Abstract Algebra : Dummit and Foote

    3. Field Theory : Roman

    4. Galois Theory : E. Artin

Prerequisite : MTH311 and/or approval of instructor

Things to brush up if you want to attend this course : Polynomial Rings, Rings and Ideals, Vector Spaces, Groups etc.

Assignment 1 07/01/2009

Projects for the course.

Test - I

Assignment 2 11/02/09

Assignment 3 19/02/09

Test - II 07/03/09

Assignment 4 30/03/09

Assignment 5 15/04/09

Test - III 28/04/09

Projects done by Students:

These are first draft of the presentations given by students. The written articels are not revised and corrected.

    1. Avi Prasanna - Origami

    2. Navi Prasad - Ring of Integers

    3. Lakshmi Priya - Inverse Galois Problem

    4. Rajesh Yadav - Constructibility of n-gon and Fermat's Prime

    5. Gaurav - Polynomials over finite field

    6. Ruchi Gupta - Luroth's Theorem

    7. Ankur Gupta - Straightedge and Compass constructions

    8. Kapil - Solving Equations by Radicals

    9. Arvind - Division Rings