galoistheory
Galois Theory (IISER,Pune)
MTH321 January-April 2009
Topics covered:
Introduction to Rings
Field Extensions
Finite Extension and Algebraic Extension
Separable and Inseparable Extensions
Splitting Field and Normal Extension
Galois Extensions
Main Theorem of Galois Theory
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 :
Algebra : Lang
Abstract Algebra : Dummit and Foote
Field Theory : Roman
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.
Avi Prasanna - Origami
Navi Prasad - Ring of Integers
Lakshmi Priya - Inverse Galois Problem
Rajesh Yadav - Constructibility of n-gon and Fermat's Prime
Gaurav - Polynomials over finite field
Ruchi Gupta - Luroth's Theorem
Ankur Gupta - Straightedge and Compass constructions
Kapil - Solving Equations by Radicals
Arvind - Division Rings