abstractalgebra
Abstract Algebra (IISER, Pune)
MTH 311 August-November 2008
References:
Abstract Algebra : Dummit and Foote
Algebra : Lang
Topics in Algebra : Herstein
Algebra : Hungerford
Advanced Linear Algebra : Roman
Further Linear Algebra : Blyth & Robertson
Course Content :
Definitions of Group, Homomorphisms etc. and Examples
Quotient Groups
Group Actions, Cayley's Theorem
Direct and Semidirect Products
Sylow's Theorem and the structure of Abelian Groups
Linear Algebra
Classical Groups
Instructor : Anupam Singh
Course : Undergraduate course, no prerequisites.
Schedule : Monday, Tuesday and Wednesday (9:00 to 10:00 AM)
Place : Room Number 215
Grading Method : Every week we will have 2 lectures and a tutorial (problem solving session) which will be an important part of grading.
There will be 4 exams (including mid-sem and end-sem) and a project (twice presentation during the semester). There will be 30% weightage for the project. Exams will count 15% each and rest of it will depend on your class performance (being enthusiastic about class, solving assignments etc.). TO GET AN "A" OR TO GET AN "F" YOU WILL HAVE TO WORK HARD.
Reading Material : We will follow mostly the book by Dummit and Foote. Occassionaly we will do exercises from other books.
All assignments put together.
Calendar:
04/08/08 definition of groups, examples
05/08/08 examples
06/08/08 examples
11/08/08 Tutorial Assignment 1
12/08/08 Lagrange's Theorem
13/08/08 Examples
18/08/08 Tutorials
19/08/08 Normalizers, Centralizers and Normal Subgroups
20/08/08 The group Q/Z, symmetric groups and alternating groups
25/08/08 Tutorial Assignment 2
26/08/08 Quotient Group
27/08/08 Quotient Groups and Examples
01/09/08 Tutorial
02/09/08 Classification of finite simple groups - a story
03/09/08 Holiday for Ganesh Chaturthi
08/09/08 TEST 1
09/09/08 Tutorial Projects for the course
10/09/08 Group Actions
15/09/08 Tutorial Assignment 3
16/09/08 Calculating Conjugacy Classes in various groups
17/09/08 Group action and X/G
22/09/08 Tutorial
23/09/08 Cayley's Theorem
24/09/08 Class Equation
29/09/08 Sylow's Theorem
30/09/08 No Class (exam preparation leave)
01/10/08 Exam & Assignment 4
06/10/08 vacation
07/10/08 vacation
08/10/08 vacation
13/10/08 Project presentation Sylow's Theorem
14/10/08 Project presentation
15/10/08 Project presentation
20/10/08 Fields and Vector Spaces
21/10/08 Linear Transformation Assignment 5
22/10/08 The Groups GL_n and SL_n
27/10/08 Holiday for Diwali
28/10/08 Holiday for Diwali
29/10/08 No Class (Extra Class on 31/10/08)
03/11/08 Tutorial + extra Tutorial
04/11/08 Conjugacy Classes in Aut(V) and GL_n(F)
05/11/08 Eigen Values, Eigen Vectors and Canonical Forms
10/11/08 Tutorial Assignment 6
11/11/08 Diagonalisation
12/11/08 Jordan Canonical Form
17/11/08 Project Presentation
18/11/08 Project Presentation
19/11/08 Project Presentation
24/11/08 Exam week All Questions
25/11/08 Exam Week
26/11/08 Exam Week