Instructor: Dr. Debrup Chakraborty
Day 
Time 
Monday 
1600 hrs to 1800 hrs 
Wednesday 
1200 hrs to 1400 hrs 
Willingness
to read and write proofs.
This course
will deal with basic algebraic structures like groups, rings, fields and vector
spaces. Specific problems related to applications of such algebraic structures
in certain problems of computer science will be explored. Specifically, we plan
to explore some elementary coding theory. This can give you a good background
for future courses like Computational Arithmetic and Cryptography and
Coding.
The
textbook for the course will be:
Topics in Algebra, by I.N. Herstein
We shall
also refer to some parts of:
A Computational Introduction to Number Theory
and Algebra by V. Shoup
(This book
is available online at: http://www.shoup.net)
We will
have four home works (60%), two tests (40%)
Problem set 1 (To be discussed on Oct, 2)
Home work 1 (Due on Sept, 27)
Home work 2 (Due on Nov, 8)
Home work 3 (Due on Nov, 20)
Home work 4 (Due on Dec, 5)
Aug 28 
Sets 

Aug 30 
Relations
and Equivalence Relations 

Sep 4 
Functions 

Sep 6 
Integers 

Sep 11 
Groups:
Introduction 

Sep 13 
Supgroups 

Sep 18 
Cosets 

Sep 20 
Normal
Subgroups 

Sep 25 
Group
Homomorphism 

Sep 27 
Permutation
Groups 

Oct 2 
Congugacy 

Oct 4 
Sylows
Theorems 

Oct 9 
Introduction
to Coding Theory 

Oct 11 
Test 1 

Oct 16 
Rings and
fields: Introduction 

Oct 18 
Basic
properties of Rings and Fields 

Oct 23 
Ring
Homomorphism and Quotient rings 

Oct 25 
Polynomial
Rings 

Oct 30 
Polynomial
Rings 

Nov 1 
Vector
Spaces 

Nov 6 
Vector
Spaces 

Nov 8 
Extension
Fields 

Nov 13 
Finite
Fields 

Nov 15 
More
number theory: Quadratic Residues 

Nov 20 
More
about primes: Primality Testing 

Nov 22 
Test 2 

Nov 27 
Review
and ending!! 
