Fundamentals of Algebra for Computer Science

Instructor: Dr. Debrup Chakraborty


Lecture Timings




1600 hrs to 1800 hrs


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:


Grading Policies

We will have four home works (60%), two tests (40%)


Practice Problems

Problem set 1 (To be discussed on Oct, 2)


Home works

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)


Schedule (Tentative)

Aug 28



Aug 30

Relations and Equivalence Relations


Sep 4



Sep 6



Sep 11

Groups: Introduction


Sep 13



Sep 18



Sep 20

Normal Subgroups


Sep 25

Group Homomorphism


Sep 27

Permutation Groups


Oct 2



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!!