MT 701 Combinatorics
1. Counting principles, arrangements and selections, arrangements and selection with
repetition, distributions, binomial identities
2. Generating function : Generating function models, calculating coefficients of
generating functions, partitions, exponential generating functions, a summation method.
3. Recurrence Relations : Recurrence relation models, divide and conquer relations,
solution of linear and inhomogeneous recurrence relation, solution with generating functions.
4. Inclusion-exclusion: Counting with Venn diagrams, inclusion – exclusion formula,
restricted positions and Rook polynomials.
Prescribed Book :
1. Alan Tucker, Applied Combinatorics (fourth edition), John Wiley & sons , New York
sections 5.1-5.6, 6.1-6.5, 7.1-7.5, 8.1-8.3.
Reference books :
1.V. Krishnamurthy, Combinatorial, Theory and Applications, East West Press, New
Delhi (1989) Scientific, (1996)
2.K.D. Joshi : Foundations of discrete mathematics,Wiley
3. Marshall Hall : Combinatorial theory ,Wiley.

MT 703 Functional Analysis

Hilbert spaces, operators on a Hilbert space, Banach spaces.

Prescribed book :

John B. Conway : A course in functional analysis. Springer (1997 ) Chapters 1,2,3.

MT 702 Field Theory

1. Field Extensions :

Basic Theory of Field Extensions

Algebraic Extensions

Classical Straightedge and Compass Constructions

Splitting Fields and Algebraic Closures

Separable and Inseparable Extensions

Cyclotomic Polynomials and Extensions

2. Galois Theory :

Basic Definitions

The Fundamental Theorem of Galois Theory

Finite Fields

Galois Groups of Polynomials

Solvable and Radical Extensions: Insolvability of the Quintic

Prescribed Book :

Dummit and Foote, Abstract Algebra, 2nd Edition, Wiley Eastern Ltd.

Chapters : 13.1 to 13.6

14.1 to 14.3, 14.6 , 14.7 (statements only)

Reference Books :

1. O. Zariski and P. Sammuel, Commutative Algebra, Vol. 1, Van Nostrand.

2. P. Bhattacharya and S. Jain, Basic Abstract Algebra, Second Edition,

Cambridge University Press.


           MT 704 Graph Theory

Paths and cycles, trees, planarity, coloring, digraphs, matchings, marriage and Mengers theorem.

Prescribed Book :

R. J. Wilson, Introduction to graph theory, Pearson, (2003) Chapters 1 – 8.

MT – 706  Cryptography


Unit 1 :  Cryptography

Some simple cryptosystems,Enciphering matrices


Unit  2 :  Public Key

The idea of public key cryptography, RSA,Discrete log ,

              Knapsack, Zero- knowledge protocols and oblivious transfer


Unit 3:  Primality and Factoring

Pseudoprimes, The rho method, Fermat factorization and factor

bases, The continued fraction method,The quadratic sieve



Unit 4:  Elliptic curves

Basic facts, Elliptic curve cryptosystems, Elliptic curve

             primality test, Elliptic curve factorization


Unit 5:  Problem solving using ‘SAGE- Free Open Source Software’


Text Book: A course in Number Theory and cryptography, Neal Koblitz

Springer, second edition.


Chapters : 3 , 4 , 5, 6


Reference Books:1. Introduction to Modern Cryptography
Jonathan Katz and Yehuda Lindell
Publisher: Chapman & Hall/CRC
               2. Handbook of Applied Cryptography,

A. Menezes, P. van Oorschotand S. Vanstone,
 CRC Press
                3. Invitation to Cryptology,  Barr,  Prentice Hall

Extra Credit course on Scilab and Latex.