Course Objectives:
The objectives of the course include teaching the students the concepts of Fourier Series, Fourier
and Laplace Transforms and their applications in the physical world.The course also introduces the
concept of groups which is very useful in studying symmetry of molecular structures.
Text Books:
1. A text book of Engineering Mathematics, by N.P Bali, Manish Goyal,Lakshmi publications,
Eighth edition
2. Algebra, Abstract and Modern, by Swamy U.M , Murthy, Pearson publications
Text books: 1. John Clark Derek Allen Holton - A first look at graph theory, Allied Publishers
2. David M Burton - Elementary Number Theory 6th Edition TMH
3. Vijay K. Khanna - Lattices and Boolean Algebras- First Concepts, Vikas Publishing
House Pvt Ltd.
Module I : Graph Theory (40Hrs)
An introduction to graph. Definition of a Graph, Graphs as models, More definitions, Vertex Degrees, Sub graphs, Paths and cycles The matrix representation of graphs (definition & example only) (Section 1.1 to 1.7 of text 1) Trees and connectivity. Definitions and Simple properties, Bridges, Spanning trees, Cut vertices and connectivity. (Section 2.1, 2.2, 2.3 & 2.6 of text 1)
Module 2 (20 Hrs) Euler Tours and Hamiltonian Cycles .Euler’s Tours, The Chinese postman problem .Hamiltonian graphs, The travelling salesman problem, Matching and Augmenting paths, Hall`s Marriage Theorem-statement only, The personnel Assignment problem, The optimal Assignment problem (Section 3.1(algorithm deleted) 3.2(algorithm deleted), 3.3, 3.4 (algorithm deleted)) Matching (Section 4.1,4.2 4.3(algorithm deleted),4.4 (algorithm deleted) of text 1
Module 3:
Introduction to Cryptography (15 Hrs)
From Caesar Cipher to Public key Cryptography, the Knapsack Cryptosystem
(Section 10.1, 10.2 only of text 2)
Module 4:
Poset and Lattices (15 Hrs)
Diagramatical Representation of a Poset, Isomorphisms, Duality, Product of two Posets,
Lattices, Semilattices, Complete Lattices, Sublattices.
( Chapter 2 of text 3 )
This is Round 1 of the quiz competition and the questions are objective in nature. Each correct answer carries 3 marks and a wrong answer will entail a negative mark (-1).
1)To give a brief idea about the applications of Differentiation and integration.
2) To get an idea about partial differentiation, chain rule and optimization in multivariable
functions.
3) To find the area and volume of regions in 2 and 3 dimensional space.
4) To get a brief idea of polar coordinates and their outcomes.
The first part of this course deals with various methods of solving polynomial equations. The second part deals with the theory of matrices and their applications.