Page 75 - CatalogNEP-PS

 Enhance the mathematical logical skills by learning different enumeration techniques.
 Be able to apply these techniques in solving problems in other areas of mathematics.
 Be trained to provide reasoning and arguments to justify conclusions.

THEORY: 45

UNIT - 1 Basics of Combinatorics (15 Hours)
Basic counting principles, Permutations and Combinations (with and without repetitions),
Binomial coefficients, Multinomial coefficients, Counting subsets of size k; Set-partitions, The
inclusion-exclusion principle and applications.

UNIT - 2 Generating Functions and Recurrence Relations (18 Hours)
Generating functions: Generating function models, calculating coefficients of generating
functions, Polynomial expansions, Binomial identity, Exponential generating functions.
Recurrence relations: Recurrence relation models, Divide-and-conquer relations, Solution of
linear recurrence relations, Solutions by generating functions.
UNIT – 3 Partition (12 Hours)
Partition theory of integers: Ordered partition, Unordered partition, Ferrers diagram, Conjugate of
partition, Self-conjugate partition, Durfee square, Euler‘s pentagonal theorem.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGESTED READINGS:

1. Sane, Sharad S. (2013). Combinatorial Techniques. Hindustan Book Agency (India).
2. Tucker, Alan (2012). Applied Combinatorics (6th ed.). John Wiley & Sons, Inc.
3. Brualdi, Richard A. (2009). Introductory Combinatorics (5th ed.). Pearson Education Inc.
4. Cameron, Peter J. (1994). Combinatorics: Topics, Techniques, Algorithms. Cambridge
University Press.

Math.222 Introduction to Graph Theory 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is to introduce:
 Problem-solving techniques using various concepts of graph theory.
 Various properties like planarity and chromaticity of graphs.
 Several applications of these concepts in solving practical problems.

LEARNING OUTCOMES:

This course will enable the students to:
 Good familiarity with all initial notions of graph theory and related results and
23. seeing them used for some real-life problems.
 Learning notion of trees and their enormous usefulness in various problems.
 Learning various algorithms and their applicability.
 Studying planar graphs, Euler theorem associated to such graphs and some
24. useful applications like coloring of graphs.

THEORY (45 Hours)

UNIT-I: Graphs, Types of Graphs and Basic Properties (12 Hours)

60