# Discrete Mathematics 2007

**Debrup
Chakraborty**

We shall review some basic combinatorial objects and techniques to
manipulate such objects in this course. No previous background would be
assumed.

The course notes would be posted in this webpage as the course progress.
The course notes would be sufficient for this course. There exist numerous nice
books which covers the topics that would be discussed in this course. Some of
them are:

*1)
**A first Course in
Combinatorial Mathematics by IAN ANDERSON*

*2)
**Introduction to
Combinatorial Mathematics by C.L. LIU*

*3)
**Applied
Combinatorics by FRED ROBERTS*

*4)
**Modern Graph Theory
by BÉLA BOLLÓBAS*

## Class Schedule

We shall
meet at 8:00 AM on Mondays and Wednesdays in the class room in the first floor.

### Grading

50% on home
work and 50% on two tests.

## Tenatative topics to be
covered

1)
**Preliminaries**

a) Sets, Relations and Functions (notes)

b) Integers (notes)

c) Infinite Sets: An introduction (notes)

d) Mathematical Induction

2)
**Combinatorics**

a) Basic Counting Techniques:
Permutations and Combinations

b) Generating Functions

c) Recurrence Relations

d) Inclusion Exclusion Principle

e) Polya’s Theory

3)
**Graph Theory**

a) Connectedness

b) Paths

c) Trees and Spanning Trees

d) Graph Coloring

e) Planer Graphs