**MA3354**

**DISCRETE
MATHEMATICS**

**COURSE
OBJECTIVES: **

•
To extend student’s logical and mathematical maturity and ability to deal with
abstraction.

•
To introduce most of the basic terminologies used in computer science courses
and application of ideas to solve
practical problems.

•
To understand the basic concepts of combinatorics and graph theory.

•
To familiarize the applications of algebraic structures.

•
To understand the concepts and significance of lattices and boolean algebra
which are widely used in computer
science and engineering.

**UNIT
I LOGIC AND PROOFS **

Propositional
logic – Propositional equivalences - Predicates and quantifiers – Nested quantifiers
– Rules of inference - Introduction to proofs – Proof methods and
strategy.

**UNIT
II COMBINATORICS**

Mathematical
induction – Strong induction and well ordering – The basics of counting –
The pigeonhole principle – Permutations
and combinations – Recurrence relations – Solving linear recurrence relations – Generating functions –
Inclusion and exclusion principle and its applications.

**UNIT
III GRAPHS **

Graphs
and graph models – Graph terminology and special types of graphs – Matrix
representation of graphs and graph
isomorphism – Connectivity – Euler and Hamilton paths.

**UNIT
IV ALGEBRAIC STRUCTURES**

Algebraic
systems – Semi groups and monoids - Groups – Subgroups – Homomorphism’s –
Normal subgroup and cosets – Lagrange’s
theorem – Definitions and examples of Rings and Fields.

**UNIT
V LATTICES AND BOOLEAN ALGEBRA**

Partial
ordering – Posets – Lattices as posets – Properties of lattices - Lattices as
algebraic systems – Sub lattices –
Direct product and homomorphism – Some special lattices – Boolean algebra –
Sub Boolean Algebra – Boolean
Homomorphism.

**COURSE
OUTCOMES: **

At
the end of the course, students would :

CO1:Have
knowledge of the concepts needed to test the logic of a program. CO2:Have an
understanding in identifying structures on many levels.

CO3:Be
aware of a class of functions which transform a finite set into another finite
set which relates to input and output
functions in computer science.

CO4:Be
aware of the counting principles.

CO5:Be
exposed to concepts and properties of algebraic structures such as groups,
rings and fields.

**TEXT
BOOKS: **

1.
Rosen. K.H., "Discrete Mathematics and its Applications", 7th
Edition, Tata McGraw Hill Pub. Co. Ltd.,
New Delhi, Special Indian Edition, 2017.

2.
Tremblay. J.P. and Manohar. R, "Discrete Mathematical Structures with
Applications to Computer Science",
Tata McGraw Hill Pub. Co. Ltd, New Delhi, 30th Reprint, 2011.

**REFERENCES:
**

1.
Grimaldi. R.P. "Discrete and Combinatorial Mathematics: An Applied Introduction", 5thEdition, Pearson Education Asia, Delhi,
2013.

2.
Koshy. T. "Discrete Mathematics with Applications", Elsevier
Publications, 2006.

3.
Lipschutz. S. and Mark Lipson., "Discrete Mathematics", Schaum’s
Outlines, Tata McGraw Hill Pub. Co. Ltd.,
New Delhi, 3rd Edition, 2010.