Savitribai Phule Pune University, Maharashtra (SPPU), Information Technology Semester 3, Discrete Mathematics Syllabus

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Unit - 1 Sets And Propositions

UNIT1

Sets and Propositions

1.1 Sets Sets combinations of sets Venn diagram Finite and infinite sets countable sets multisets

1.2 Principal of inclusion and exclusion

1.3 Mathematical induction

1.4 Propositions Propositions logical connectives conditional and Biconditional proposition

1.5 Logical equivalences

1.6 Validity of arguments by using truth tables

1.7 Predicates quantifiers and normal forms

1.8 Application of sets and propositions

Unit - 2 Combinatorics And Discrete Probability

UNIT2

Combinatorics and discrete probability

2.1 Rules of sum and product permutations and combinations

2.2 Discrete probability

2.3 Conditional probability

2.4 Bayes theorem

2.5 Information and mutual information

2.6 Application of combinatorics and discrete probability

Unit - 3 Graph Theory

UNIT3

Graph theory

3.1 Graphs Basic terminology multigraphs Weighted Graphs Sub Graphs Isomorphic graphs Complete Graphs Regular Graphs Bipartite Graphs

3.2 Operations on Graphs Paths Circuits.

3.3 Hamiltonian and Eulerian graphs Travelling Salesman Problem Factors of Graphs Planar Graphs Graph Colouring

3.4 Trees Tree Terminologies Rooted Trees Path Length in Rooted Trees Prefix Codes Spanning Trees

3.5 Fundamental Cut Sets and Circuits Max flow –Min Cut Theorem Transport Network

3.6 Applications of Graph Theory.

Unit - 4 Relations And Functions

UNIT4

RELATIONS AND FUNCTIONS.

4.1 Relations

4.2 Functions

4.3 Recurrence relations

Unit - 5 Introduction To Number Theory

UNIT5

INTRODUCTION TO NUMBER THEORY.

5.1 Properties of divisibility.

5.2 Division Algorithm.

5.3 Greatest common divisor and its properties.

5.4 Euclidean Algorithm and Extended Euclidean Algorithm.

5.5 Prime factorization theorem.

5.6 Congruence relation.

5.7 Modular Athematic.

5.8 Euler’s phi function and Euler’s theorem.

5.9 Fermat’s little theorem.

5.10 Additive and Multiplicative Inverses.

5.11 Chinese Reminder theorem.

Unit - 6 Algebraic structures

UNIT6

Algebraic structures.

6.1 Introduction to semigroup Monoid.

6.2 Group and Abelian group.

6.3 Permutation groups and cosets.

6.4 Normal subgroup.

6.5 Codes and group codes.

6.6 Ring Integral Domain Field.

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Other Subjects of Semester-1
Basics of computer network
Data structure & algorithms
Object-oriented programming
Logic design & computer organization
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