Rashtrasant Tukadoji Maharaj Nagpur University, Maharashtra, Artificial Intelligence Semester 3, Discrete Mathematics and Graph Theory Syllabus

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Unit - 1 Set Theory, Relations and Functions

Unit 1

Set theory relations and functions

1.1 Sets Review of propositions and logical operations

1.2 Principal of mathematical induction

1.3 Review of sets types and operations on sets

1.4 Relations Ordered pairs and ntuples types of relations composite relation

1.5 Transitive closure of a relation partially ordered set Hasse diagram

1.6 Functions Definition composition of functions types of functions

1.7 Characteristic function and its properties

Unit - 2 Fuzzy Set and Fuzzy Logic

Unit 2

Fuzzy set and fuzzy logic

2.1 Fuzzy sets and system crisp set

2.2 Operations and combinations on fuzzy sets

2.3 Relation between crisp sets and fuzzy sets

2.4 Fuzzy relations Overview of fuzzy logic and classical logic

Unit - 3 Group Theory and Ring Theory

Unit 3

Group theory and ring theory

3.1 Binary operation algebraic structure

3.2 Groupoid Semigroup monoid group subgroup normal subgroup only def. And examples

3.3 Ring commutative ring ring with unity

3.4 Zero divisor integral domain fieldonly def. And simple examples

Unit - 4 Graph Theory

Unit 4

Graph theory

4.1 Basic concept of graph theory diagraph basic definitions

4.2 Matrix representation of graphs subgraphs and quotient graphs

4.3 Isomorphic graphs paths and circuit

4.4 Reachability and connectedness node base Euler’s path Hamilton’s path

4.5 Tree binary tree undirected tree spanning tree weighted graphsOnly def. And simple examples

4.6 Minimal spanning tree by prim’s algorithm Kruskal’s algorithm

4.7 Representation of algebraic expressions by Venn diagram and binary tree

Unit - 5 Combinatorics

Unit 5

Combinatorics

5.1 Permutations and combinations

5.2 Pigeonhole principle with simple applications

5.3 Recurrence relations Concept and def only

5.4 Generating functions solution of recurrence relation using generating functions

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Other Subjects of Semester-3
Data structures
Operating systems
Digital circuits & microprocessor
Computer architecture & organization
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