Biju Patnaik University of Technology, Odisha, Computer Engineering Semester 4, Discrete Mathematics Syllabus

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Unit - 1 Sets and Propositions

1.1 Principle of Inclusion and Exclusion

1.2 Mathematical induction

1.3 Propositions

1.4 Logical Connectives

1.5 Conditionals and Biconditionals

1.6 Logical Equivalences

1.7 Predicate Calculus

1.8 Quantifiers

1.9 Theory of inference

1.10 Methods of proof

Unit - 2 Relations and Functions

2.1 Properties of binary relations

2.2 Closure of relations

2.3 Warshall’s algorithm

2.4 Equivalence relations

2.5 Partial ordering relations

2.6 Lattices Chains and antichains

2.7 Functions

2.8 Composition of Functions

2.9 Invertible Functions Recursive Functions

2.10 Pigeonhole principle

Unit - 3 Numeric Functions and Generating Functions

3.1 Discrete Numeric functions

3.2 Generating Functions

3.3 Recurrence Relations and Recursive Algorithms

3.4 Linear recurrence relations with constant coefficients

3.5 Solution of recurrence relations by the method of generating functions

3.6 Divide and conquer algorithms

Unit - 4 Groups and Rings

4.1 Groups and subgroups

4.3 Codes and Group codes Error detection and correction using Group codes

4.4 Isomorphism

4.5 Homomorphism and normal subgroups

4.6 Rings Integral domains and Fields

4.7 Boolean Algebras

4.8 Lattices and algebraic systems

4.9 Principle of duality

4.10 Distributive and complemented lattices

4.11 Boolean functions and Boolean expressions

4.12 Simplification of logic expressions using Karnaugh Map

4.13 Design and Implementation of Digital Networks Switching Circuits

Unit - 5 Graphs and Trees

5.1 Basic terminology

5.2 Digraphs and relations

5.3 Representation of Graphs

5.4 Operations on graphs

5.5 Paths and circuits

5.6 Graph traversals

5.7 Shortest path in weighted graphs

5.8 Eulerian paths and circuits

5.9 Hamiltonian paths and circuits

5.10 Traveling sales person’s problem

5.11 Planar graphs

5.12 Graph Coloring

5.13 Trees

5.14 Rooted trees

5.15 Binary search trees

5.16 Spanning trees

5.17 Minimum spanning trees

5.18 Kruskal’s Algorithm

5.19 Prim’s Algorithm

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Other Subjects of Semester-2
Constitution of india
Organisational behaviour
Analog electronic circuits
Design and analysis of algorithms
Microprocessor and microcontroller
Computer organization and architecture
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