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Demo university, Civil Engineering Semester 3, Mathematics III Syllabus

Mathematics III Lecture notes | Videos | Free pdf Download | Previous years solved question papers | MCQs | Question Banks| Syllabus

Unit - 1 Set Theory and Logic

1.1 Introduction and significance of discrete mathematics

1.2 SetsCantorian set theory axiomatic set theory set operations cardinality of sets principal of inclusion and exclusion

1.3 Types of sets Bounded and unbounded sets diagonalization argument countable and uncountable sets finite and infinite sets countably infinite and uncountably infinite sets power set

1.4 Propositional logic logic propositional equivalences application of propositional logic translating English sentences

1.5 Proof by mathematical induction and strong mathematical induction

Unit - 2 Relations and Functions

2.1 Relations and their properties

2.2 Nary relations and their applications

2.3 Representing relations Closures of relations

2.4 Partial orderings partitions Hasse diagram

2.5 Lattices chain and antichain

2.6 Transitive closure and Warshall’s algorithm

2.7 Functions Surjective injective bijective functions identity functions partial functions invertible function constant function inverse functions and composition of functions

2.8 The Pigeonhole principle.

Unit - 3 Counting

3.1 The basics of counting Rule of sum and product

3.2 Permutations and combinations

3.3 Binomial coefficients and identities

3.4 Generalized permutations and combinations

3.5 Algorithms for generating permutations and combinations.

Unit - 4 Graph Theory

4.1 Graph terminology and special types of graphs.

4.2 Representing graphs and Graph isomorphism connectivity.

4.3 Euler and Hamiltonpaths The Handshaking Lemma.

4.4 Single source shortest pathDijkstra’s Algorithm.

4.5 Planar Graphs Graph Coloring.

Unit - 5 Tree

5.1 Introduction

5.2 Properties of trees

5.3 Binary search tree

5.4 Tree traversal

5.5 Decision tree

5.6 Prefix codes and Huffman coding cut sets.

5.7 Spanning trees and Minimum spanning tree

5.8 Kruskal’s and Prim’s algorithms

5.9 The maxflowmin cut theorem Transport network