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Unit - 1 Set Theory

Unit – 1Set Theory Functions and Natural Numbers

1.1 Set Theory Introduction

1.2 Combination of sets

1.3 Multisets

1.4 Ordered pairs

1.5 Proofs of some general identities on sets

1.6 Relations Definition Operations on relations Properties of relations

1.7 Composite Relations

1.8 Equality of relations

1.9 Recursive definition of relation

1.10 Order of relations

1.11 Functions Definition Classification of functions Operations on functions

1.12 Recursively defined functions

1.13 Growth of Functions

1.14 Natural Numbers Introduction

1.15 Mathematical Induction

1.16 Variants of Induction

1.17 Induction with Nonzero Base cases

1.18 Proof Methods Proof by counter – example

1.19 Proof by contradiction

Unit - 2 Algebraic Structures

Unit 2Algebraic Structures

2.1 Definition

2.2 Groups

2.3 Subgroups and order

2.4 Cyclic Groups

2.5 Cosets

2.6 Lagranges theorem

2.7 Normal Subgroups

2.8 Permutation and Symmetric groups

2.9 Group Homomorphisms

2.10 Definition and elementary properties of Rings and Fields

Unit - 3 Lattices

Unit 3Lattices

3.1 Lattices Definition

3.2 Properties of lattices – Bounded Complemented Modular and Complete lattice

3.3 Boolean Algebra Introduction

3.4 Axioms and Theorems of Boolean algebra

3.5 Algebraic manipulation of Boolean expressions

3.6 Simplification of Boolean Functions

3.7 Karnaugh maps

3.8 Logic gates

3.9 Digital circuits and Boolean algebra

Unit - 4 Propositional Logic

Unit – 4Propositional and Predicate Logic

4.1 Propositional Logic Proposition well formed formula Truth tables Tautology Satisfiability Contradiction Algebra of proposition Theory of Inference

4.2 Predicate Logic First order predicate well formed formula of predicate quantifiers Inference theory of predicate logic

Unit - 5 Trees And Graphs

Unit 5Trees Graphs and Combinatorics

5.1 Trees Definition

5.2 Binary tree

5.4 Binary search tree

5.5 Graphs Definition and terminology

5.6 Representation of graphs

5.7 Multigraphs

5.8 Bipartite graphs

5.9 Planar graphs

5.10 Isomorphism and Homeomorphism of graphs

5.11 Euler and Hamiltonian paths

5.12 Graph coloring

5.13 Recurrence Relation Generating function

5.14 Recursive definition of functions

5.15 Recursive algorithms

5.16 Method of solving recurrences

5.17 Combinatorics Introduction Counting Techniques

5.18 Pigeonhole Principle

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