Set Theory , Relations , Functions , Natural numbers , Algebraic Structures , Partial order set , Boolean algebra , Propositional Logic , Predicate logic , Trees , Graphs , Recurrence Relation & Generating function , Combinatorics ,
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SYLLABUS

Unit-I

Set Theory: Introduction, Combination of sets, Multisets, Ordered pairs,Set Identities.

Relations: Definition, Operations on relations, Properties of relations, Composite Relations,

Equality of relations, Order of relations.

Functions: Definition, Classification of functions,Operations on functions, Recursively

defined functions.

Natural Numbers: Introduction, Mathematical Induction, Variants of Induction, Induction

with Nonzero Base cases.

Unit-II

Algebraic Structures: Definition, Groups, Subgroupsand order, Cyclic Groups,

Cosets,Lagrange's theorem, Normal Subgroups, Permutation and Symmetric groups, Group

Homomorphisms, Definition and elementary propertiesof Rings and Fields, Integers Modulo n.

Unit-III

Partial order sets: Definition, Partial order sets,Combination of partial order sets, Hasse

diagram.

Lattices: Definition, Properties of lattices – Bounded, Complemented, Modular and Complete

Lattice,Morphisms of lattices.

Boolean Algebra: Introduction, Axioms and Theorems of Boolean algebra, Algebraic

manipulation of Boolean expressions. Simplificationof Boolean Functions, Karnaugh maps,

Logic gates, Digital circuits and Boolean algebra. Combinational and sequential Circuits.

Unit-IV

Propositional Logic: Proposition, well formed formula, Truth tables, Tautology, Satisfiability,

Contradiction, Algebra of proposition, Theory of Inference ,Natural Deduction.

Predicate Logic: First order predicate, well formedformula of predicate, quantifiers, Inference

theory of predicate logic.

Unit-V

Trees : Definition, Binary tree, Binary tree traversal, Binary search tree.

Graphs: Definition and terminology, Representation of graphs, Multigraphs, Bipartite graphs,

Planar graphs, Isomorphism and

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