Krishna's Discrete Structures & Graph Theory

SYLLABUS- DISCRETE STRUCTURES & GRAPH THEORY, Unit-I
Set Theory: Introduction, Combination of sets, Multisets, Ordered pairs. Proofs of some general identities on
sets.
Relations: Definition, Operations on relations, Properties of relations, Composite Relations, Equality of
relations, Recursive definition of relation, Order of relations.
Functions: Definition, Classification of functions, Operations on functions, Recursively defined functions.
Growth of Functions.
Natural Numbers: Introduction, Mathematical Induction, Variants of Induction, Induction with Nonzero
Base cases. Proof Methods, Proof by counter example, Proof by contradiction.
Unit-II
Algebraic Structures: Definition, Groups, Subgroups and order, Cyclic Groups, Cosets, Lagrange's theorem,
Normal Subgroups, Permutation and Symmetric groups, Group Homomorphisms, Definition and
elementary properties of 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.
Boolean Algebra: Introduction, Axioms and Theorems of Boolean algebra, Algebraic manipulation of
Boolean expressions. Simplification of Boolean Functions, Karnaugh maps, Logic gates, Digital circuits and Boolean algebra.
Unit-IV
Propositional Logic: Proposition, well formed formula, Truth tables, Tautology, Satisfiability, Contradiction,
Algebra of proposition, Theory of Inference. Predicate Logic: First order predicate, well formed formula 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 Homeomorphism of graphs, Euler and Hamiltonian paths, Graph coloring,
Recurrence Relation & Generating function: Recursive definition of functions, Recursive algorithms,
Method of solving recurrences.
Combinatories: Introduction, Counting Techniques, Pigeonhole Principle, Polya's Counting Theory.