## Book Details

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.
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.
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. Simplification of Boolean functions, Karnaugh maps, Logic gates, Digital circuits and Boolean algebra. Combinational and sequential circuits.
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 formed formula of predicate, Quantifiers, Inference theory of predicate logic.
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 Hamitonian paths, Graph coloring.
Recurrence relation and generating function : Recursive definition of functions, Recursive algorithms, Method of solving recurrences.
Combinatorics : Introduction, Counting techniques, Pigeonhole principle.