MCS-013: Discrete Mathematics

This book is useful for IGNOU BCA & MCA students. A perusal of past questions papers gives an idea of the type of questions asked, the paper pattern and so on, it is for this benefit, we provide these IGNOU MCS-013: Discrete Mathematics Notes. Students are advised to refer these solutions in conjunction with their reference books. It will help you to improve your exam preparations.

This book covers Discrete Mathematical Structures, Formal Methods: Introduction and Analogy, Abstraction.

Fundamentals: Sets & Relations- Sets, Types of Sets, Multi Sets, Operations on Sets, Relations and Properties of Relations, Representation of Relations, Equivalence Relation, Closures of Relations, Methods of Proof-Direct Proofs, Indirect Proofs, Mathematical Induction, Method of Contradiction.

Combinatorics: Permutations and Combinations, Pigeon Hole Principle, Principle of Inclusion and Exclusion, Generating Functions.

Mathematical Logic, Posets and Lattices: Partial Order Set, Bounding Elements, Well Ordered Set, Topological Sorting, Lattices, Principle of Duality, Bounded, Distributed, and Complemented Lattices, Proposition and Propositional Calculus.
Graphs and Group Theory: Basic Introduction of Graphs- Types of Graphs, Path and Circuits, Eulerian Path and Circuits, Hamiltonian Path and Circuits, Shortest Path Algorithms, Group.

Definitions and Properties, Coset& Subgroup, Normal subgroup, Homomorphism of groups, Cyclic Group, Permutation Group.

Finite State Machines and Languages: Grammar and Languages- Phrase structure Grammar, Types of Grammars and Languages, Finite State Machines and Languages, Minimization of Finite State Machines.