ANNA UNIVERSITY, CHENNAI

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REGULATIONS 2021

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• Department: Department of Science and Humanities

• Subject Code: MA3354

• Subject Name: DISCRETE MATHEMATICS

• Study Material Description: Lecture Notes

• Format Type: PDF

• Edition / Version Details: MSAJCE 2024 Edition

Introduction to Discrete Mathematics:

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. It deals with objects that can be counted, enumerated, and analyzed in a finite or countable manner.

It provides the foundational concepts and tools used in various areas of computer science, including algorithms, data structures, cryptography, and theoretical computer science.

Set Theory:

Sets are fundamental mathematical objects in discrete mathematics. A set is a collection of distinct objects, called elements, which can be anything from numbers to abstract entities.

Basic set operations include union, intersection, complement, and difference.

Set theory provides the foundation for various mathematical structures such as relations, functions, and graphs.

Logic and Propositional Calculus:

Logic deals with reasoning and the study of valid inference. Propositional logic is concerned with propositions or statements that can be either true or false.

Propositional calculus involves studying logical operations such as conjunction (AND), disjunction (OR), negation (NOT), implication (IF-THEN), and equivalence (IF AND ONLY IF).

Logical laws and rules, such as De Morgan's laws and the laws of inference, are essential in proving the validity of logical arguments.

Predicate Logic:

Predicate logic extends propositional logic by introducing predicates, which are statements containing variables that can be quantified over a domain.

Quantifiers, including universal quantifier (∀) and existential quantifier (∃), are used to express statements about all or some elements of a domain.

Predicate logic is used to express properties of objects and to formalize mathematical proofs.

Relations and Functions:

Relations are sets of ordered pairs representing the connections or associations between elements of two sets. Common types of relations include reflexive, symmetric, transitive, and equivalence relations.

Functions are special kinds of relations that map elements from one set (domain) to another set (codomain). They play a crucial role in modeling mathematical and computational processes.

Combinatorics:

Combinatorics deals with counting, arranging, and selecting objects without considering their specific properties. It includes topics such as permutations, combinations, and the binomial theorem.

Combinatorial techniques are widely used in computer science for analyzing algorithms, designing data structures, and solving optimization problems.

Graph Theory:

Graph theory studies the properties and applications of graphs, which are mathematical structures consisting of vertices (nodes) connected by edges (links).

Graphs are used to model various real-world phenomena, such as social networks, transportation systems, and communication networks. Graph algorithms are essential for solving problems in network optimization, routing, and scheduling.

Conclusion:

Discrete mathematics forms the mathematical foundation for computer science and plays a crucial role in various technological applications. Understanding the fundamental concepts covered in this course is essential for students pursuing degrees in computer science, mathematics, and related fields.

These lecture notes cover the foundational concepts of discrete mathematics as per the Anna University, Chennai, curriculum for MA3354. They provide an introduction to key topics such as set theory, logic, relations, functions, combinatorics, and graph theory, which are essential for understanding and applying discrete mathematical principles in various contexts.

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