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MA3354Actively Used

Discrete Mathematics

This course is part of the B.E. Computer Science Engineering curriculum under Anna University Regulation 2021. The knowledge from this course continues to be actively applied in professional software development.

Semester 3 (Second Year)
4 Credits
60 Lecture Hours

Course Overview

  • UniversityAnna University
  • Regulation2021
  • Semester3
  • Credits4
  • TypeCore
  • Units5

Course Objectives

1

To understand propositional logic and proof methods

2

To learn combinatorics and counting techniques

3

To understand graph theory concepts

4

To learn algebraic structures

5

To understand lattices and Boolean algebra

Syllabus

Detailed unit-wise breakdown of the course curriculum as per Anna University Regulation 2021.

1

LOGIC AND PROOFS

12 Hours
Propositional logicPropositional equivalencesPredicates and quantifiersNested quantifiersRules of inferenceIntroduction to proofsProof methods and strategy
2

COMBINATORICS

12 Hours
Mathematical inductionStrong induction and well orderingThe basics of countingThe pigeonhole principlePermutations and combinationsRecurrence relationsSolving linear recurrence relationsGenerating functionsInclusion and exclusion principle
3

GRAPHS

12 Hours
Graphs and graph modelsGraph terminologySpecial types of graphsMatrix representation of graphsGraph isomorphismConnectivityEuler and Hamilton paths
4

ALGEBRAIC STRUCTURES

12 Hours
Algebraic systemsSemi groups and monoidsGroupsSubgroupsHomomorphismsNormal subgroup and cosetsLagrange's theoremDefinitions of Rings and Fields
5

LATTICES AND BOOLEAN ALGEBRA

12 Hours
Partial orderingPosetsLattices as posetsProperties of latticesLattices as algebraic systemsSub latticesDirect product and homomorphismSpecial latticesBoolean algebraSub Boolean AlgebraBoolean Homomorphism

Course Outcomes

Upon completion of this course, students will be able to:

CO1

Apply propositional and predicate logic

CO2

Use combinatorial techniques for counting

CO3

Model problems using graph theory

CO4

Understand algebraic structures

CO5

Apply Boolean algebra in digital systems

Industry Application & Relevance

How the concepts learned in this course are applied in real-world software development projects across Banking, Healthcare, and Enterprise domains over 20+ years of experience.

Professional Application

Algorithm analysis, cryptography, database theory

Textbooks & References

Textbooks

  • Kenneth H. Rosen, 'Discrete Mathematics and its Applications', McGraw Hill
  • C.L. Liu, D.P. Mohapatra, 'Elements of Discrete Mathematics', McGraw Hill

Reference Books

  • Ralph P. Grimaldi, 'Discrete and Combinatorial Mathematics', Pearson
  • J.P. Tremblay, R. Manohar, 'Discrete Mathematical Structures', McGraw Hill

Related Courses from Semester 3

Other courses from the same semester that are actively used in professional work.

CS3351Digital Principles and Computer Organization

Hardware-software interface, performance optimization

CS3352Foundations of Data Science

Big data analytics, business intelligence, data-driven decisions

CS3301Data Structures

Core of all software development - Arrays, Trees, Graphs, HashMaps

CS3391Object Oriented Programming

Java, Spring Boot, enterprise application development