DISCRETE MATHEMATICAL STRUCTURES (BCS405A)

DISCRETE MATHEMATICAL STRUCTURES

Course Code BCS405A 
CIE Marks 50
Teaching Hours/Week (L:T:P:S) 2:2:0:0 
SEE Marks 50
Total Hours of Pedagogy 40 
Total Marks 100
Credits 03 
Exam Hours 03
Examination type (SEE) Theory

Module-1: Fundamentals of Logic

Basic Connectives and Truth Tables, Logic Equivalence – The Laws of Logic, Logical Implication –

Rules of Inference. The Use of Quantifiers, Quantifiers, Definitions and the Proofs of Theorems.

 (8 hours)

(RBT Levels: L1, L2 and L3)

Module-2: Properties of the Integers

Mathematical Induction, The Well Ordering Principle – Mathematical Induction, Recursive

Definitions.

Fundamental Principles of Counting: The Rules of Sum and Product, Permutations, Combinations –

The Binomial Theorem, Combinations with Repetition. (8 Hours)

 (RBT Levels: L1, L2 and L3)

Module-3: Relations and Functions

Cartesian Products and Relations, Functions – Plain and One-to-One, Onto Functions. The Pigeonhole Principle, Function Composition and Inverse Functions.

Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs, Partial

Orders – Hasse Diagrams, Equivalence Relations and Partitions. (8 hours)

(RBT Levels: L1, L2 and L3)

Module-4: The Principle of Inclusion and Exclusion

The Principle of Inclusion and Exclusion, Generalizations of the Principle, Derangements – Nothing is

in its Right Place, Rook Polynomials.

Recurrence Relations: First Order Linear Recurrence Relation, The Second Order Linear

Homogeneous Recurrence Relation with Constant Coefficients. (8 Hours)

(RBT Levels: L1, L2 and L3)

Module-5: Introduction to Groups Theory

Definitions and Examples of Particular Groups Klein 4-group, Additive group of Integers modulo n,

Multiplicative group of Integers modulo-p and permutation groups, Properties of groups, Subgroups,

cyclic groups, Cosets, Lagrange’s Theorem. (8 Hours)

 (RBT Levels: L1, L2 and L3)

Suggested Learning Resources:

Books 

1. Ralph P. Grimaldi, B V Ramana: “Discrete Mathematical Structures an Applied

Introduction”, 5th Edition, Pearson Education, 2004.

2. Ralph P. Grimaldi: “Discrete and Combinatorial Mathematics”, 5th Edition, Pearson

Education. 2004.

Reference Books:

1. Basavaraj S Anami and Venakanna S Madalli: “Discrete Mathematics – A Concept-based

approach”, Universities Press, 2016

2. Kenneth H. Rosen: “Discrete Mathematics and its Applications”, 6th Edition, McGraw Hill,

2007.

3. Jayant Ganguly: “A Treatise on Discrete Mathematical Structures”, Sanguine-Pearson,

2010.

4. D.S. Malik and M.K. Sen: “Discrete Mathematical Structures Theory and Applications,

Latest Edition, Thomson, 2004.

5. Thomas Koshy: “Discrete Mathematics with Applications”, Elsevier, 2005, Reprint 2008.

Web links and Video Lectures (e-Resources):

• http://nptel.ac.in/courses.php?disciplineID=111

• http://www.class-central.com/subject/math(MOOCs)

• http://academicearth.org/

• VTU e-Shikshana Program

• VTU EDUSAT Program.

• http://www.themathpage.com/

• http://www.abstractmath.org/

• http://www.ocw.mit.edu/courses/mathematics/