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DISCRETE MATHEMATICAL STRUCTURES
DISCRETE MATHEMATICAL STRUCTURES
[As per Choice Based Credit System (CBCS) scheme]
SEMESTER - III
15CS 35
Subject Code
15CS35
IA Marks
20
Number of Lecture
04
Exam Marks
80
Hours/Week
Total Number of
50
Exam Hours
03
Lecture Hours
Course objectives:
. This course will enable students to· Prepare for a background in abstraction, notation, and
critical thinking for the mathematics most directly related to computer science.
· Understand and apply logic, relations, functions, basic set theory, countability and counting
arguments, proof techniques,
· Understand and apply mathematical induction, combinatorics, discrete probability, recursion,
sequence and recurrence, elementary number theory
· Understand and apply graph theory and mathematical proof techniques.
Module -1
Teaching
RBT
Hours
Levels
Set Theory: Sets and Subsets, Set Operations and the Laws of Set
Theory, Counting and Venn Diagrams, A First Word on Probability,
Countable and Uncountable Sets.
10 Hours
L2, L3
Fundamentals of Logic: Basic Connectives and Truth Tables,
Logic Equivalence –The Laws of Logic, Logical Implication – Rules
of Inference.
Module -2
Fundamentals of Logic contd.: The Use of Quantifiers, Quantifiers,
Definitions and the Proofs of Theorems, Properties of the Integers:
10 Hours
L3, L4
Mathematical Induction, The Well Ordering Principle –
Mathematical Induction, Recursive Definitions
Module – 3
Relations and Functions: Cartesian Products and Relations,
Functions – Plain and One-to-One, Onto Functions – Stirling
L3,L4,
10 Hours
Numbers of the Second Kind, Special Functions, The Pigeon-hole
L5
Principle, Function Composition and Inverse Functions.
Module-4
Relations contd.: Properties of Relations, Computer Recognition –
L3,L4,
Zero-One Matrices and Directed Graphs, Partial Orders – Hasse
10 Hours
L5
Diagrams, Equivalence Relations and Partitions.
Module-5
Groups: Definitions, properties, Homomrphisms, Isomorphisms,
Cyclic Groups, Cosets, and Lagrange’s Theorem. Coding Theory
and Rings: Elements of CodingTheory, The Hamming Metric, The
Parity Check, and Generator Matrices. Group Codes: Decoding
with Coset Leaders, Hamming Matrices. Rings and Modular
Arithmetic: The Ring Structure – Definition and Examples, Ring
Properties and Substructures, The Integer modulo n.
DEPT. OF CSE, SJBIT
10 Hours
L3,L4,
L5
Page 1

DISCRETE MATHEMATICAL STRUCTURES
15CS 35
Course outcomes:
After studying this course, students will be able to:
1. Verify the correctness of an argument using propositional and predicate logic and truth tables.
2. Demonstrate the ability to solve problems using counting techniques and combinatorics in the
context of discrete probability.
3. Solve problems involving recurrence relations and generating functions.
4. Perform operations on discrete structures such as sets, functions, relations, and sequences.
5. Construct proofs using direct proof, proof by contraposition, proof by contradiction, proof by
cases, and mathematical induction.
Graduate Attributes (as per NBA)
1. Engineering Knowledge
2. Problem Analysis
3. Conduct Investigations of Complex Problems
4. Design/Development of Solutions
Question paper pattern:
The question paper will have ten questions.
There will be 2 questions from each module.
Each question will have questions covering all the topics under a module.
The students will have to answer 5 full questions, selecting one full question from each module.
Text Books:
1.Ralph P. Grimaldi: Discrete and Combinatorial Mathematics, , 5th Edition, Pearson Education.
2004. (Chapter 3.1, 3.2, 3.3, 3.4, Appendix 3, Chapter 2, Chapter 4.1, 4.2, Chapter 5.1 to 5.6,
Chapter 7.1 to 7.4, Chapter 16.1, 16.2, 16.3, 16.5 to 16.9, and Chapter 14.1, 14.2, 14.3).
Reference Books:
1. Kenneth H. Rosen: Discrete Mathematics and its Applications, 6th Edition, McGraw Hill,
2007.
2. JayantGanguly: A TreatCSE on Discrete Mathematical Structures, Sanguine-Pearson, 2010.
3. D.S. Malik and M.K. Sen: Discrete Mathematical Structures: Theory and Applications,
Thomson, 2004.
4. Thomas Koshy: Discrete Mathematics with Applications, Elsevier, 2005, Reprint 2008.
DEPT. OF CSE, SJBIT
Page 2

DISCRETE MATHEMATICAL STRUCTURES
INDEX SHEET
Module s
Contents
15CS 35
Page No.
Set Theory: Sets and Subsets, Set Operations and the Laws of Set
Theory, Counting and Venn Diagrams, A First Word on Probability,
Module -1
Countable and Uncountable Sets.
Fundamentals of Logic: Basic Connectives and Truth Tables, Logic
04-26
Equivalence –The Laws of Logic, Logical Implication – Rules of
Inference.
Fundamentals of Logic contd.: The Use of Quantifiers, Quantifiers,
Module -2
Definitions and the Proofs of Theorems, Properties of the Integers:
Mathematical Induction, The Well Ordering Principle – Mathematical
27-40
Induction, Recursive Definitions
Relations and Functions: Cartesian Products and Relations, Functions
Module -3
– Plain and One-to-One, Onto Functions – Stirling Numbers of the
Second Kind, Special Functions, The Pigeon-hole Principle, Function
41-68
Composition and Inverse Functions.
Relations contd.: Properties of Relations, Computer Recognition –
Module -4
Zero-One Matrices and Directed Graphs, Partial Orders – Hasse
69-76
Diagrams, Equivalence Relations and Partitions.
Groups: Definitions, properties, Homomrphisms, Isomorphisms,
Cyclic Groups, Cosets, and Lagrange’s Theorem. Coding Theory and
Rings: Elements of CodingTheory, The Hamming Metric, The Parity
Module -5
Check, and Generator Matrices. Group Codes: Decoding with Coset
77-114
Leaders, Hamming Matrices. Rings and Modular Arithmetic: The
Ring Structure – Definition and Examples, Ring Properties and
Substructures, The Integer modulo n
DEPT. OF CSE, SJBIT
Page 3

DISCRETE MATHEMATICAL STRUCTURES
Module 1: Set Theory:
15CS 35
Sets and Subsets,
Set Operations and the Laws of Set Theory,
Counting and Venn Diagrams,
A First Word on Probability,
Countable and
Uncountable Sets
Fundamentals of Logic:
Basic Connectives and Truth Tables,
Logic Equivalence –The Laws of Logic,
Logical Implication – Rules of Inference.
DEPT. OF CSE, SJBIT
Page 4

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