Course Code
UMAT101L
Pre-requisite
Course Title
Discrete Mathematics
NIL
L T P C
3 0 0 3
Syllabus version
1.0
Course Objectives:
1. To motivate the learners for understanding the counting techniques,
inference logic in programming.
2. To acquire the required knowledge for computer science such as lattices,
Boolean algebra, semigroups, groups and graph theoretical approaches
with applications.
3. To implement the learned discrete mathematical ideas in realistic projects of
computer science, theoretical computer skills, computer algorithms, networks
and data structures.
Course Outcomes:
1. Apply the principles of counting, permutations, and combinations for realistic
problems.
2. Learn the concepts of statement calculus, inference theory and predicate
calculus on logic.
3. Use the lattice and Boolean algebra techniques in execution of digital circuits.
4. Use the algebraic structures in computer science applications.
5. Solve science and engineering problems using graph theoretical techniques.
Module:1 Basics of Counting
7 hours
Sum Rule – Product Rule, Set Inclusion and Exclusion – Pigeonhole Principle –
Permutation and Combination With and Without Repetitions.
Module:2 Statement Calculus and Inference
6 hours
Theory
Introduction – Statements and Notation – Connectives – Tautologies – Logical
Equivalence – Implications – Normal Forms – Inference theory for the Statement
Calculus.
Module:3 Predicate Calculus
6 hours
The Predicate Calculus – The Statement Function: Variables and Quantifiers –
Predicate Formulas – Free and Bound Variable – The Universe of Discourse –
Inference Theory for the Predicate Calculus.
Module:4 Lattice Theory and Boolean Algebra
6 hours
Partially Ordered Set – Lattices as POSETS – Hasse Diagram – Boolean algebra
– Boolean Functions – Truth Table – Duality – Representation and Minimization of
Boolean Functions Karnaugh Map – Logic gates, an application to digital computer
design (using AND, OR and NOT Gate).
Module:5 Algebraic Structures
6 hours
Semigroups – Monoids – Groups – Lagranges Theorem – Homomorphism, Kernel
and Properties.
Module:6 Fundamental of Graphs
6 hours
Basic Concepts of Graph Theory – Planar and Complete graph – Matrix
Representation of Graphs – Euler and Hamilton Paths – Shortest Path Algorithms
(only TSP).
Module:7 Trees, Spanning Trees and Tree
6 hours
Traversals
Trees – Properties of Trees – Distance and Centres in Tree – Spanning Trees –
Prim’s and Kruskal’s Algorithms – Tree Traversals.
Module:8 Contemporary Issues
2 hours
Total Lecture hours:
45 hours
Text Book(s)
1. J.P. Tremblay and R. Manohar, Discrete Mathematical Structures with
Applications to Computer Science, 2017, Tata McGraw Hill, New Delhi. (only
for Modules 2 and 3)
2. Kenneth H. Rosen, Discrete Mathematics and its applications, 2019, 8th
Edition, Tata McGraw Hill, New York.
Reference Books
1. Joe L. Mott, Abraham Kandel and Theodore P. Baker, Discrete mathematics for
computer scientists and mathematicians, 2015, 2nd Edition, Pearson Education
India.
2. Narsingh Deo, Graph theory with application to Engineering and Computer
Science, 2016, Prentice Hall, USA.
3. Richard Johnsonbaugh, Discrete Mathematics, 2017, 8th Edition, Pearson,
New York.
4. Susanna S. Epp, Discrete Mathematics with Applications, 2018, 5th Edition,
Cengage Learning, USA.
5. D. B. West, Introduction to Graph Theory, 2015, 3rd Edition, Prentice-Hall,
USA.
Mode of Evaluation: CAT, Written Assignment, Quiz, FAT.
Recommended by Board of Studies 06-06-2023
Approved by Academic Council
No. 70
Date
24-06-2023