Discrete Mathematical Structures and Applications (MAL6330)
July-November, 2025
Lectures : Monday, Wednesday at 4:00 PM, Friday at 3:00 PM
Office Hour : Wednesday from 2:00PM to 4:00 PM
Evaluation:
Minor Examination - 25%
Major Examination - 45%
Quizzes - 30%
Quizzes will be held on Aug 29, Oct 10 and Oct 31, 2025
Attendance Policy:
A student is expected to have full attendance in the course unless student takes leave of absence for
valid medical or bonafide reasons. In any case, at least 75% attendance in the course is mandatory.
Objectives:
The Instructor will:
1. Introduce the methods of analytical, abstract and critical thinking.
2. Provide logical and mathematical tools for problem solving skills.
3. Provide formal definitions in combinatorics and graph theory with their applications.
Learning Outcomes:
The students are expected to have the ability to:
1. Understand the notion of mathematical thinking, mathematical proofs,and algorithmic thinking, and be able to apply them in problem solving.
2. Understand some basic properties of graphs and related discrete structures, and be able to relate these to practical examples.
Topics to be covered:
Mathematical Logic : Propositional Logic, First Order Logic, Proof techniques, Mathematical Induction, application to verify the algorithms and processes.
Set Theory and Algebra : Sets, Paradoxes in Set Theory, Inductive Definitions of Sets and Proof by Induction, Relations, Functions, Partial Orders, Lattice, Boolean Algebra, Groups and Rings : Examples and Basic Properties, Error-correcting codes, Secret sharing, Applications in Cryptography specifically in RSA cryptography, (k, n)- threshold scheme and visual cryptography
Combinatorics : Recurrence relations, common techniques for solving recursions, Permutations, Combinations, Counting, Polya Counting, Stirling numbers, Bell numbers, Combinatorial Sums, Applications of combinatorics in Machine Learning and Number Theory
Graph Theory : Connectivity, Trees and its properties, Cut vertices & edges, Covering, Matching, Independent sets, Coloring, Planarity, Isomorphism, Applications of Graphs in Supply Chain, Networks and Marketing Analytics.
Text Books
1. Rosen, K. H. , (1999), Discrete Mathematics and Its Applications, McGraw-Hill.
2. Epp, S. S. , (2004) Discrete Mathematics with Applications, Thomson-Brooks/Cole.
Reference Books
1. K. A. Ross and C. R. B. Wright, (2003) Discrete Mathematics (Fifth Edition), Prentice Hall.
2. Van Lint, J. H. and Wilson, R. M., (2009), A Course in Combinatorics, Cambridge University Press
3. Matousek, J. and Nesetril, J., (2008), Invitation to Discrete Mathematics, Oxford University Press.
Course
1-August-2025 : Introduction to the Course, Propositional Logic
4,6,8 -August-2025 : Propositional Logic, First Order Logic
Assignment-I
11,13 -August-2025 : Proof Techniques, Sets, Paradoxes in Set Theory
18,20,22-August-2025 : Mathematical Induction, Applications of Mathematical Induction,
25,27,29-August-2025 : Relations, Functions, Partial Orders, Quiz-I
Assignment-II
1,3 -September-2025 : Lattice, Boolean Algebra, Groups and Rings : Examples and Basic Properties
8,10,12, 15,16-September-2025 : Error-correcting codes, Secret sharing, Applications in Cryptography specifically in RSA cryptography, (k, n)- threshold scheme and visual cryptography
Assignment-III
17- 20-September-2025 : Minor Examination
22,24,26 -September-2025 : Recurrence relations, common techniques for solving recursions,
29-September-2025 : Permutations, Combinations.
1,3-October-2025 : Counting, Polya Counting
Assignment-IV
8,10-October-2025 : Stirling numbers, Bell numbers, Quiz-II
13,15,17-October-2025 : Combinatorial Sums, Applications of combinatorics
Assignment-V
22, 24-October-2025: Graphs, Connectivity,
27,29,31-October-2025 : Trees and its properties, Cut vertices and edges, Covering, Matching, Quiz -III
3-November-2025 : Independent sets
Assignment-VI
10,12,14-November-2025 : Coloring, Planarity, Isomorphism of graphs,
17,18-November-2025 : Applications of Graphs
20-26 November 2025: Major Examination