Discrete Mathematical Structures and Applications
Discrete Mathematical Structures and Applications
Lectures : Monday, Tuesday, Thursday at 2:00 PM
Office Hour : Wednesday from 11:30AM to 1:30 PM
Minor Examination - 30%
Major Examination - 40%
Quizzes - 30% (Best Three Quizzes will be considered)
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 cryptographyCombinatorics : 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 TheoryGraph 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.1-August-2024 : Introduction to the Course, Propositional Logic
5,6,8 -August-2024 : Propositional Logic, First Order Logic
12,13 -August-2024 : Proof Techniques, Sets, Paradoxes in Set Theory
20,22-August-2024 : Mathematical Induction, Quiz I
28,29-August-2024 : Applications of Mathematical Induction, Relations, Functions, Partial Orders,
2,3,5 -September-2024 : Lattice, Boolean Algebra, Groups and Rings : Examples and Basic Properties, Quiz II
9,10,12, 17-September-2024 : Error-correcting codes, Secret sharing, Applications in Cryptography specifically in RSA cryptography, (k, n)- threshold scheme and visual cryptography
19,20, 21-September-2024 : Minor Examination
23,24,26 -September-2024 : Recurrence relations, common techniques for solving recursions,
30-September-2024 : Permutations, Combinations.
1,3-October-2024 : Counting, Polya Counting
7,8-October-2024 : Stirling numbers, Bell numbers, Combinatorial Sums
14,15,17-October-2024 : Applications of combinatorics in Machine Learning and Number Theory, Quiz-III
21,22, 24-October-2024: Graphs, Connectivity, Trees and its properties
28,29-October-2024 : Cut vertices and edges, Covering, Matching, Independent sets, Quiz-IV
4,5,7-November-2019 : Coloring, Planarity, Isomorphism of graphs
11,12,14,18-November-2024 : Applications of Graphs in Supply Chain, Networks and Marketing Analytics.
20-26 November 2024: Major Examination