| Course Name | Discrete Mathematics |
| Course Code | 25MAT102 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | 1 |
| Credits | 3 |
| Campus | Mysuru |
Logic, Mathematical Reasoning and Counting: Logic, Prepositional Equivalence, Predicate and Quantifiers, Theorem Proving. Recursive Definitions, Recursive Algorithms, Basics of Counting, Pigeonhole Principle, Permutation and Combinations. (Sections: 1.1 -1.3, 1.5 -1.7, 2.3, 4.1 – 4.4, 5.1 – 5.3 and 5.5)
Relations and Their Properties: Representing Relations, Closure of Relations, Partial Ordering, Equivalence Relations and partitions. (Sections: 7.1, 7.3 – 7.6)
Advanced Counting Techniques and Relations: Recurrence Relations, Solving Recurrence Relations, Generating Functions, Solutions of Homogeneous Recurrence Relations, Divide and Conquer Relations, Inclusion-Exclusion. (Sections: 6.1 – 6.6)
Graph Theory: Graphs and Sub graphs, isomorphism, matrices associated with graphs, degrees, walks, connected graphs, shortest path algorithm. Euler and Hamilton Graphs: Euler graphs, Euler’s theorem. Fleury’s algorithm for Eulerian trails. Hamilton cycles, Chinese-postman problem, approximate solutions of traveling salesman problem. Closest neighbour algorithm.
Lab Practice Problems: Verifications of logical statements, truth table, tautology. Recursive algorithms. Graph problems, degree, shortest path algorithm, Euler’s algorithm and closest neighbour algorithm.
Course Objectives:
The course objective is to provide students with an overview of discrete mathematics. Students will learn about topics such as logic and proofs, sets and functions, relations, recursion, graph theory, and other important discrete mathematics concepts.
Course Outcomes:
| COs | Description |
| CO1 | Construct mathematical arguments using logical connectives and quantifiers. |
| CO2 | Apply counting techniques to solve problems. |
| CO3 | Apply the concepts of generating functions to solve the recurrence relations. |
| CO4 | Apply the concepts of divide and conquer method to solve some simple algorithms in discrete mathematics. |
| CO5 | Demonstrate an understanding of relations and functions and be able to determine their properties |
| CO6 | Demonstrate the basic concepts of graph theory and model problems in computer science using graphs. |
CO-PO Mapping
| PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PSO1 |
PSO2 |
PSO3 |
PSO4 |
| CO | ||||||||||||||
| CO1 | 2 | – | 2 | 3 | 3 | – | 1 | – | – | – | – | 1 | 2 | – |
| CO2 | 3 | – | 1 | 3 | 2 | – | 1 | – | – | – | – | 1 | 3 | – |
| CO3 | 2 | – | 2 | 3 | 2 | – | 1 | – | – | – | – | 1 | 2 | – |
| CO4 | 2 | – | 2 | 3 | 3 | – | 1 | – | – | – | – | 1 | 3 | – |
| CO5 | 2 | – | 3 | 3 | 2 | – | 1 | – | – | – | – | 1 | 2 | – |
| CO6 | 2 | – | 1 | 2 | 3 | – | 2 | – | – | – | – | 2 | 3 |
TextBooks:
1) Kenneth H. Rosen, “Discrete Mathematics and its Applications”, Tata McGraw- Hill Publishing Company Limited, New Delhi, Sixth Edition, 2007.
2) James Strayer, Elementary Number Theory, Waveland Press, 2002.
REFERENCES:
1) R.P. Grimaldi, “Discrete and Combinatorial Mathematics”, Pearson Education, Fifth Edition, 2007.
2) Thomas Koshy, “Discrete Mathematics with Applications”, Academic Press, 2005.
3) Liu, “Elements of Discrete Mathematics”, Tata McGraw- Hill Publishing Company Limited, 2004.
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