Module 1 (10 hours):
Concept of a set, Operations with sets, Relation, Equivalence relations, Function, Natural Numbers, Mathematical Induction, Pigeonhole principle, Division algorithm, Partial and total orderings, Well Ordering Principle.

Module 2 (10 hours):
Fundamental counting principles, Permutations, Derangements, Combinations, Permutations and combinations with repetitions, Binomial theorem, Inclusion and exclusion principle, Discrete probability.

Module 3 (5 hours):
Linear and non-linear recurrence relations, Methods of solving recurrence relations: iteration, characteristic equations, and generating functions.

Module 4 (10 hours):
Graphs, Paths, Cycles, Complete Graphs, Eulerian and Hamiltonian graphs, Planner graphs, Graph colouring.

Module 5 (5 hours):
Matrices associated with graphs, Adjacency Matrix, Laplacian Matrix, Spectra of graphs.

To learn basic concepts of sets, relations, functions and matrices.

To introduce the basic counting principles, binomial theorem, generalized inclusion and exclusion principle and discrete probability.

To learn principle of mathematical induction, Euclid's division algorithm, and to study methods to solve recurrence relations.

To have a brief introduction to graph theory and its applications.

CO1: Students develop a strong foundation in fundamental mathematical concepts, including sets, relations, functions. They learn how these tools form the basis for various mathematical structures and problem-solving techniques, which are essential for advanced studies in mathematics and related fields.

CO2: Students gain a thorough understanding of basic counting principles, such as the rules of permutation and combination, and their real-world applications. Additionally, they explore important mathematical tools, including the Principle of Mathematical Induction for proving statements, Euclid's Division Algorithm for computing greatest common divisors, and methods for determining the solvability of Diophantine equations, which are integral to number theory.

CO3: Students study recurrence relations, which describe sequences recursively, and explore various analytical and computational methods to solve them. They examine linear and non-linear recurrence relations, as well as techniques such as iteration, characteristic equations, and generating functions, which are widely used in algorithm analysis, combinatorics, and applied mathematics.

CO4: Students explore the combinatorial properties of graphs, focusing on structural and numerical characteristics such as connectivity, planarity, graph coloring, and paths.

CO5: Students are introduced to the fundamentals of spectral graph theory, which studies the relationship between graphs and the eigenvalues and eigenvectors of their associated matrices. They explore key concepts such as the adjacency matrix, Laplacian matrix, and their applications.

K. H. Rosen, Discrete Mathematics and its Applications, McGraw Hill , 7th Edition, 2011

J. A. Bondy, U.S.R. Murty, Graph Theory with Applications, Elsevier , 1976

J. P. Tremblay, R. Manohar, Discrete Mathematical Structures with Applications to Computer Science, McGraw Hill , 1st Edition

R. A. Brualdi, Introductory Combinatorics, Pearson , 5th Edition, 2018