Logic and Proofs – Propositional logic, equivalences, Predicates and quantifiers, Nested quantifiers, Rules of inference, Introduction to proofs, Proof methods
Basic structures – Sets and their operations, functions, sequences and summations.

Algorithms, integers and matrices – Growth of functions, Complexity of integers and divisions, Primes and GCD, Matrices.
Induction and Recursion – Mathematical induction, Strong induction, Recursive defintions and well ordering.

Counting – Basics, Pigeonhole principle, Permutation and Combinations, Binomial Coefficeints, Generalized Permuations and Combinations.
Recurrence relations, Divide and Conquer algorithms, Generating functions and inclusion-exclusion.

Relations- Relations and their properties, n-ary relations, representations, closure, equivalence relations, partial orders.
Graph theory- Graph representation, terminology, isomorphism, Connectivity, Euler and Hamiltonian paths, Shortest paths, Planar Graphs. Trees.

Algebraic structures and coding theory- Introduction, structure of algebras, Semigroups, Monoids, Groups, Fields, Rings, Integral domains
Number Theory

To discuss mathematical reasoning for understanding logic and to address the methods of valid proof such as mathematical induction.

To discuss important problem-solving skills with the basic techniques of counting. Discussing combinatorial analysis to solve counting problems and to analyze algorithms.

To understand abstract mathematical structures used to represent discrete objects and relationships between these objects. These discrete structures include sets, permutations, relations, graphs, trees, and finite-state machines.

To learn a particular set of mathematical facts with algorithmic thinking and how to apply them.

After reading this subject, students will be able to:
1. Understand set theory, propositions, predicate calculus which will help to improve their mathematical reasoning.
2. Improving skills on permutations and combinations, relations and functions and their applications in Problem solving.
3. Learn concepts of groups, rings and field along with basics of graph theory.
4. Understand recurrence relations and the methods to find out their solutions.
5. Enhance skills in Modeling and algorithmic thinking with discrete mathematics to develop their own models in computer science and data networking applications.

Kenneth H. Rosen, Discrete Mathematics and its Applications, McGraw Hill Education (India) Pvt. Ltd. , 2011

B. Kolman and R. C. Busby, Discrete Mathematical Structures for Computer Science, Prentice Hall of India , 2018

Michel O Albertson and Joan P Hutchinson, Discrete Mathematics with Algorithms, Wiley , 1988

N. Deo, Graph Theory with applications to Engineering & Computer Science, Prentice Hall of India , 2006

SODA, STOC, FOCS, ELECTRONIC JOURNAL OF COMBINATORICS