Syllabus
Concept of Mathematical Proof, Logic, Proof by contradiction, Mathematical Induction, Constructive Proofs, Sets, Relations, Illustration of Proof Techniques in various mathematical topics.
Combinatorics: Basic Counting Principles, Inclusion-Exclusion Principle, Binomial/Multinomial Coefficients, Bijections, Double Counting, Pigeon-Hole Principle, Recurrence Relations.
Introduction to Graphs: Basic terminology/Definitions, Isomorphism, Connectivity, Trees, Planarity.
Introduction to abstract algebra: Basics of Groups, Rings, Field, Polynomial Rings.
Text Books
- Kenneth Rosen, Discrete Mathematics and Applications, McGraw-Hill, 2019.
- Susanna S. Epp, Discrete Mathematics with Applications, Cengage Learning, 2018.
References
- David Hunter, Essentials of Discrete Mathematics, Jones Bartlett Learning, 2015.
- Thomas Koshy, Discrete Mathematics with Applications, Elsevier Science, 2004.