Discrete mathematics offers a language for finite structures and a collection of methods for reasoning about them. A puzzle about tiling a chessboard, a way to count a family of objects, or a question about routes through a network can all become an opportunity to choose and develop a proof.
This collection follows the broad introductory course taught at IIT Gandhinagar. The continuing notes and resources sit alongside dated editions, so the subject can grow without erasing the history of a particular class.
Ways of thinking
Proof and logic: direct arguments, the pigeonhole principle, induction, propositions, quantifiers and inference.
Sets and maps: set operations, functions, relations, equivalence classes and counting through bijections.
Counting: permutations, combinations, binomial coefficients and double counting.
Graphs: Euler tours, matchings, Hall’s theorem, coloring and planarity.
Probability: conditional probability and the probabilistic method.
Algebraic methods: linear algebra in combinatorics, symmetries, groups and number theory.
The archived course begins without prerequisites and is intended to be accessible across disciplines. Examples and puzzles are used to develop mathematical methods rather than as isolated tricks.