Discrete Mathematics

Counting as the starting point

This very long NPTEL course from IIT Ropar, with 466 lectures, begins with counting. Its opening sessions use concrete puzzles such as paper folding and the Rubik's cube to motivate why counting arguments matter, then move into factorials and the rule of sum and rule of product.

What the early lectures cover

• Motivation for counting and the Catalan numbers.
• Factorials, including proofs that build on them.
• Permutations, worked through in several parts.

How to use a course this long

At this length, the course works best as a reference you dip into by topic rather than a series to finish in one go. Learners who want a short, exam-focused path should expect to supplement it with practice problems, since the listing shows a strong emphasis on proof-style reasoning.