The Art of Counting

Overview

The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

Skills you'll practise

Mathematics Science & Math

Advantages and disadvantages

Advantages

The real MIT course: lecture notes, problem sets and exams, often with solutions.
Free, with no sign-up or deadlines.
Taught by Massachusetts Institute of Technology, one of the strongest names in its field.
Completely free.
Self-paced: start any time.

Disadvantages

No certificate, no grading and no forum: you need to be self-driven.
Many courses are recordings of past semesters and some have notes only, no videos.
No certificate.

Some points apply to every course of this kind; see how we rank.

Free to learn

Free: All the materials are free to use, with no sign-up. MIT OpenCourseWare gives no certificate.

Taught by

Prof. Richard Stanley

Massachusetts Institute of Technology is in Tier 1: world-leading universities and India's top institutes of our institution ranking (98/100). OpenCourseWare is the gold standard for free university material.