The Art of Counting
MIT OpenCourseWare offers this introduction to enumerative combinatorics, the branch of mathematics concerned with counting the elements of finite sets. The course centers on bijective proofs, showing two sets have equal size by constructing a one-to-one correspondence between them, illustrated with problems like counting the ways to write a positive integer n as an ordered sum of positive integers (2^(n-1) ways). The material requires little prior background yet reaches open research questions, and students are encouraged to pursue original problems. Course materials include lecture notes, problem sets, and readings from MIT's OpenCourseWare site, free to access under a Creative Commons license with no certificate offered. It suits anyone curious about combinatorics who wants a low-barrier entry point into active mathematical research.