Notes on the combinatorial fundamentals of algebra

This is a set of notes originally written for a PRIMES 2015 reading project (but extended since). In its current version, it provides a detailed introduction to permutations and determinants (from a combinatorial viewpoint -- no linear algebra is presumed), as well as some basic material on binomial coefficients and recurrent sequences. It contains about 80 exercises with solutions, and a few exercises without.

Up-to-date PDF files can be downloaded from my website:

• Full version (with solutions).

• Version without solutions. (Use this if you want to solve the problems on your own and prefer not to see spoilers.)

These notes also appear on the arXiv: arXiv:2008.09862. However, they won't likely be updated frequently on the arXiv.

-- Darij Grinberg (firstnamelastname@gmail.com)