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 (firstname**lastname**@gmail.com)