Notes on the Combinatorial Fundamentals of Algebra
by Darij Grinberg
Publisher: arXiv.org 2021
Number of pages: 1359
This is a detailed survey, with rigorous and self-contained proofs, of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is entirely expository and written to a large extent as a repository for folklore proofs; no new results appear.
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by Edward A. Bender, S. Gill Williamson - Dover Publications
This introduction to combinatorics, the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. Some ability to construct proofs is assumed.
by David Guichard - Whitman College
The book covers the classic parts of Combinatorics and graph theory, with some recent progress in the area. Contents: Fundamentals; Inclusion-Exclusion; Generating Functions; Systems of Distinct Representatives; Graph Theory; Polya-Redfield Counting.
by Mitchel T. Keller, William T. Trotter - Georgia Institute of Technology
The purpose of the course is to give students a broad exposure to combinatorial mathematics, using applications to emphasize fundamental concepts and techniques. Our approach to the course is to show students the beauty of combinatorics.
by S. E. Payne - University of Colorado
These notes deal with enumerative combinatorics. The author included some traditional material and some truly nontrivial material, albeit with a treatment that makes it accessible to the student. He derives a variety of techniques for counting.