Combinatorics and Finite Geometry

This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized.

Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.

Provides a gentle introduction to combinatorics, finite geometry and related topics Covers a broad range of related topics including error-connecting codes, cryptology and combinatorial game theory Includes numerous examples and exercises that illustrate the theory

Auteur

Steven Dougherty is a Professor at the University of Scranton, Pennsylvannia. The author of over 100 papers and 2 books, he has lectured over 60 times in 11 countries and was awarded the 2005 Merten M. Hasse prize.

Résumé

"The author's style is direct and clear. The text is illustrated with many examples, proofs are written in sufficient ... detail and the reviewer suspects that an advanced undergraduate could tackle large sections of the text independently." (Padraig Ó Catháin, Irish Mathematical Society Bulletin, Issue 90, 2022)

"The author's writing style is reasonably clear ... . an instructor looking for a text for a somewhat unusual combinatorics course should certainly take a look at this book. The students ... will get a good idea of how the subject of combinatorics intersects with other branches of mathematics, such as algebra, geometry and number theory." (Mark Hunacek, MAA Reviews, August 1, 2021)

Contenu
1 Foundational Combinatorial Structures.- 2 Foundational Algebraic Structures.- 3 Mutually Orthogonal Latin Squares.- 4 Affine and Projective Planes.- 5 Graphs.- 6 Higher Dimensional Finite Geometry.- 7 Designs.- 8 Combinatorial Objects.- 9 Discrete Probability - A Return to Counting.- 10 Automorphism Groups.- 11 Codes.- 12 Cryptology.- 13 Games and Designs.- 14 Epilogue.- References.- Glossary.- Solutions to Selected Odd Problems.- Index.