Combinatorics: An Introduction

by Theodore G. Faticoni

Bridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems. Detailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geometry, this book provides discussion on logic and paradoxes; sets and set notations; power sets and their cardinality; Venn diagrams; the multiplication principal; and permutations, combinations, and problems combining the multiplication principal. Additional features of this enlightening introduction An Introduction is an excellent book for discrete and finite mathematics courses at the upper-undergraduate level. This book is also ideal for readers who wish to better understand the various applications of elementary combinatorics.

336 pages, Hardcover

First published December 1, 2012

Reviews

[Jack Henry · Rating 3 out of 5]

This text covered the material adequately. It provided exercises, and relevant problems such as those typically involving poker, dice, and coins. There are proofs and justifications that are critical for students to understand the undeniable truth of something. As is mentioned in the final chapter, mathematics deals in the region of absolute truths. The proofs for the formulas and methods are all rigorously done for the reader.

However, in doing so, Faticoni tends to neglect the intuitive understanding of formulas. Some of the problems are wrong. The solutions can end up being on the same line as the question, so one occasionally sees the answer before starting the problem. There are no images, or much engaging material. Finally, the proofs can occasionally get to bogged down by formalisms, and problems can have unecessarily long-winded explanations.

I enjoyed when Faticoni included mathematical figures (although perhaps Fermat and Pascal could have been cut down, I'm not sure there need to be several pages of dialogue to discuss the probability theorems that were simply explained previously). This book will teach the relevant material, but I would suggest a different text for combinatorics. This text fell flat in cultivating interest and had practical issues in explanation.

[Josh · Rating 4 out of 5]

One of the better books if you're solo studying. Content and proofs build at a steady pace. My only gripe's with the book are the quantity of errors, compounded by the lack of an errata. Price is ridiculous but that's probably out of the Authors control.

[Daisy Aguilar · Rating 5 out of 5]

Review for portions of the Textbook

I really enjoyed the fact that the author really wrestled with these ideas in a logical way (without all of the fluff). I recommend this book to anyone who would like to know about logic in a fun read.

[Katia N · Rating 3 out of 5]

Very good approach to boost understanding. (combining basics of logic, applicable set theory and probability and using it to make combinatorics easy to understand). However, the book requires a good edit. Even I managed to find quite a few mistakes when a part of mathematical expression is simply omitted. I am sure those are not the author's error, but it makes the book quite tricky to appreciate.