Introduction to Combinatorial Mathematics - by JMS Simões Pereira

This book is an expanded version of another, by the same author, published in Portugal, in 2006, by Editora Luz da Vida, with the title "Discrete Mathematics: Tópicos de Combinatória". The basic themes of Combinatorics are covered, such as the historic magic, Latin and Euler squares, arrangements, permutations and combinations, Newton's binomial and multinomial, distributions or occupations, substitutions and their groups. The principles of inclusion/exclusion and pigeon cages, generating functions, the most common counting theories, and the most common difference equations are also covered. Numerous applications are mentioned, from the measurement of power, with the example of the UN Security Council, to the theory of sharing, from the nomenclature of large numbers to the notation of arrows and Ackermann functions, from the symmetries of geometric figures to the functions of circuit, from the golden ratio to the interest and amortization equations. The author is concerned not to omit details that are sometimes overlooked in introductory works. Bibliography is recommended for those who want to delve deeper into the subjects, and 216 exercises are proposed and possible solutions suggested for everyone.