Guide to discrete mathematics. An accessible introduction to the history, theory, logic and applications (Q318842)

This book is not intended as a regular textbook on discrete mathematics, but rather as an encyclopedic overview of topics of and related to discrete mathematics in the broad sense, including many topics from computer science and software engineering. The aim is to motivate the reader for discrete mathematics and to show the large variety of applications in computing. The list of topics is impressive and is organized into 20 chapters that are on average 20 pages long. Starting with a chapter on the history of mathematics from early societies to the Romans, topics covered are sets and functions, number theory, combinatorics, algebra, automata, matrices, graphs, cryptography, coding, languages, computability, logic, software engineering and specification, probability and statistics (in selection). Of course: due to lack of space often nothing more than first definitions and fundamentals or some appetizers can be given. There are some exceptions, e.g., the chapters about sets and relations, number theory, block codes, logic and Z-specification language, where the beginning of a systematic development and some proofs are given. The nice proof of the undecidability of the halting problem on page 215 deserves explicit mention. The aim of providing a broad guide to the reader is in general achieved, but the reader must be willing to jump around at times because some concepts are used that are explained only in later chapters. For instance, Chapters 12 and 13 better swapped places with Chapters 14 and 15. Sometimes, the chosen topics are kind of miscellaneous, e.g., triangular numbers, palindromic primes or financial calculations. Occasionally, inaccuracies can be found: so, according to the given definitions, 1 would be a prime number, and in statistics it is asserted that the errors of the first and second kind are usually of the same size. By the way: long passages of the book are found verbatim in former books of the same author. Each chapter has a summary and a list of review question which help the reader to recapitulate the contents, but don't give enough material for self-study. In any case, for each topic the reader is able to grasp the specific flavor and can move forward to more specific and advanced literature. To help him here, the literature given at the end of each chapter could have been more extensive.