The Mathematics of Ciphers

The mathematical underpinnings of games, whether they are strategic or games of chance, have been known for centuries, but are usually only understood by players and aficionados who have a background in mathematics. The author has succeeded in making that knowledge accessible, entertaining, and useful to everyone who likes to play and win. The information applies to such diverse and popular games as Roulette, Monopoly, Chess, Go, numerous card games, and many more. He reviews the mathematical foundations, probability, combinatorics, and mathematical game theory, the field that won John Nash of A Beautiful Mind the Nobel Prize, and emphasizes the implementation of these techniques so that players can put them to work immediately. An extensive bibliogr...

This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical an...

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations.The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering a...