This is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the “Tower of London”, are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.

Search has been vital to artificial intelligence from the very beginning as a core technique in problem solving. The authors present a thorough overview of heuristic search with a balance of discussion between theoretical analysis and efficient implementation and application to real-world problems. Current developments in search such as pattern databases and search with efficient use of external memory and parallel processing units on main boards and graphics cards are detailed. Heuristic search as a problem solving tool is demonstrated in applications for puzzle solving, game playing, constraint satisfaction and machine learning. While no previous familiarity with heuristic search is necessary the reader should have a basic knowledge of algorithms, data structures, and calculus. Real-world case studies and chapter ending exercises help to create a full and realized picture of how search fits into the world of artificial intelligence and the one around us. - Provides real-world success stories and case studies for heuristic search algorithms - Includes many AI developments not yet covered in textbooks such as pattern databases, symbolic search, and parallel processing units

Eschewing the often standard dry and static writing style of traditional textbooks, Discrete Encounters provides a refreshing approach to discrete mathematics. The author blends traditional course topics and applications with historical context, pop culture references, and open problems. This book focuses on the historical development of the subject and provides fascinating details of the people behind the mathematics, along with their motivations, deepening readers’ appreciation of mathematics. This unique book covers many of the same topics found in traditional textbooks, but does so in an alternative, entertaining style that better captures readers’ attention. In addition to standard discrete mathematics material, the author shows the interplay between the discrete and the continuous and includes high-interest topics such as fractals, chaos theory, cellular automata, money-saving financial mathematics, and much more. Not only will readers gain a greater understanding of mathematics and its culture, they will also be encouraged to further explore the subject. Long lists of references at the end of each chapter make this easy. Highlights: Features fascinating historical context to motivate readers Text includes numerous pop culture references throughout to provide a more engaging reading experience Its unique topic structure presents a fresh approach The text’s narrative style is that of a popular book, not a dry textbook Includes the work of many living mathematicians Its multidisciplinary approach makes it ideal for liberal arts mathematics classes, leisure reading, or as a reference for professors looking to supplement traditional courses Contains many open problems Profusely illustrated

The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. It is published on a print?on?demand basis by Information Age Publishing and the electronic version is hosted by the Department of Mathematical Sciences? University of Montana. The journal is not affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education? North America] through special issues on various research topics.

This book looks at classic puzzles from the perspective of their structures and what they tell us about the brain. It uses the work on the neuroscience of mathematics from Dehaene, Butterworth, Lakoff, Núñez, and many others as a lens to understand the ways in which puzzles reflect imaginative processes blended with rational ones. The book is not about recreational or puzzle-based mathematics in and of itself but rather about what the classic puzzles tell us about the mathematical imagination and its impact on the discipline. It delves into the history of classic math puzzles, deconstructing their raison d’être and describing their psychological features, so that their nature can be fleshed out in order to help understand the mathematical mind. This volume is the first monographic treatment of the psychological nature of puzzles in mathematics. With its user-friendly technical level of discussion, it is of interest to both general readers and those who engage in the disciplines of mathematics, psychology, neuroscience, and/or anthropology. It is also ideal as a textbook source for courses in recreational mathematics, or as reference material in introductory college math courses.

SCIENCE AND EMPIRES: FROM THE INTERNATIONAL COLLOQUIUM TO THE BOOK Patrick PETITJEAN, Catherine JAMI and Anne Marie MOULIN The International Colloquium "Science and Empires - Historical Studies about Scientific De velopment and European Expansion" is the product of an International Colloquium, "Sciences and Empires - A Comparative History of Scien tific Exchanges: European Expansion and Scientific Development in Asian, African, American and Oceanian Countries". Organized by the REHSEIS group (Research on Epistemology and History of Exact Sciences and Scientific Institutions) of CNRS (National Center for Scientific Research), the colloquium was held from 3 to 6 April 1990 in the UNESCO building in Paris. This colloquium was an idea of Professor Roshdi Rashed who initiated this field of studies in France some years ago, and proposed "Sciences and Empires" as one of the main research programmes for the The project to organize such a colloquium was a bit REHSEIS group. of a gamble. Its subject, reflected in the title "Sciences and Empires", is not a currently-accepted sub-discipline of the history of science; rather, it refers to a set of questions which found autonomy only recently. The terminology was strongly debated by the participants and, as is frequently suggested in this book, awaits fuller clarification.