The Tower Of Hanoi Myths And Maths

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The Tower of Hanoi – Myths and Maths

Andreas M. Hinz,Sandi Klavžar,Uroš Milutinović,Ciril Petr
The Tower of Hanoi Myths and Maths Book PDF

Author : Andreas M. Hinz,Sandi Klavžar,Uroš Milutinović,Ciril Petr
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 45,5 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9783034802376

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The Tower of Hanoi – Myths and Maths by Andreas M. Hinz,Sandi Klavžar,Uroš Milutinović,Ciril Petr Pdf

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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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.

The Tower of Hanoi – Myths and Maths

Andreas M. Hinz,Sandi Klavžar,Ciril Petr
The Tower of Hanoi Myths and Maths Book PDF

Author : Andreas M. Hinz,Sandi Klavžar,Ciril Petr
Publisher : Birkhäuser
Page : 452 pages
File Size : 49,9 Mb
Release : 2018-04-17
Category : Mathematics
ISBN : 9783319737799

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The Tower of Hanoi – Myths and Maths by Andreas M. Hinz,Sandi Klavžar,Ciril Petr Pdf

The solitaire game “The Tower of Hanoi" was invented in the 19th century by the French number theorist Édouard Lucas. The book presents its mathematical theory and offers a survey of the historical development from predecessors up to recent research. In addition to long-standing myths, it provides a detailed overview of the essential mathematical facts with complete proofs, and also includes unpublished material, e.g., on some captivating integer sequences. 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, together with their correctness proofs, form an essential part of the book. In view of the most important practical applications, namely in physics, network theory and cognitive (neuro)psychology, the book also addresses other structures related to the Tower of Hanoi and its variants. The updated second edition includes, for the first time in English, the breakthrough reached with the solution of the “The Reve's Puzzle" in 2014. This is a special case of the famed Frame-Stewart conjecture which is still open after more than 75 years. 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. Excerpts from reviews of the first edition: “The book is an unusual, but very welcome, form of mathematical writing: recreational mathematics taken seriously and serious mathematics treated historically. I don’t hesitate to recommend this book to students, professional research mathematicians, teachers, and to readers of popular mathematics who enjoy more technical expository detail.” Chris Sangwin, The Mathematical Intelligencer 37(4) (2015) 87f. “The book demonstrates that the Tower of Hanoi has a very rich mathematical structure, and as soon as we tweak the parameters we surprisingly quickly find ourselves in the realm of open problems.” László Kozma, ACM SIGACT News 45(3) (2014) 34ff. “Each time I open the book I discover a renewed interest in the Tower of Hanoi. I am sure that this will be the case for all readers.” Jean-Paul Allouche, Newsletter of the European Mathematical Society 93 (2014) 56.

Discrete Encounters

Craig Bauer
Discrete Encounters Book PDF

Author : Craig Bauer
Publisher : CRC Press
Page : 668 pages
File Size : 42,7 Mb
Release : 2020-05-14
Category : Mathematics
ISBN : 9780429682889

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Discrete Encounters by Craig Bauer Pdf

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

Bharath Sriraman
The Mathematics Enthusiast Book PDF

Author : Bharath Sriraman
Publisher : IAP
Page : 300 pages
File Size : 55,9 Mb
Release : 2014-12-01
Category : Education
ISBN : 9781681230177

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The Mathematics Enthusiast by Bharath Sriraman Pdf

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.

The Mathematics of Various Entertaining Subjects

Jennifer Beineke,Jason Rosenhouse
The Mathematics of Various Entertaining Subjects Book PDF

Author : Jennifer Beineke,Jason Rosenhouse
Publisher : Princeton University Press
Page : 408 pages
File Size : 46,8 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9780691171920

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The Mathematics of Various Entertaining Subjects by Jennifer Beineke,Jason Rosenhouse Pdf

The history of mathematics is filled with major breakthroughs resulting from solutions to recreational problems. Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects now returns with a brand-new compilation of fascinating problems and solutions in recreational mathematics. This latest volume gathers together the top experts in recreational math and presents a compelling look at board games, card games, dice, toys, computer games, and much more. The book is divided into five parts: puzzles and brainteasers, geometry and topology, graph theory, games of chance, and computational complexity. Readers will discover what origami, roulette wheels, and even the game of Trouble can teach about math. Essays contain new results, and the contributors include short expositions on their topic’s background, providing a framework for understanding the relationship between serious mathematics and recreational games. Mathematical areas explored include combinatorics, logic, graph theory, linear algebra, geometry, topology, computer science, operations research, probability, game theory, and music theory. Investigating an eclectic mix of games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.

A Richer Picture of Mathematics

David E. Rowe
A Richer Picture of Mathematics Book PDF

Author : David E. Rowe
Publisher : Springer
Page : 461 pages
File Size : 51,6 Mb
Release : 2018-02-13
Category : Mathematics
ISBN : 9783319678191

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A Richer Picture of Mathematics by David E. Rowe Pdf

Historian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the “Years Ago” column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe’s various and many-faceted contributions to the history of mathematics. Centered on the Göttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow recount episodes relating to the section’s overall theme. All of the essays in this collection, with the exception of two, appeared over the course of more than 30 years in The Mathematical Intelligencer. Based largely on archival and primary sources, these vignettes offer unusual insights into behind-the-scenes events. Taken together, they aim to show how Göttingen managed to attract an extraordinary array of talented individuals, several of whom contributed to the development of a new mathematical culture during the first decades of the twentieth century.

Games of No Chance 5

Urban Larsson
Games of No Chance 5 Book PDF

Author : Urban Larsson
Publisher : Cambridge University Press
Page : 499 pages
File Size : 54,5 Mb
Release : 2019-05-09
Category : Computers
ISBN : 9781108485807

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Games of No Chance 5 by Urban Larsson Pdf

Surveys the state-of-the-art in combinatorial game theory, that is games not involving chance or hidden information.

Heuristic Search

Stefan Edelkamp,Stefan Schroedl
Heuristic Search Book PDF

Author : Stefan Edelkamp,Stefan Schroedl
Publisher : Elsevier
Page : 712 pages
File Size : 51,7 Mb
Release : 2011-05-31
Category : Computers
ISBN : 0080919731

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Heuristic Search by Stefan Edelkamp,Stefan Schroedl Pdf

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

Unconventional Computation and Natural Computation

Martyn Amos,Anne Condon
Unconventional Computation and Natural Computation Book PDF

Author : Martyn Amos,Anne Condon
Publisher : Springer
Page : 197 pages
File Size : 46,6 Mb
Release : 2016-06-17
Category : Computers
ISBN : 9783319413129

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Unconventional Computation and Natural Computation by Martyn Amos,Anne Condon Pdf

This book constitutes the refereed proceedings of the 15th International Conference on Unconventional Computation and Natural Computation, UCNC 2016, held in Manchester, UK, in July 2016. The 15 revised full papers presented together with 5 invited papers were carefully reviewed and selected from 30 submissions. The papers cover a wide range of topics including molecular, cellular, quantum, optical and chaos computing; cellular automata; neural and evolutionary computation; artificial immune systems; Ant algorithms and swarm intelligence; amorphous computing; membrane computing; computational systems biology and computational neuroscience; and synthetic biology.

The Zeroth Book of Graph Theory

Martin Charles Golumbic,André Sainte-Laguë
The Zeroth Book of Graph Theory Book PDF

Author : Martin Charles Golumbic,André Sainte-Laguë
Publisher : Springer Nature
Page : 122 pages
File Size : 46,6 Mb
Release : 2021-02-09
Category : Mathematics
ISBN : 9783030614201

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The Zeroth Book of Graph Theory by Martin Charles Golumbic,André Sainte-Laguë Pdf

Marking 94 years since its first appearance, this book provides an annotated translation of Sainte-Laguë's seminal monograph Les réseaux (ou graphes), drawing attention to its fundamental principles and ideas. Sainte-Laguë's 1926 monograph appeared only in French, but in the 1990s H. Gropp published a number of English papers describing several aspects of the book. He expressed his hope that an English translation might sometime be available to the mathematics community. In the 10 years following the appearance of Les réseaux (ou graphes), the development of graph theory continued, culminating in the publication of the first full book on the theory of finite and infinite graphs in 1936 by Dénes König. This remained the only well-known text until Claude Berge's 1958 book on the theory and applications of graphs. By 1960, graph theory had emerged as a significant mathematical discipline of its own. This book will be of interest to graph theorists and mathematical historians.

The Best Writing on Mathematics 2014

Mircea Pitici
The Best Writing on Mathematics 2014 Book PDF

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 360 pages
File Size : 55,6 Mb
Release : 2014-11-23
Category : Mathematics
ISBN : 9780691164175

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The Best Writing on Mathematics 2014 by Mircea Pitici Pdf

Collects essays on mathematics, from the importance of big data and the varying forms of Klein bottles to fountain design and the possible shape of the universe.

Mathematics and Its Connections to the Arts and Sciences (MACAS)

Claus Michelsen,Astrid Beckmann,Viktor Freiman,Uffe Thomas Jankvist,Annie Savard
Mathematics and Its Connections to the Arts and Sciences MACAS Book PDF

Author : Claus Michelsen,Astrid Beckmann,Viktor Freiman,Uffe Thomas Jankvist,Annie Savard
Publisher : Springer Nature
Page : 560 pages
File Size : 46,9 Mb
Release : 2022-12-19
Category : Education
ISBN : 9783031105180

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Mathematics and Its Connections to the Arts and Sciences (MACAS) by Claus Michelsen,Astrid Beckmann,Viktor Freiman,Uffe Thomas Jankvist,Annie Savard Pdf

This book celebrates the 15th anniversary of the bi-annual symposium series Mathematics and its Connections to the Arts and Sciences (MACAS), which was first held in 2005 following the continued collaboration of an international group of researchers from ICME Topic Study Group 21. The MACAS-conferences bring together scientists and educators who are interested in the connection between mathematics, arts and science in educational curriculum, while emphasizing on, as well as researching about, the role of mathematics. By pooling together these different approaches and viewpoints between mathematics, arts and sciences, this book reveals possible synergies and paths for collaborations. In view of the challenges of the 21st century, a modern approach to education with a focus on multi- and interdisciplinarity is more important than ever. The role of mathematics assumes a key role in this approach as it is connected to all other disciplines, such as STEM education, physics, chemistry, biology, aesthetics and language, and can serve as a bridge between them. This book discusses, amongst others, the curricular approaches to integrate mathematics and other disciplines, the importance of mathematical modelling and the interdisciplinarity ways for learning and studying of mathematics, as well as the intercultural dimensions of mathematics and mathematics in the digital era. All topics will be presented from very different perspectives and regarding very different contexts, including digitization, culture and sustainability. This unique collection will serve as a very valuable and compact source for all above mentioned scientists and educators, as well as for use in advanced teacher education courses.

Graph and Network Theory

Michael A. Henning,Jan H. van Vuuren
Graph and Network Theory Book PDF

Author : Michael A. Henning,Jan H. van Vuuren
Publisher : Springer Nature
Page : 782 pages
File Size : 52,9 Mb
Release : 2022-06-03
Category : Business & Economics
ISBN : 9783031038570

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Graph and Network Theory by Michael A. Henning,Jan H. van Vuuren Pdf

This textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.

Fibonacci Cubes With Applications And Variations

Omer Egecioglu,Sandi Klavzar,Michel Mollard
Fibonacci Cubes With Applications And Variations Book PDF

Author : Omer Egecioglu,Sandi Klavzar,Michel Mollard
Publisher : World Scientific
Page : 303 pages
File Size : 41,5 Mb
Release : 2023-02-17
Category : Mathematics
ISBN : 9789811269165

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Fibonacci Cubes With Applications And Variations by Omer Egecioglu,Sandi Klavzar,Michel Mollard Pdf

Fibonacci Cubes have been an extremely popular area of research since the 1990s.This unique compendium features the state of research into Fibonacci Cubes. It expands the knowledge in graph theoretic and combinatorial properties of Fibonacci Cubes and their variants.By highlighting various approaches with numerous examples, it provides a fundamental source for further research in the field. This useful reference text surely benefits advanced students in computer science and mathematics and serves as an archival record of the current state of the field.

Ahmes’ Legacy

Marcel Danesi
Ahmes Legacy Book PDF

Author : Marcel Danesi
Publisher : Springer
Page : 164 pages
File Size : 44,6 Mb
Release : 2018-08-11
Category : Mathematics
ISBN : 9783319932545

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Ahmes’ Legacy by Marcel Danesi Pdf

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.