The Tower Of Hanoi Myths And Maths

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The Tower of Hanoi – Myths and Maths

Author : Andreas M. Hinz
Publisher : Springer Science & Business Media
ISBN 13 : 3034802374
Total Pages : 340 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Tower of Hanoi – Myths and Maths by : Andreas M. Hinz

Download or read book The Tower of Hanoi – Myths and Maths written by Andreas M. Hinz and published by Springer Science & Business Media. This book was released on 2013-01-31 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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

Author : Andreas M. Hinz
Publisher : Birkhäuser
ISBN 13 : 9783034807692
Total Pages : 0 pages
Book Rating : 4.8/5 (76 download)

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Book Synopsis The Tower of Hanoi – Myths and Maths by : Andreas M. Hinz

Download or read book The Tower of Hanoi – Myths and Maths written by Andreas M. Hinz and published by Birkhäuser. This book was released on 2015-07-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Andreas M. Hinz
Publisher : Birkhäuser
ISBN 13 : 3319737791
Total Pages : 452 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis The Tower of Hanoi – Myths and Maths by : Andreas M. Hinz

Download or read book The Tower of Hanoi – Myths and Maths written by Andreas M. Hinz and published by Birkhäuser. This book was released on 2018-04-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Heuristic Search

Author : Stefan Edelkamp
Publisher : Elsevier
ISBN 13 : 9780080919737
Total Pages : 712 pages
Book Rating : 4.9/5 (197 download)

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Book Synopsis Heuristic Search by : Stefan Edelkamp

Download or read book Heuristic Search written by Stefan Edelkamp and published by Elsevier. This book was released on 2011-05-31 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

1089 and All that

Author : D. J. Acheson
Publisher : Oxford University Press, USA
ISBN 13 : 9780198516231
Total Pages : 200 pages
Book Rating : 4.5/5 (162 download)

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Book Synopsis 1089 and All that by : D. J. Acheson

Download or read book 1089 and All that written by D. J. Acheson and published by Oxford University Press, USA. This book was released on 2002 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent book, written by the established author David Acheson, makes mathematics accessible to everyone. Providing an entertaining and witty overview of the subject, the text includes several fascinating puzzles, and is accompanied by numerous illustrations and sketches by world famouscartoonists. This unusual book is one of the most readable explanations of mathematics available.

Discrete Encounters

Author : Craig Bauer
Publisher : CRC Press
ISBN 13 : 0429682883
Total Pages : 668 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Discrete Encounters by : Craig Bauer

Download or read book Discrete Encounters written by Craig Bauer and published by CRC Press. This book was released on 2020-05-14 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Ahmes’ Legacy

Author : Marcel Danesi
Publisher : Springer
ISBN 13 : 3319932543
Total Pages : 164 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Ahmes’ Legacy by : Marcel Danesi

Download or read book Ahmes’ Legacy written by Marcel Danesi and published by Springer. This book was released on 2018-08-11 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : P. Petitjean
Publisher : Springer Science & Business Media
ISBN 13 : 9401125945
Total Pages : 419 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Science and Empires by : P. Petitjean

Download or read book Science and Empires written by P. Petitjean and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Handbook of Mathematical Discourse

Author : Charles Wells
Publisher : Infinity Publishing
ISBN 13 : 0741416859
Total Pages : 1 pages
Book Rating : 4.7/5 (414 download)

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Book Synopsis A Handbook of Mathematical Discourse by : Charles Wells

Download or read book A Handbook of Mathematical Discourse written by Charles Wells and published by Infinity Publishing. This book was released on 2003 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topics in Graph Theory

Author : Wilfried Imrich
Publisher : CRC Press
ISBN 13 : 1439865337
Total Pages : 219 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Topics in Graph Theory by : Wilfried Imrich

Download or read book Topics in Graph Theory written by Wilfried Imrich and published by CRC Press. This book was released on 2008-10-27 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way,

The Philosophy of Mathematics Education

Author : Paul Ernest
Publisher : Springer
ISBN 13 : 3319405691
Total Pages : 33 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis The Philosophy of Mathematics Education by : Paul Ernest

Download or read book The Philosophy of Mathematics Education written by Paul Ernest and published by Springer. This book was released on 2016-07-15 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.

The Mathematics Enthusiast

Author : Bharath Sriraman
Publisher : IAP
ISBN 13 : 1681230178
Total Pages : 300 pages
Book Rating : 4.6/5 (812 download)

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Book Synopsis The Mathematics Enthusiast by : Bharath Sriraman

Download or read book The Mathematics Enthusiast written by Bharath Sriraman and published by IAP. This book was released on 2014-12-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Developing Atlas Skills Through Crosswords

Author : George Moore
Publisher :
ISBN 13 : 9781846540318
Total Pages : 41 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Developing Atlas Skills Through Crosswords by : George Moore

Download or read book Developing Atlas Skills Through Crosswords written by George Moore and published by . This book was released on 2005 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features photocopiable resources to expand pupils' knowledge of the world; and, pupils use of atlases, the Internet and other reference sources to complete geographical crosswords. This title also offers information on latitude and longitude, scales and the eight compass points. It is suitable for class, group, individual and homework use.

Metaphors We Live By

Author : George Lakoff
Publisher : University of Chicago Press
ISBN 13 : 0226470997
Total Pages : 292 pages
Book Rating : 4.2/5 (264 download)

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Book Synopsis Metaphors We Live By by : George Lakoff

Download or read book Metaphors We Live By written by George Lakoff and published by University of Chicago Press. This book was released on 2008-12-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The now-classic Metaphors We Live By changed our understanding of metaphor and its role in language and the mind. Metaphor, the authors explain, is a fundamental mechanism of mind, one that allows us to use what we know about our physical and social experience to provide understanding of countless other subjects. Because such metaphors structure our most basic understandings of our experience, they are "metaphors we live by"—metaphors that can shape our perceptions and actions without our ever noticing them. In this updated edition of Lakoff and Johnson's influential book, the authors supply an afterword surveying how their theory of metaphor has developed within the cognitive sciences to become central to the contemporary understanding of how we think and how we express our thoughts in language.

Automatic Sequences

Author : Jean-Paul Allouche
Publisher : Cambridge University Press
ISBN 13 : 9780521823326
Total Pages : 592 pages
Book Rating : 4.8/5 (233 download)

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Book Synopsis Automatic Sequences by : Jean-Paul Allouche

Download or read book Automatic Sequences written by Jean-Paul Allouche and published by Cambridge University Press. This book was released on 2003-07-21 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.

The Music of the Primes: Why an unsolved problem in mathematics matters (Text Only)

Author : Marcus du Sautoy
Publisher : HarperCollins UK
ISBN 13 : 0007375875
Total Pages : 371 pages
Book Rating : 4.0/5 (73 download)

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Book Synopsis The Music of the Primes: Why an unsolved problem in mathematics matters (Text Only) by : Marcus du Sautoy

Download or read book The Music of the Primes: Why an unsolved problem in mathematics matters (Text Only) written by Marcus du Sautoy and published by HarperCollins UK. This book was released on 2012-05-31 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: (This ebook contains a limited number of illustrations.) The ebook of the critically-acclaimed popular science book by a writer who is fast becoming a celebrity mathematician.

A Philosophy of War

Author : Alexander Moseley
Publisher : Algora Publishing
ISBN 13 : 0875861830
Total Pages : 280 pages
Book Rating : 4.8/5 (758 download)

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Book Synopsis A Philosophy of War by : Alexander Moseley

Download or read book A Philosophy of War written by Alexander Moseley and published by Algora Publishing. This book was released on 2002 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: "War's origins are complex: they are found in the nebulous systems of thoughts generated in cultures over time. But while reason and explication can unravel those origins - and explain why man wages war - the task of abolishing war can never be completed.