The Tower of Hanoi – Myths and Maths PDF Download
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Author: Andreas M. Hinz
Publisher: Springer Science & Business Media
ISBN: 3034802374
Category : Mathematics
Languages : en
Pages : 340
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Book Description
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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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.
Author: Andreas M. Hinz
Publisher: Springer Science & Business Media
ISBN: 3034802374
Category : Mathematics
Languages : en
Pages : 340
Get Book Here
Book Description
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.
Author: Stefan Edelkamp
Publisher: Elsevier
ISBN: 0080919731
Category : Computers
Languages : en
Pages : 865
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Book Description
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
Author: Craig Bauer
Publisher: CRC Press
ISBN: 0429682883
Category : Mathematics
Languages : en
Pages : 740
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Book Description
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
Author: Charles Wells
Publisher: Infinity Publishing
ISBN: 0741416859
Category : Education
Languages : en
Pages : 1
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Book Description
Author: Bharath Sriraman
Publisher: IAP
ISBN: 1681230178
Category : Education
Languages : en
Pages : 301
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Book Description
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.
Author: Timothy Revell
Publisher: Aurum Press
ISBN: 9781781316900
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Man vs Maths explains the complexities of the mathematics of modern life, showing how understanding a little more maths can improve your life and how to use it to your advantage. Plus along the way you'll discover how social media trends work, why the universe has a favourite number and what this means for you. Mathematics is inescapable. Wherever you go, whatever you do, however you live your life, mathematics plays an important role. From controlling a city’s traffic to finding love, spending money online to building a skyscraper, the mathematics at play in our world is fascinating. Yet despite its ubiquity, for many of us, how the maths of today really works remains complex. â??Mathematician Timothy Revell distills these complexities in this essential guide to modern-day mathematics, exploring questions such as; Could we solve queuing with an equation? How do algorithms control our news? What is the secret behind encryption codes?
Author: Marcel Danesi
Publisher: Springer
ISBN: 3319932543
Category : Mathematics
Languages : en
Pages : 174
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Book Description
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.
Author: Fadi A. Bardawil
Publisher: Duke University Press
ISBN: 1478007583
Category : Social Science
Languages : en
Pages : 188
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Book Description
The Arab Revolutions that began in 2011 reignited interest in the question of theory and practice, imbuing it with a burning political urgency. In Revolution and Disenchantment Fadi A. Bardawil redescribes for our present how an earlier generation of revolutionaries, the 1960s Arab New Left, addressed this question. Bardawil excavates the long-lost archive of the Marxist organization Socialist Lebanon and its main theorist, Waddah Charara, who articulated answers in their political practice to fundamental issues confronting revolutionaries worldwide: intellectuals as vectors of revolutionary theory; political organizations as mediators of theory and praxis; and nonemancipatory attachments as impediments to revolutionary practice. Drawing on historical and ethnographic methods and moving beyond familiar reception narratives of Marxist thought in the postcolony, Bardawil engages in "fieldwork in theory" that analyzes how theory seduces intellectuals, cultivates sensibilities, and authorizes political practice. Throughout, Bardawil underscores the resonances and tensions between Arab intellectual traditions and Western critical theory and postcolonial theory, deftly placing intellectuals from those traditions into a much-needed conversation.
Author: Wilfried Imrich
Publisher: CRC Press
ISBN: 1439865337
Category : Mathematics
Languages : en
Pages : 214
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Book Description
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,
Author: Brian Overland
Publisher: Addison-Wesley Professional
ISBN: 0134688279
Category : Computers
Languages : en
Pages : 1224
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Book Description
Praise for this book, Python Without Fear “This is really a great book. I wish I’d had it when I was learning Python.” –John M. Wargo, author of Apache Cordova 4 Programming Praise for the previous book in the series, C++ Without Fear “I’m in love with your C++ Without Fear book. It keeps me awake for hours during the night. Thanks to you, I got most of the idea in just a few hours.” –Laura Viral, graduate physics student at CERN and Istanbul, Turkey “It’s hard to tell where I began and ended with your book. I felt like I woke up and literally knew how to write C++ code. I can’t overstate the confidence you gave me.” – Danny Grady, senior programmer/analyst at a Fortune 500 Company Whether you’re new to programming or moving from another language, Python Without Fear will quickly make you productive! Brian Overland’s unique approach to Python includes: Taking you by the hand while teaching topics from the very basics to intermediate and advanced features of Python Teaching by examples that are explained line by line Heavy emphasis on examples that are fun and useful, including games, graphics, database applications, file storage, puzzles, and more! How to think “Pythonically” and avoid common “gotchas” Register your product at informit.com/register for convenient access to downloads, updates, and/or corrections as they become available.
