Muutke küpsiste eelistusi

E-raamat: Tower of Hanoi - Myths and Maths

5.00/5 (2 hinnangut Goodreads-ist)
, , ,
  • Formaat: PDF+DRM
  • Ilmumisaeg: 31-Jan-2013
  • Kirjastus: Birkhauser Verlag AG
  • Keel: eng
  • ISBN-13: 9783034802376
Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 61,74 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Tower of Hanoi - Myths and MathsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 31-Jan-2013
  • Kirjastus: Birkhauser Verlag AG
  • Keel: eng
  • ISBN-13: 9783034802376
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

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thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material.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

Arvustused

The Tower of Hanoi isnt just a recreational problem, it is also a substantial area worthy of study, and this book does this area full justice. I havent enjoyed reading a popular mathematics book as much for quite some time, and I dont 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, Vol. 37, 2015)

This book takes the reader on an enjoyable adventure into the Tower of Hanoi puzzle (TH) and various related puzzles and objects. The style of presentation is entertaining, at times humorous, and very thorough. The exercises ending each chapter are an essential part of the explication providing some definitions and some proofs of the theorems or statements inthe main text. As such, the book will be an enjoyable read for any recreational mathematician . (Andrew Percy, zbMATH, Vol. 1285, 2014)

This research monograph focuses on a large family of problems connected to the classic puzzle of the Tower of Hanoi. The authors explain all the combinatorial concepts they use, so the book is completely accessible to an advanced undergraduate student. Summing Up: Recommended. Comprehensive mathematics collections, upper-division undergraduates through researchers/faculty. (M. Bona, Choice, Vol. 51 (3), November, 2013)

The Tower of Hanoi is an example of a problem that is easy to state and understand, yet a thorough mathematical analysis of the problem and its extensions is lengthy enough to make a book. there is enough implied mathematics in the action to make it interesting to professional mathematicians. It was surprising to learn that the simple problem of the Tower of Hanoi could be the subject of a full semester special topics course in advanced mathematics. (Charles Ashbacher, MAA Reviews, May, 2013)

Gives an introduction to the problem and the history of the TH puzzle and other related puzzles, but it also introduces definitions and properties of graphs that are used in solving these problems. Thus if you love puzzles, and more in particular the mathematics behind it, this is a book for you. Also if you are looking for a lifelasting occupation, then you may find here a list of open problems that will keep you busy for a while. (A. Bultheel, The European Mathematical Society, February, 2013)

Foreword v
Ian Stewart
Preface vii
0 The Beginning of the World
1(52)
0.1 The Legend of the Tower of Brahma
1(2)
0.2 History of the Chinese Rings
3(3)
0.3 History of the Tower of Hanoi
6(17)
0.4 Puzzles and Graphs
23(13)
0.5 Quotient Sets
36(5)
0.5.1 Equivalence
37(2)
0.5.2 Group Actions and Burnside's Lemma
39(2)
0.6 Early Mathematical Sources
41(9)
0.6.1 Chinese Rings
41(2)
0.6.2 Tower of Hanoi
43(7)
0.7 Exercises
50(3)
1 The Chinese Rings
53(18)
1.1 Theory of the Chinese Rings
53(7)
1.2 The Gros Sequence
60(5)
1.3 Two Applications
65(3)
1.4 Exercises
68(3)
2 The Classical Tower of Hanoi
71(60)
2.1 Perfect to Perfect
71(11)
2.2 Regular to Perfect
82(12)
2.3 Hanoi Graphs
94(11)
2.4 Regular to Regular
105(23)
2.4.1 The Average Distance on Hn3
113(8)
2.4.2 Pascal's Triangle and Stern's Diatomic Sequence
121(3)
2.4.3 Romik's Solution to the P2 Decision Problem
124(3)
2.4.4 The Double P2 Problem
127(1)
2.5 Exercises
128(3)
3 Lucas's Second Problem
131(10)
3.1 Irregular to Regular
131(5)
3.2 Irregular to Perfect
136(4)
3.3 Exercises
140(1)
4 Sierpinski Graphs
141(24)
4.1 Sierpinski Graphs With Base 3
141(8)
4.2 General Sierpinski Graphs
149(11)
4.2.1 Distance Properties
150(5)
4.2.2 Other Properties
155(3)
4.2.3 Sierpinski Graphs as Interconnection Networks
158(2)
4.3 Connections to Topology: Sierpinski Curve and Lipscomb Space
160(3)
4.4 Exercises
163(2)
5 The Tower of Hanoi with More Pegs
165(46)
5.1 The Reve's Puzzle and the Frame-Stewart Conjecture
165(5)
5.2 Frame-Stewart Numbers
170(9)
5.3 Numerical Evidence for The Reve's Puzzle
179(5)
5.4 Even More Pegs
184(6)
5.5 Hanoi Graphs Hnp
190(10)
5.6 Numerical Results and Largest Disc Moves
200(9)
5.6.1 Path Algorithms
201(1)
5.6.2 Largest Disc Moves
202(7)
5.7 Exercises
209(2)
6 Variations of the Puzzle
211(16)
6.1 What is a Tower of Hanoi Variant?
211(7)
6.2 The Tower of Antwerpen
218(4)
6.3 The Bottleneck Tower of Hanoi
222(4)
6.4 Exercises
226(1)
7 The Tower of London
227(14)
7.1 Shallice's Tower of London
227(4)
7.2 More London Towers
231(7)
7.3 Exercises
238(3)
8 Tower of Hanoi Variants with Oriented Disc Moves
241(20)
8.1 Solvability
241(4)
8.2 An Algorithm for Three Pegs
245(6)
8.3 More Than Three Pegs
251(5)
8.4 Exponential and Sub-Exponential Variants
256(3)
8.5 Exercises
259(2)
9 The End of the World
261(4)
A Hints and Solutions to Exercises 265(28)
Glossary 293(4)
Bibliography 297(22)
Name Index 319(4)
Subject Index 323(10)
Symbol Index 333
Andreas M. Hinz is Professor at the Department of  Mathematics, University of Munich (LMU), Germany. He has worked at the University of Geneva (Switzerland), King's College London (England), the Technical University of Munich (Germany), and the Open University in Hagen (Germany). His main fields of research are real analysis, the history of science, mathematical modeling, and discrete mathematics.

Sandi Klavar is Professor at the Faculty of Mathematics and Physics, University of Ljubljana, Slovenia, and at the Department of Mathematics and Computer Science, University of Maribor, Slovenia. He is an author of three books on graph theory and an editorial board member of numerous journals including Discrete Applied Mathematics, European Journal of Combinatorics, and MATCH Communications in Mathematical and in Computer Chemistry.

Uro Milutinovi is Professor at the Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia. His mainfields of research are topology and discrete mathematics.

Ciril Petr is a researcher at the Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97830348023762e.html
Märksõnad: