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The Resource The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor
The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor
Resource Information
The item The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 The 3x+1 problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer x is odd then "multiply by three and add one", while if it is even then "divide by two." The 3x+1 problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite this simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving the history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem. Finally, the book reprints six early papers on the problem and related questions.  from Back Cover
 Language
 eng
 Extent
 xiv, 344 pages
 Contents

 The 3x+1 problem: an overview
 The 3x+1 problem and its generalizations / Jeffrey C. Lagarias
 Survey papers. A 3x+1 survey: number theory and dynamical systems / Marc Chamberland
 Generalized 3x+1 mappings: Markov chains and ergodic theory / K.R. Matthews
 Generalized 3x+1 functions and the theory of computation / Pascal Michel and Maurice Margenstern
 Stochastic modelling and computation papers. Stochastic models for the 3x+1 and 5x+1 problems and related problems / Alex V. Kontorovich and Jeffrey C. Lagarias
 Empirical verification of the 3x+1 and related conjectures / Tomás Oliveira E Silva
 Reprinted early papers. Cyclic sequences and frieze patterns (The fourth Felix Behrend Memorial Lecture) / H.S.M. Coxeter
 Unpredictable iterations / J.H. Conway
 Iteration of the numbertheoretic function: f(2n) = n, f(2n +1) = 3n + 2 / C.J. Everett
 Don't try to solve these problems! / Richard K. Guy
 On the motivation and origin of the (3n + 1)problem / Lothar Collatz
 FRACTRAN: a simple universal programming language for arithmetic / J.H. Conway
 The 3x+1 problem: an annotated bibliography (19631999) / Jeffrey C. Lagarias
 Isbn
 9780821849408
 Label
 The ultimate challenge : the 3x+1 problem
 Title
 The ultimate challenge
 Title remainder
 the 3x+1 problem
 Statement of responsibility
 Jeffrey C. Lagarias, editor
 Subject

 CollatzProblem
 CollatzProblem
 Computer science  Theory of computing  None of the above, but in this section
 Dynamical systems and ergodic theory  Ergodic theory  Relations with number theory and harmonic analysis
 Folge
 Harmonic analysis
 Harmonic analysis
 Harmonic analysis
 Harmonic analysis
 Iteration
 MarkovKette
 Number theory  Sequences and sets  Recurrences
 Number theory  Sequences and sets  Special sequences and polynomials
 Polynom
 Polynomials
 Polynomials
 Polynomials
 Polynomials
 Reihe
 Sequences (Mathematics)
 Sequences (Mathematics)
 Sequences (Mathematics)
 Sequences (Mathematics)
 Language
 eng
 Summary
 The 3x+1 problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer x is odd then "multiply by three and add one", while if it is even then "divide by two." The 3x+1 problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite this simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving the history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem. Finally, the book reprints six early papers on the problem and related questions.  from Back Cover
 Cataloging source
 DLC
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA292
 LC item number
 .U48 2010
 Literary form
 non fiction
 Nature of contents
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1949
 http://library.link/vocab/relatedWorkOrContributorName
 Lagarias, Jeffrey C.
 http://library.link/vocab/subjectName

 Sequences (Mathematics)
 Polynomials
 Harmonic analysis
 Harmonic analysis
 Polynomials
 Sequences (Mathematics)
 CollatzProblem
 Number theory
 Dynamical systems and ergodic theory
 Number theory
 Computer science
 Reihe
 Iteration
 Polynom
 Folge
 MarkovKette
 Label
 The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 The 3x+1 problem: an overview  The 3x+1 problem and its generalizations / Jeffrey C. Lagarias  Survey papers. A 3x+1 survey: number theory and dynamical systems / Marc Chamberland  Generalized 3x+1 mappings: Markov chains and ergodic theory / K.R. Matthews  Generalized 3x+1 functions and the theory of computation / Pascal Michel and Maurice Margenstern  Stochastic modelling and computation papers. Stochastic models for the 3x+1 and 5x+1 problems and related problems / Alex V. Kontorovich and Jeffrey C. Lagarias  Empirical verification of the 3x+1 and related conjectures / Tomás Oliveira E Silva  Reprinted early papers. Cyclic sequences and frieze patterns (The fourth Felix Behrend Memorial Lecture) / H.S.M. Coxeter  Unpredictable iterations / J.H. Conway  Iteration of the numbertheoretic function: f(2n) = n, f(2n +1) = 3n + 2 / C.J. Everett  Don't try to solve these problems! / Richard K. Guy  On the motivation and origin of the (3n + 1)problem / Lothar Collatz  FRACTRAN: a simple universal programming language for arithmetic / J.H. Conway  The 3x+1 problem: an annotated bibliography (19631999) / Jeffrey C. Lagarias
 Dimensions
 27 cm
 Extent
 xiv, 344 pages
 Isbn
 9780821849408
 Isbn Type
 (alk. paper)
 Lccn
 2010035270
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number

 (OCoLC)660161866
 (OCoLC)ocn660161866
 Label
 The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 volume
 Carrier category code

 nc
 Carrier MARC source
 rdacarrier
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 The 3x+1 problem: an overview  The 3x+1 problem and its generalizations / Jeffrey C. Lagarias  Survey papers. A 3x+1 survey: number theory and dynamical systems / Marc Chamberland  Generalized 3x+1 mappings: Markov chains and ergodic theory / K.R. Matthews  Generalized 3x+1 functions and the theory of computation / Pascal Michel and Maurice Margenstern  Stochastic modelling and computation papers. Stochastic models for the 3x+1 and 5x+1 problems and related problems / Alex V. Kontorovich and Jeffrey C. Lagarias  Empirical verification of the 3x+1 and related conjectures / Tomás Oliveira E Silva  Reprinted early papers. Cyclic sequences and frieze patterns (The fourth Felix Behrend Memorial Lecture) / H.S.M. Coxeter  Unpredictable iterations / J.H. Conway  Iteration of the numbertheoretic function: f(2n) = n, f(2n +1) = 3n + 2 / C.J. Everett  Don't try to solve these problems! / Richard K. Guy  On the motivation and origin of the (3n + 1)problem / Lothar Collatz  FRACTRAN: a simple universal programming language for arithmetic / J.H. Conway  The 3x+1 problem: an annotated bibliography (19631999) / Jeffrey C. Lagarias
 Dimensions
 27 cm
 Extent
 xiv, 344 pages
 Isbn
 9780821849408
 Isbn Type
 (alk. paper)
 Lccn
 2010035270
 Media category
 unmediated
 Media MARC source
 rdamedia
 Media type code

 n
 Other physical details
 illustrations
 System control number

 (OCoLC)660161866
 (OCoLC)ocn660161866
Subject
 CollatzProblem
 CollatzProblem
 Computer science  Theory of computing  None of the above, but in this section
 Dynamical systems and ergodic theory  Ergodic theory  Relations with number theory and harmonic analysis
 Folge
 Harmonic analysis
 Harmonic analysis
 Harmonic analysis
 Harmonic analysis
 Iteration
 MarkovKette
 Number theory  Sequences and sets  Recurrences
 Number theory  Sequences and sets  Special sequences and polynomials
 Polynom
 Polynomials
 Polynomials
 Polynomials
 Polynomials
 Reihe
 Sequences (Mathematics)
 Sequences (Mathematics)
 Sequences (Mathematics)
 Sequences (Mathematics)
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