The Resource The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor

The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor

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
Contributor
Subject
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)
  • Collatz-Problem
  • Number theory
  • Dynamical systems and ergodic theory
  • Number theory
  • Computer science
  • Reihe
  • Iteration
  • Polynom
  • Folge
  • Markov-Kette
Label
The ultimate challenge : the 3x+1 problem, Jeffrey C. Lagarias, editor
Instantiates
Publication
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 number-theoretic 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 (1963-1999) / 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
Publication
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 number-theoretic 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 (1963-1999) / 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

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