£47.85

The Ultimate Challenge: The $3x+1$ Problem (Miscellaneous Book Series)

Mathematical Theory

Price data last checked 19 day(s) ago - will refresh soon

View at Amazon

We'll watch every seller, every day. One email when your price arrives.

About as cheap as it gets. The only time it was cheaper was 2 months ago.

£48 today · all-time low £47 (Apr 2026) · usually £48

NEW HERE?

Amazon shows you one price. We show you all of them.

Tosheroon watches Amazon prices so you don't have to. Every product on Amazon has a price history — we make it visible. Set the price you'd actually pay, and we'll email you the second it gets there. No app, no account, one email.

WHAT'S ON THIS PAGE

↓ Price chart
when this has been cheap or pricey

↓ Forecast
where the price is heading next

↓ Statistics
all-time high & low, recent range

↑ Price alert
name your number, we'll email you

Price History & Forecast

Grey patches = out of stock. Cheaper = lower on the chart. Hover for exact prices.

Last 72 days • 72 data points (No recent data available)

Historical

Generating forecast...

Price Distribution

Price distribution over 72 days • 2 price levels

Days at Price

Current Price

Price Analysis

Most common price: £48 (44 days, 61.1%)

Price range: £48 - £56

Price levels: 2 different prices over 72 days

Description

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 its 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 history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic 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, which verify its truth for $x <5.4 \cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.

Key Features

The Ultimate Challenge: The $3X 1$ Problem Miscellaneous Book Series

Product Type: Abis Book

Language: English

Product Specifications

Format: paperback
ASIN: 1470472899
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Theory
Domain: Amazon UK
Release Date: 01 January 2010
Listed Since: 10 March 2023

Barcode

No barcode data available

The Ultimate Challenge: The $3x+1$ Problem (Miscellaneous Book Series)

About as cheap as it gets. The only time it was cheaper was 2 months ago.

Price History & Forecast

Price Distribution

Price Analysis

Description

Key Features

Product Specifications

Barcode

Similar Products You Might Like

Chapman and Hall/CRC Generalized Notions of Continued Fractions

Poincare's Legacies: Pages from Year Two of a Mathematical Blog Pt. 1 (Monograph Books)

Encyclopaedia of Mathematics: Fibonacci Method — H: 4

Applications of Fibonacci Numbers: Volume 6 Proceedings of ‘The Sixth International Research Conference on Fibonacci Numbers and Their Applications’, ... Pullman, Washington, U.S.A., July 18-22, 1994

Analytic Number Theory: In Honor of Helmut Maier’s 60th Birthday

Wiley Fibonacci and Lucas Numbers Volume 2 - Mathematics Text

Combinatorics, Modeling, Elementary Number Theory: From Basic To Advanced

THINKING ABOUT GODEL AND TURING: ESSAYS ON COMPLEXITY, 1970-2007

Wolfram's New Kind of Science Vol IV - Nonlinear Dynamics

Recurrence in Ergodic Theory and Combinatorial Number Theory (Princeton Legacy Library): 14 (Porter Lectures)

The Arithmetic of Dynamical Systems: 241 (Graduate Texts in Mathematics, 241)

World Scientific Eulerian Numbers: 5 Number Theory Book

Ultrafilters Across Mathematics (Contemporary Mathematics): International Congress Ultramath 2008: Applications of Ultrafilters and Ultraproducts in Mathematics, June 1-7, 2008, Pisa, Italy

Number Theory in the Spirit of Liouville: Series Number 76 (London Mathematical Society Student Texts, Series Number 76)

Number Theory for the Millennium I: 1

The Fibonacci Numbers and Integer Structure: Foundations for a Modern Quadrivium

The Triangle-Free Process and the Ramsey Number $R(3,k)$ (Memoirs of the American Mathematical Society)

Discrete Analogues in Harmonic Analysis: Bourgain, Stein, and Beyond (Graduate Studies in Mathematics)

Ergodic Theory: with a view towards Number Theory: 259 (Graduate Texts in Mathematics, 259)

Hilbert's Tenth Problem: An Introduction to Logic, Number Theory, and Computability (Student Mathematical Library)

Automorphic Forms and Applications (IAS/Park City Mathematics): Mathematics Series Volume 12 (IAS/Park City Mathematics Series)

Topics in Harmonic Analysis and Ergodic Theory (Contemporary Mathematics): December 2-4, 2005 Depaul University, Chicago, Illinois

Ergodic Theory: 2 (Cambridge Studies in Advanced Mathematics, Series Number 2)

Markov's Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings