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  1. Conjectures: P Versus Np Problem, Poincaré Conjecture, Collatz Conjecture, Hilbert's Problems, Catalan's Conjecture, Sierpinski Number
  2. Optimization Problems (Applied Mathematical Sciences) (Volume 0) by L. Collatz, W. Wetterling, 1975-07-23
  3. Numerical Treatment of Free Boundary Value Problems: WORKSHOP NUMER.TREATMEnt Free Bound.Value Probl.Oberwolfach (International Series of Numerical Mathematics) by ALBRECHT, COLLATZ, et all 1982-06-14
  4. Constructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations: CONFERENCE AT THE OBERwolfach Math.Res.Inst.,19.-25.11.1978 (International Series of Numerical Mathematics) by ALBRECHT, COLLATZ, et all 1979-01-01
  5. Numerical Treatment of Eigenvalue Problems, Vol. 3 (International Series of Numerical Mathematics) by ALBRECHT, COLLATZ, et all 1984-05-31
  6. NUMERICAL TREATMENT OF FREE BOUNDARY VALUE PROBLEMS by J.; Collatz, L.; et al; editors Albrecht, 1982
  7. Numerical Treatment of Eigenvalue Problems: Workshop in Oberwafach, February 25-March 3, 1990/Numerische Behandlung Von Eigenwertaufgaben : Tagung (International Series of Numerical Mathematics) by J. Albrecht, Lothar Collatz, et all 1991-05
  8. Numerical Treatment of Eigenvalue Problems (International Series of Numerical Mathematics)
  9. OPTIMIZATION PROBLEMS.Translated by P.Wadsack.*(Applied Mathematical Sciences,17) by L./Wetterling,W. Collatz, 1975-01-01
  10. The Dynamical System Generated by the 3n+1 Function (Lecture Notes in Mathematics) by Günther J. Wirsching, 1998-03-20

21. Collatz Problem
Collatz Problem. Science Math - Number Theory - Open Problems - Collatz Problem; The Collatz 3n+1 Conjecture is Unprovable - A paper by Craig Alan
http://www.science.remnet.pl/?kat=Math/Number_Theory/Open_Problems/Collatz_Probl

22. Java Programming - Collatz Problem
http//en.wikipedia.org/wiki/collatz_problem. the code i want to make is to find the number less than 1 million which will form the longest chain(ie will
http://forum.java.sun.com/thread.jspa?threadID=5129481&messageID=9463436

23. The Engineering Network Directory - Science: Math: Number Theory: Open Problems:
The Collatz, Syracuse or 3x+1 problem Welcome to your engineering network directory of websites. Explore engineering, the scientific field of technology and
http://www.enghitech.com/directory/?cat=Science/Math/Number_Theory/Open_Problems

24. Collatz Problem Open Problems Number Theory
Collatz Problem Open Problems Number Theory The Collatz, Syracuse or 3x+1 problem Collatz Problem.
http://www.iaswww.com/apr/Science/Math/Number_Theory/Open_Problems/Collatz_Probl
Collatz Problem Open Problems Number Theory
Collatz Problem
The Collatz, Syracuse or 3x+1 problem
Top
Science Math Number Theory ... Open Problems Collatz Problem
  • - Katholische Universit¤t Eichst¤tt, Germany; 56 August 1999. On-line proceedings and group photo.
  • - A survey article by Jeff Lagarias.
  • - Observations posted by Ken Conrow to stimulate further research.
  • - Papers by Peter Schorer describing several new approaches.
  • - Results up to 2^60 by Tom¡s Oliveira e Silva.
  • - Properties and predictive models for the Collatz Problem and relative functions.
  • - A survey by Keith Matthews [PDF].
  • - By Andrew Shapira. The intensity of a point denotes the time taken to terminate.
  • - These pages supply numerical data and propose some conjectures on this innocent looking problem. All numbers up to 29,300 * 10^12 ( ~ 26 * 2^50 ) have been checked for convergence.
  • - By Jeffrey Lagarias, 1997.
  • - An online calculator by Alfred Wassermann.
  • - A paper by Craig Alan Feinstein arguing that the Collatz Conjecture cannot be formally proved.
  • - From Eric Weissten's World of Mathematics. Article with references and links.

25. Collatz Problem | Number Theory
Buy online the book 5 Major Theoretical Breakthroughs in the Superior Mathematics wrote by Romanian Mathematician Vasiliu Lucilius.
http://www.number-theory.eu/collatz_problem.php
A study on Collatz Problem
About Me My Work The Riemann Hypothesis Guestbook ... Contact
Mathematician Vasiliu Lucilius

Five Major Theoretical Breakthroughs in the Superior Mathematics
Chapter 1.

Fractional powers with rational exponent of the monotonous operators of class on
Chapter 2.

Using the symmetry group in demonstrating the radiality of several semilinear biharmonic equations' solutions
Chapter 3.

A study on zeroes of the function (z) of Riemann
Chapter 4.

The problem of invariant Subspaces Chapter 5. A study on Navier-Stokes equations Collatz Problem Go back to Chapter 6 Go to Chapter 8 About Vasiliu Lucilius The Work of Vasiliu Lucilius ... Contact Vasiliu Lucilius

26. Science: Math: Number Theory: Open Problems: Collatz Problem
Find Gr8 information and additional resources about Science Math Number Theory Open Problems Collatz Problem on Gr8ScienceSites.com.
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27. Crossroad, Ulam's Conjecture Will Be Proven Using Sufficient Bifucations
Ulam s conjecture (Collatz Problem) www.j4.com collatz_problem.htm. Every whole number can be reduced to 1 by repeating the following steps.
http://www.sum-it.nl/en200209.html
SUMit Roster Software Nut's Weekly February 2002 Nederlands ... Search...
Crossroad
Monday, 25 February 2002 December 2001 January 2001 February 2002 Bean Expired Immigrant Crossroad March 2001 April 2002 vii vi v 5 x 3 + 1 = 16 iv iii ii i Ulam's conjecture (Collatz Problem) www.j4.com...Collatz_Problem.htm Every whole number can be reduced to 1 by repeating the following steps.
  • Even: Divide by 2
  • Odd: Times 3 plus 1
The number 20 needs 7 steps to reach 1. Other numbers are more tricky. The number 9 for example needs a total of 19 steps. Does every number have a path leading to 1?
Diagram
www.onezero.org/collatz.html shows a interesting diagram that relates a number to the number of required steps. I haven't seen a diagram that shows the paths yet. So, I am proud to present the diagram below, visualising the paths.
  • Numbers run from left to right.
  • The steps required show from top to bottom.
  • A line connecting two numbers represents one step.
Step Number xix xviii xvii xvi xv xiv xiii xii xi x ix viii vii vi v iv iii ii i
Do all paths end at 1?
The diagram above shows that all paths for numbers up to 17 end in 1. Yet, I haven't seen a convincing proof yet for all numbers.

28. Dominion Web Directory :
Search the Directory Options. entire directory, this category only. advanced. Top Science Math Number_Theory Open_Problems collatz_problem
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29. Open Directory Project > Science> Math> Number Theory> Open Problems> Collatz Pr
Search. the entire directory, only in Open_Problems/collatz_problem. Top Science Math Number_Theory Open_Problems collatz_problem
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31. From Lake Geneva To The Finland Station: More Readings
http//site.voila.fr/collatz_problem There is something wrong here. When all you have is a hammer, everything looks like a nail? Posted by jimcp at 230 PM
http://jimcaprioli.blogspot.com/2005/01/more-readings.html
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From Lake Geneva to the Finland Station
Thursday, January 27, 2005
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http://site.voila.fr/Collatz_Problem There is something wrong here. When all you have is a hammer, everything looks like a nail? Posted by jimcp at 2:30 PM
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32. Search > Science : Math : Number Theory : Open Problems : Collatz Problem
http//site.voila.fr/collatz_problem. The Generalised 3x+1 Problem. A survey by Keith Matthews PDF. http//www.numbertheory.org/pdfs/survey.pdf
http://www.cooltoad.com/links/show.php?c=460332&PHPSESSID=4f

33. OYP Directory - Science Math Number Theory Open Problems
OYP.In Online B2B B2C Yellow Pages that brings you the most relevant result that no other directory service can provide.
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ABC_Conjecture; Catalan_Conjecture; collatz_problem. Goldbach_Conjecture; Riemann_Hypothesis. 7 Sites in Open Problems. Advice to Research Students
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Open Problems, collatz_problem1. Tables, Misc.1. Publications, Journals1. People, N1. Analytic, Riemann_Hypothesis1. Prime Numbers, Primality_Tests1
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36. Porydd
ABC_Conjecture; Catalan_Conjecture; collatz_problem; Goldbach_Conjecture; Lychrel_Numbers. Jump To. Software Updated 29 December, 2005
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37. The World's Top Collatz Problem Websites
http//site.voila.fr/collatz_problem Website popularity rank 2698 The 3x+1 Problem Annotated Bibliography By Jeffrey Lagarias, 1997.
http://websbiggest.com/dir-top.cfm?cat=/Top/Science/Math/Number_Theory/Open_Prob

38. Open_Problems [TAG]
Papers by Peter Schorer describing several new approaches. Science Math Number_Theory Open_Problems collatz_problem Top. Saved by 1 user(s)
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Number Theory Conjectures
A collection of easily stated conjectures which are still open. Each conjecture is stated along with a collection of references. Science Math Top Saved by 1 user(s)
Advice to Research Students
Some tips for solving problems in number theory, collected by the Cardiff University group. Science Math Top Saved by 1 user(s)
Seva Lev's Problem Page
A collection of research problems. Science Math Top Saved by 1 user(s)
Unsolved Problems and Rewards
By Clark Kimberling. Offers prizes for solutions of some problems in number theory. Science Math Top Saved by 1 user(s)
L-functions and Random Matrix Theory
Conjectures and open problems concerning L-functions, focussing on the areas in which there has been recent progress using results from Random Matrix Theory. Maintained at AIM. Science Math Top Saved by 1 user(s)
Open Problems
Some questions compiled by Jon Perry.

39. Directopedia : Directory : Science : Math : Number Theory : Open Problems : Coll
http//site.voila.fr/collatz_problem. 3x+1.html Ranking. Details + Preview. http//www.math.lsa. http//www.math.lsa.umich.edu/~lagarias/3x+1.html
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idliste = [1488073,1488074,1488075,1488076,1488077,1488078,1488079,1488081,1488082,1488083,1488084]; Papers on the 3x + 1 / 3n + 1 Problem, Fermat's Last Theorem, and other Mathematical Problems A paper by Peter Schorer describing a new approach to the 3x + 1 Problem, an approach based on two remarkably simple structures that underlie the 3x + 1 function. The paper includes a possible solution to the Problem. Details + Preview
Keywords:
Pete Schorer, 3x+1 Problem, 3n+1 Problem, 3x+1, Collatz Conjecture, Fermat's Last Theorem, Simple, Proof, of, Fermat's, Last, Theorem, Syracuse Problem, Collatz Problem, Goldbach's Conjecture, Occam's Razor, Ockam's Razor, Newcomb's Paradox, Paradox, of, the, Unexpected, Hanging, Unexpected Hanging, Self-Representation, Self-Similarity, Fractals, 3n+1, Mathematical Proofs, Mathematical Problems

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Collatz Problem From MathWorld
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40. 1Up Science > Links Directory >Math:Number Theory:Open Problems:Collatz Problem
1UpInfo Science Math Number_Theory Open_Problems collatz_problem. The Collatz, Syracuse or 3x+1 problem. Link to this page
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