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Unsolved Problems:     more books (100)

Unsolved Problems in Number Theory (Problem Books in Mathematics) (v. 1) by Richard K. Guy, 1994-07 Old and New Unsolved Problems in Plane Geometry and Number Theory (Dolciani Mathematical Expositions) by Victor Klee, Stan Wagon, 1996-09-05 Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire, 2004-05-25 Ball Lightning: An Unsolved Problem in Atmospheric Physics by Mark Stenhoff, 2010-11-02 Unsolved Problems in Geometry (Problem Books in Mathematics / Unsolved Problems in Intuitive Mathematics) by Hallard T. Croft, Kenneth J. Falconer, et all 1991-05-28 Unsolved Problems in Mathematical Systems and Control Theory The World's 20 Greatest Unsolved Problems by John R. Vacca, 2004-07-07 The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles Of Our Time by Keith J. Devlin, 2003-10-16 The Five Biggest Unsolved Problems in Science by Arthur W. Wiggins, Charles M. Wynn, 2003-09-12 Unsolved Problems in Astrophysics The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh, 2004-05-26 Unsolved Problems in Stellar Evolution (Space Telescope Science Institute Symposium Series) Unsolved Problems in Number Theory (Problem Books in Mathematics / Unsolved Problems in Intuitive Mathematics) by Richard Guy, 2004-07-13 Unsolved Problems Of Science by A.W. Haslett, 2007-03-15

lists with details

1. Unsolved Problems
   Including the list of 50 problems of Bondy and Murty with current status. Compiled by Stephen C. Locke.Category Science Math Combinatorics Graph Theory Open Problemsunsolved problems. You can contact Stephen C. Locke at LockeS@fau.edu.Several people have asked me about unsolved problems. I  
   http://www.math.fau.edu/locke/unsolved.htm
   
   Extractions: You can contact Stephen C. Locke at LockeS@fau.edu Several people have asked me about unsolved problems. I will take the easy way out: see the list of 50 problems in Bondy and Murty . I hope it will not annoy the authors of that text if I will reproduce that list here, and perhaps (eventually) add to it. Problems number above 50 are from other sources. Some of these problems have been solved (and thus the title is slightly incorrect) and I won't claim to be familiar with all current results. If you find that one of them has been solved (or even that some reasonable progress has been made), please e-mail me . Also, I'm not giving you all of the references in Bondy and Murty . You should get yourself a copy of that book. Problems 26-56 Problems 57-61 The reconstruction conjecture . (S.M. Ulam, 1960) 2. A graph G is embeddable in a graph H if G is isomorphic to a subgraph of H . Characterise the graphs embeddable in the k -cube. (V.V. Firsov, 1965) 3. Prove: Every 4-regular simple graph contains a 3-regular subgraph. (N. Sauer, 1973)

2. Unsolved Problems
   Mathematical research often concerns questions which are so abstract and technically complicated that only a small number of experts in that particular field can fully understand the problems and their significance. gathered a handful of problems which to my knowledge and to this date are still unsolved although they can be understood  
   http://abel.math.umu.se/~frankw/unsolved.html
   
   Extractions: Mathematical research often concerns questions which are so abstract and technically complicated that only a small number of experts in that particular field can fully understand the problems and their significance. Therefore one is easily led to the conclusion that every problem is difficult to understand. This is not so. On this page I have gathered a handful of problems which to my knowledge and to this date are still unsolved although they can be understood by any one who has a working knowledge of, say, the high-school mathematics curriculum. Can every even integer number greater be written as the sum of two prime numbers? We have for example that: and so on, but is it true for every even number? Nobody knows, but most mathematicians seem to think that it is true. (The conjecture is known to be true for all even integers less than 20 000 000 000 or so. It is also known that every "sufficiently large" even integer can be written as the sum of a prime number and an integer with at most two prime factors.) Two consecutive odd numbers which are both prime are called twin primes, e.g. 5 and 7, or 41 and 43, or 1,000,000,000,061 and 1,000,000,000,063. But is there an infinite number of twin primes?

3. Unsolved Problems In OR
   A good collection.Category Science Math Operations Researchunsolved problems in OR. This page contains a list of open problems thatI find intriguing. They are not as difficult or as significant  
   http://www.statslab.cam.ac.uk/~rrw1/research/unsolved.html
   
   Extractions: This page contains a list of open problems that I find intriguing. They are not as difficult or as significant as the question of whether P does or not equal NP. But these are problems that are easy to state and understand, but whose solution has defied the efforts of good researchers over a number of years. Most of these problems are in the realm of stochastic optimization. I would love to see a solution to any of these problems. This page is under construction. I plan to write something about the following problems, and others, in due course. The bomber problem See description The rendezvous problem See description Search for a moving target See abstract Non-preemptive release of stochastic jobs to uniform machines See abstract The unimportance of inserted idle time in non-preemptive stochastic scheduling to minimize flow time on parallel machines home page

4. Unsolved Problems In Function Theory
   Notes by Alexandre Eremenko.  
   http://www.math.purdue.edu/~eremenko/uns.html

5. Unsolved Problems And Conjectures
   Regarding equal sums of like powers, compiled by Chen Shuwen.  
   http://member.netease.com/~chin/eslp/unsolve.htm
   
   Extractions: Unsolved Problems and Conjectures The Prouhet-Tarry-Escott Problem Is it solvable in integers for any n How to find new solutions for n = 10 and How to find the general solution for n How to find a new solution of the type ( k =1, 2, 3, 4, 5, 6, 7, 8 ) How to find non-symmetric ideal solutions of ( k =1, 2, 3, 4, 5, 6, 7, 8 ) and ( k =1, 2, 3, 4, 5, 6, 7, 8, 9 ) How to find a solution chain of the type ( k = 1, 2, 3, 4 ) Some other open problems are present on Questions by Lander-Parkin-Selfrige (1967) a k + a k + ... + a m k = b k + b k + ... + b n k Is ( k m n ) always solvable when m n k Is it true that ( k m n ) is never solvable when m n k For which k m n such that m n k is ( k m n ) solvable ?

6. Unsolved Problems
   me on to math were some simple sounding but unsolved problems that were easy for a high school student to understand.  
   http://www.math.utah.edu/~alfeld/math/conjectures.html
   
   Extractions: Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah One of the things that turned me on to math were some simple sounding but unsolved problems that were easy for a high school student to understand. This page lists some of them. To understand them you need to understand the concept of a prime number A prime number is a natural number greater than 1 that can be divided evenly only by 1 and itself. Thus the first few prime numbers are You can see a longer list of prime numbers if you like. Named after the number theorist Christian Goldbach (1690-1764). The problem: is it possible to write every even number greater than 2 as the sum of two primes? The conjecture says "yes", but nobody knows. You can explore the Goldbach conjecture interactively with the Prime Machine applet.

7. Alexandre Eremenko Home Page
   Alexandre Eremenko (Purdue University). Mainly in analysis.Category Science Math Analysis edu Courses that I teach and do not teach. My favorite unsolved problems.How do I choose journals to publish my papers. Papers. Recent  
   http://www.math.purdue.edu/~eremenko/
   
   Extractions: My favorite unsolved problems How do I choose journals to publish my papers Papers Recent preprints (available in ps and pdf format) CO-AUTHORS: A. Atzmon, I. N. Baker, W. Bergweiler (3), V. Boichuk, M. Bonk (4), J. Clunie, N. Eremenko, B. Fuglede, A. Gabrielov (5), Yu. Gaida, A. A. Goldberg (6), D. Hamilton, W. Hayman J. Langley (2), L. Lempert, S. Merenkov D. Novikov , G. Levin (3), J. Lewis , T. Lyons, M. Lyubich (5), I. Ostrovskii (3), M. Ostrovskii, M. Petrika, J. Rossi (2), L. Rubel (2), D. Shea, M. Sodin (16). OTHER SITES MAG journal (Kharkov) Tom Korner Curt McMullen John Milnor Fedja Nazarov ... XXX archive (Los Alamos) Jahrbuch uber die Fortschritte der Mathematik Zentralblatt

8. Some Unsolved Problems
   Mainly in analysis. By Jörg Winkelmann.Category Science Math Analysis To my knowledge they are all unsolved. Of course, this is not a completelist of all unsolved problems in mathematics. For instance  
   http://www.math.unibas.ch/~winkel/problem.html
   
   Extractions: This is a collection of some mathematical questions, which I encountered somehow, mostly in the context of my own research. To my knowledge they are all unsolved. Of course, this is not a complete list of all unsolved problems in mathematics. For instance, I omitted those problems which everybody knows anyway (like the Jacobi conjecture). Furthermore the choice is made following my personal taste and prejudices. I certainly do not want to claim that these are the most important problems in today mathematics. Nevertheless, I am very curious about the problems listed below. If anybody is able to solve one or more or knows some results in these directions, please tell me. Does there exists a compact Riemann surface M of genus at least two which can be embedded into a quotient of SL C by a discrete cocompact subgroup? (This is a question raised by A.T.Huckleberry.) Remark: This question is discussed in my Book on parallelizable manifolds and some partial results are derived. In particular, such a curve can never arise as a zero-section of a rank two vector bundle. Let S be a complex semisimple Lie group

9. Unsolved Problems -- From MathWorld
   In 1900, David Hilbert proposed a list of 23 outstanding problems in mathematics (Hilbert's problems, a number of which have now been solved, but some of which remain open. unsolved problems. There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as  
   http://mathworld.wolfram.com/UnsolvedProblems.html
   
   Extractions: There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture 2. The Riemann hypothesis 3. The 4. The conjecture that there exists a Hadamard matrix for every positive multiple of 4. 5. The twin prime conjecture (i.e., the conjecture that there are an infinite number of twin primes 6. Determination of whether NP-problems are actually P-problems 7. The Collatz problem 8. Proof that the 196-algorithm does not terminate when applied to the number 196. 9. Proof that 10 is a solitary number 10. Finding a formula for the probability that two elements chosen at random generate the symmetric group 11. Solving the happy end problem for arbitrary n 12. Finding an Euler brick whose space diagonal is also an integer. 13. Proving which numbers can be represented as a sum of three or four (positive or negative) cubic numbers Lehmer's Mahler measure problem and Lehmer's totient problem on the existence of composite numbers n such that , where is the totient function 15. Determining if the

10. UNSOLVED PROBLEMS AND REWARDS
    By Clark Kimberling. Offers prizes for solutions of some problems in number theory.Category Science Math Number Theory Open Problemsunsolved problems and Rewards. Richard K. Guy, unsolved problems in Number Theory,second edition, SpringerVerlag, 1994. The problem originates in.  
    http://faculty.evansville.edu/ck6/integer/unsolved.html
    
    Extractions: Stated below are a few challenging problems. If you are first to publish a solution, let me know, and collect your reward! 1. The Kolakoski sequence: This sequence is is identical to its own runlength sequence. Reward: $200.00 for publishing a solution of any one of the five problems stated in Integer Sequences and Arrays. The sequence originates in William Kolakoski , "Self generating runs, Problem 5304," American Mathematical Monthly 72 (1965) 674. For a proof that the Kolakoski sequence is not periodic, see the same Monthly See also Kolakoski Sequence (Eric Weisstein's The World of Mathematics

11. Unsolved Problems In Playing-Card Research
    unsolved problems in PlayingCard Research In the January/February 1999 issue of The Playing-Card (Vol XXVII No 4), IPCS president Robert Kissel invited members to contribute to a list of unsolved problems in playing-card research.  
    http://www.pagat.com/ipcs/problis1.html
    
    Extractions: Home Join IPCS Publications Calendar ... Links In the January/February 1999 issue of The Playing-Card (Vol XXVII No 4), IPCS president Robert Kissel invited members to contribute to a list of unsolved problems in playing-card research. This would be the playing-card equivalent of the famous list of unsolved mathematical problems published by David Hilbert 100 years ago. Can the type of cards, both regular and Tarots (not standardised nearly enough to form a standard pattern), called by Sylvia Mann 'archaic' be definitely assigned to Ferrara, as conjectured by Dummett, to Venice, as supposed by almost everyone else, or to any other city? Can definite evidence be found to assign the standard pattern exemplified by early Trappola cards from north of the Alps to Venice, or perhaps to Trent or some other city? Two questions relate to Piedmont. The first is this: Various features of Tarot games played in Piedmont indicate a connection with Bolgna: the treatment of the four ' Papi 'Empress, Popess, Emperor and Popeas of equal rank, any one of them played later to a trick beating one played earlier;

12. Unsolved Problems (Part 2)
    unsolved problems (Part 2). You can contact Stephen C. Locke at LockeS@fau.edu.Several people have asked me about unsolved problems.  
    http://www.math.fau.edu/locke/unsolv2.htm
    
    Extractions: You can contact Stephen C. Locke at LockeS@fau.edu Several people have asked me about unsolved problems. I will take the easy way out: see the list of 50 problems in Bondy and Murty . I hope it will not annoy the authors of that text if I will reproduce that list here, and perhaps (eventually) add to it. Problems number above 50 are from other sources. Some of these problems have been solved (and thus the title is slightly incorrect) and I won't claim to be familiar with all current results. If you find that one of them has been solved (or even that some reasonable progress has been made), please e-mail me . Also, I'm not giving you all of the references in Bondy and Murty . You should get yourself a copy of that book.

13. Unsolved Mathematics Problems
    s of some unsolved problems and numerous links to other collections.Compiled by Steven Finch.  
    http://www.mathsoft.com/asolve/

14. Unsolved Problems
    and Math Miscellany. unsolved problems. unsolved problems. unsolved problems in Operations Research. Unsolved Problem of  
    http://www.spartanburg2.k12.sc.us/links/problems.htm

15. Open Problems List
    A collection of papers outlining unsolved problems in the field of dynamical systems.  
    http://www.math.sunysb.edu/dynamics/open.html

16. [gr-qc/0107090] Current Trends In Mathematical Cosmology
    A review of current unsolved problems in mathematical cosmology  
    http://xxx.lanl.gov/abs/gr-qc/0107090
    
    Extractions: We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current, seemingly unrelated trends of this subject. We discuss problems associated with the definition and asymptotic structure of the notion of cosmological solution and also problems related to the qualification of approximations and to the ranges of validity of given cosmologies. References and citations for this submission:

17. Combinatorial Game Theory
    Includes Gamesman Toolkit, which implements the mathematics of twoplayer games in Winning Ways; and Richard K. Guy's paper unsolved problems in Combinatorial Games.  
    http://www.gac.edu/~wolfe/papers-games/
    
    Extractions: Current ongoing discussion concerning the game clobber Current ongoing discussion concerning the games born on day n. The Mar 9, 2002 version of the Gamesman's Toolkit sh file (or as a .tar.gz file) ``Undergraduate Research Opportunities in Combinatorial Games,'' Joint Mathematics Meetings, January, 1995. Journal of Undergraduate Mathematics and its Applications , Vol. 16, No. 1, 1995. Handout in postscript . Talk slides in postscript Jeff Erickson's web page on combinatorial games Unsolved Problems in Combinatorial Games, by Richard Guy and Richard Nowakowski from More Games of No Chance . The article is available as a pdf file or as a postscript file compressed with gzip.

18. Hilbert's Problems -- From MathWorld
    A set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total, ten were presented at the Second International Congress in Paris on August 8, 1900.  
    http://mathworld.wolfram.com/HilbertsProblems.html
    
    Extractions: A set of (originally) unsolved problems in mathematics proposed by Hilbert Of the 23 total, ten were presented at the Second International Congress in Paris on August 8, 1900. Furthermore, the final list of 23 problems omitted one additional problem on proof theory (Thiele 2001). Hilbert's problems were designed to serve as examples for the kinds of problems whose solutions would lead to the furthering of disciplines in mathematics, and are summarized in the following list. 1a. Is there a transfinite number between that of a denumerable set and the numbers of the continuum ? This question was answered by and Cohen to the effect that the answer depends on the particular version of set theory assumed. 1b. Can the continuum of numbers be considered a well ordered set ? This question is related to Zermelo's axiom of choice . In 1963, the axiom of choice was demonstrated to be independent of all other axioms in set theory , so there appears to be no universally valid solution to this question either. 2. Can it be proven that the

19. Mathsoft: Mathsoft Unsolved Problems
    Statistics Resources. unsolved problems. Engineering Standards. Mathsoft Constants. UnsolvedProblems on Other Sites. On a Generalized FermatWiles Equation.  
    http://www.mathsoft.com/mathresources/problems/0,,0,00.html
    
    Extractions: search site map about us  + news  + ... Statistics Resources Unsolved Problems Engineering Standards Mathsoft Constants Math Resources Welcome! This evolving collection of unsolved mathematics problems is not systematic or complete; it is only an eclectic gathering of questions and partial answers which have come to my attention over the years. Unsolved Problems on Other Sites On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras Sleeping Habits of Armadillos ... contact us

20. Mathsoft: Mathsoft Unsolved Problems: Unsolved Problems On Other Sites
    unsolved problems on Other Sites. Jeff Martin); Richard Weber's UnsolvedProblems in Operations Research (University of Cambridge);  
    http://www.mathsoft.com/mathresources/problems/article/0,,1999,00.html
    
    Extractions: search site map about us  + news  + ... Unsolved Problems Unsolved Problems Links On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras Sleeping Habits of Armadillos Engineering Standards ... Math Resources Unsolved Problems on Other Sites Jeff Lagarias' 3x+1 problem and related problems The Generalized 3x+1 Mapping (University of Queensland) and 1999 Conference on the Collatz Problem Proceedings Alex Lopez-Ortiz's sci.math FAQ on Famous Problems in Mathematics (University of New Brunswick) Chris Caldwell's Riemann Hypothesis (University of Tennessee at Martin); also Daniel Bump's Riemann Hypothesis (Stanford University) and Barry Cipra's A Prime Case of Chaos MathPro Press Unsolved Math Problem of the Week column and General References Twin Primes Conjecture and Goldbach's Conjecture, discussed in Prime Numbers: Some Unsolved Problems , part of MacTutor History of Mathematics (University of St Andrews); also Chris Caldwell's Prime Conjectures and Open Questions (University of Tennessee at Martin) Jan Otto Munch Pedersen's Known Amicable Pairs (Vejle Business College, Denmark) and Chris Caldwell's

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