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 Problems......unsolved 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

Unsolved Problems 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) Conjecture 3 was proved in 1985 by L. Zhang: Every 4-regular simple graph contains a 3-regular subgraph, J. of Changsha Railway Institute 1 (1985), 130-154.

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

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 Research......unsolved 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

Unsolved Problems in OR 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

My favorite unsolved problems GEOMETRIC FUNCTION THEORY AND POTENTIAL THEORY: ps pdf Some constants studied by Littlewood (Updated Oct 2002). ps pdf Exceptional set in Gross' Theorem. ps pdf "Hawaii Conjecture" (attributed to Gauss). ps pdf Does every universe contain a place where you can stay at rest? (Lee Rubel) ps pdf Erdos' problem on the length of lemniscates (at least $200 prize). DIFFERENTIAL EQUATIONS AND ITERATION IN THE COMPLEX DOMAIN: ps pdf Wandering domains of entire functions. TRANSCENDENTAL HOLOMORPHIC CURVES: ps pdf Modified Cartan's Conjecture. ps pdf Holomorphic curves with few inflection points. RATIONAL FUNCTIONS AND RATIONAL CURVES: ps pdf Rational curves with real inflection points (B. and M. Shapiro, for more info, see F. Sottile's page Other interesting items in this site: Progress report on some problems from Hayman's Collection When exactly had function theory became a secondary subject? (Excerpt from a letter of Mittag-Leffler to Kowalevski.) What is mathematics? Some expert's opinions. jokes related to complex analysis some problems, whose solutions I do know (level: undergraduate+)

5. Unsolved Problems And Conjectures Regarding equal sums of like powers, compiled by Chen Shuwen. http://member.netease.com/~chin/eslp/unsolve.htm

Equal Sums of Like Powers Unsolved Problems and Conjectures The Prouhet-Tarry-Escott Problem a k + a k + ... + a n k = b k + b k + ... + b n k k n Is it solvable in integers for any n Ideal solutions are known for n = 1, 2, 3, 4, 5, 6, 7, 8 ,9, 11 and no other integers so far. How to find new solutions for n = 10 and How to find the general solution for n The general solution is known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) only. The complete symmetric solution have been found for ( k = 1, 2, 3, 4 ) 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 ) a a a a a b b b b b c c c c c ( k = 1, 2, 3, 4 ) Solution chains are known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) and ( k = 1, 2, 3, 4, 5 ) so far. 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

Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah Some Simple Unsolved Problems 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. Prime Number Problems 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. The Goldbach Conjecture. 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/

Alexandre Eremenko picture vita Mathematics Department, Purdue University 149 N. University Street West Lafayette, IN 47907-2068 OFFICE: Math 612, HOURS: Mo and We, 2-3. PHONE: (765)494-1975, FAX: (765)494-0548 EMAIL: eremenko@math.purdue.edu Courses that I teach and do not teach 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

Some Mathematical Problems 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

Foundations of Mathematics Mathematical Problems Unsolved Problems Unsolved Problems 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 Problems......unsolved 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

Unsolved Problems and Rewards 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 2. A Shuffle. Is every positive integer a term of this sequence: Reward: $300.00. To see how to generate the sequence, visit Kimberling Sequence (Eric Weisstein's The World of Mathematics For a discussion and variant of the problem, see Richard K. Guy Unsolved Problems in Number Theory, second edition , Springer-Verlag, 1994. The problem originates in C. Kimberling, Problem 1615

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

Home Join IPCS Publications Calendar ... Links Unsolved Problems in Playing-Card Research Background 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. Submissions by Sir Michael Dummett, February 10th, 1999 Unsolved Problems concerning Tarot and Italian Cards 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

Unsolved Problems (Part 2) 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 1-25 Problems 57-61 26. Prove that every n -chromatic graph G has r(G,G) >= r(n,n) Message from Stephan Brandt Disproved by Faudree and McKay [ J. Comb. Math. Comb. Comp. 13 Counterexample: Wheel with 5 spokes has Ramsey number 17 < r(4,4).

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

Math Problems, Games, and Puzzles Algorithmic Information Theory Brain Teasers Fermi Questions Library Ideas, Concepts, and Definitions ... What Good is Math?

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

Open Problems in Dynamical Systems Open problems in holomorphic dynamics Two lists of problems are currently available on-line: Conformal Dynamics Problem List Ed. by B. Bielefeld, IMS at Stony Brook Preprint 1990/1 and more recent Problems in Holomorphic Dynamics Ed. by B. Bielefeld and M. Lyubich, IMS at Stony Brook Preprint 92/7 In addition some open questions may be found in these surveys Open problems in dynamics in several complex variables is a part of Several complex variables problems list available from Several complex variables preprint server in Indiana. Please send your problems to Gregery Buzzard at gbuzzard@iu-math.math.indiana.edu Problems in Low-Dimensional Topology a 380 pages PostScript file edited by Rob Kirby contain some problems on Topological Dynamics. Topology of hyperbolic attractors. A problem submitted by Christian Bonatti. A collection maintained by Sergiy Kolyada and Michal Misiurewicz Is entropy effectively computable? A problem by John Milnor We are soliciting open problems in various areas of Dynamical Systems for posting on this page. You can post a problem by filling out this form or by sending an e-mail to webmaster@math.sunysb.edu

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

General Relativity and Quantum Cosmology, abstract gr-qc/0107090 ): Fri, 27 Jul 2001 17:32:02 GMT (13kb) Date (revised v2): Sat, 28 Jul 2001 14:53:55 GMT (13kb) Current Trends in Mathematical Cosmology Authors: Spiros Cotsakis Comments: 16 pages, LaTeX. To appear in the Proceedings of the 2nd Hellenic Cosmology Workshop, (Kluwer, 2001) 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. Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Links to: arXiv gr-qc find abs

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/

Combinatorial game theory 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) Source code for a toolkit for implementing the mathematics of combinatorial games in Winning Ways (Berlekamp, Conway, Guy.) You may also want to print out postscript instructions for using the toolkit, or a set of exercises and solutions so you can practice using the toolkit and quickly get up to speed. This is probably the last version of the C toolkit before I switch over to Java. ``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

Foundations of Mathematics Mathematical Problems Problem Collections Hilbert's Problems 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

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

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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