81. Open Problems Unsolved Mathematics Problems collected by Steven Finch Bounty problems collected by unsolved problems in Geometry by Hallard Croft, Kenneth Falconer, http://compgeom.cs.uiuc.edu/~jeffe/open/

Open Problems These are open problems that I've encountered in the course of my research . Not surprisingly, almost all the problems are geometric in nature. A name in brackets is the first person to describe the problem to me; this may not be original source of the problem. If there's no name, either I thought of the problem myself (although I was certainly not the first to do so), or I just forgot who told me. Problems in bold are described in more detail than the others, and are probably easier to understand without a lot of background knowledge. If you have any ideas about how to solve these problems, or if you have any interesting open problems you'd like me to add, please let me know . I'd love to hear them! 30 Jul 2003: Complete or partial solutions for several of these problems have been discovered in the two years since I last updated this site. Over the next few weeks, I'm planning to add pointers to these new results, as well as descriptions of several new open problems. (Search for "soon" on this page.) Stay tuned! Existence Problems: Does Object X exist?

82. Some Unsolved Problems In Coding Theory Some unsolved problems in coding theory. In another attempt to make these problems easier, we could ask for something less accurate but still useful. http://web.usna.navy.mil/~wdj/book/node138.html

Next: Coding theory exercises using Up: Error-correcting codes Previous: Quadratic residue codes Contents Index Some unsolved problems in coding theory To begin, a ``code'' in this section is any subset of , where is a finite field. More precisely, a code is a map , where represents the original message space and the space of transmitted messages. Question : Given and , what is the largest for which there is a code of size and minimum distance ? At the moment, this is only known for or if and is relatively small (depending on ). To make the problem easier, let use restrict to the subclass of linear codes. In the case of linear codes, the question can be worded more precisely. Question : Given and , what is the largest for which there is a linear code of length , dimension , and minimum distance ? Again, this isn't known, except in special cases. Back to general codes. Question : Given and , what is the smallest for which there is a code of size and minimum distance ? This related problem is not known either (except for some very special cases, as above). Again, to make the problem easier, let use restrict to the subclass of linear codes. In the case of linear codes, the question can be worded more precisely. Question : Given and , what is the smallest for which there is a code of length , dimension , and minimum distance ? Again, in general this isn't known. In another attempt to make these problems easier, we could ask for something less accurate but still useful. For example, in the last question, instead of fixing

83. Unsolved Problems In Systems And Control unsolved problems in Mathematical Systems and Control Theory. Vincent D. Blondel and Alexandre Megretski. Princeton University Press, 2004 http://www.inma.ucl.ac.be/~blondel/books/unsolved/

Unsolved Problems in Mathematical Systems and Control Theory Vincent D. Blondel and Alexandre Megretski Princeton University Press, 2004 ISBN: 0-691-11748-9 The book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science. The book can by purchased (for about 40 USD) from the publisher's book website . Princeton University Press has also kindly agreed to post a free electronic version of the book (in PDF). Editors: Vincent Blondel , University of Louvain, Belgium Alexander Megretski, Massachusetts Institute of Technology, USA Associated editors: Roger Brockett, Harvard University, USA Jean-Michel Coron, University of Paris (Orsay), France

84. Two Unsolved Problems In Library Work by William Warner Bishop. It was his President s address at the meeting of the District of Columbia Library Association, December 13, 1911, and was first http://www.libr.org/rory/wbm13.html

Two Unsolved Problems in Library Work by William Warner Bishop. It was his President's address at the meeting of the District of Columbia Library Association, December 13, 1911, and was first published in Library Journal , January, 1912. It was reprinted in the 1926 collection of Bishop's writings, The Backs of Books and Other Essays in Librarianship Occasionally one hears in professional circles, generally from a comparatively recent recruit, some pronouncement to the effect that most fundamental problems of library work have been settled long ago, and that the only tasks now before librarians are those involved in adapting principles already will established to new conditions or in expanding small activities into larger fields. Such expressions are not infrequently coupled with a generous consciousness of the preeminent excellence of Ameribyothers.html library methods in contrast with those of the rest of the world. We are all more or less familiar with this sort of talk, and are perhaps inclined to be more or less consciously infuenced by it. It may, therefore, be wholesome and profitable to turn out attention to at least two problems which are fundamental to the successful prosecution of our calling and which not only are unsolved ehre as yet, but are - at least in part - in a fair way to solution elsewhere. When a reader or inquirer comes to a library and asks for a book whose author and title he knows, he presents our first problem in its most simple form. Where is the book he wants? If it is at once produced, either by the ready membory of the librarian, the aid of an author or a title entry in the catalog, or by whatever other means are used, the problem is solved, and ceases to be more than a matter of ordinary routine. When the work is not readily identified or not readily found, and further search of catalogs or shelves is required, the problem, although complicated somewhat, still remains fairly easy, if the book byothers.html be produced in good time. But when the book byothers.htmlnot be produced there arise at once two questions: first, "Is the book here, but for the moment concealed through some of the intricacies or deficiencies of cataloging or failure of other library machinery?" and second, "If not here, where is it?"

85. UnSolved Problems In 'PUZZLE FUN' Follow unsolved problems from back issues of my magazine PUZZLE FUN. Try to solve some problem that no one solve and send me Your, possibly partial, http://anduin.eldar.org/~problemi/pfun/pfununso.html

PUZZLE FUN top page UnSolved problems in PUZZLE FUN Follow UnSolved Problems from back issues of my magazine PUZZLE FUN Try to solve some problem that no one solve and send me Your, possibly partial, solutions. Your name, if you like, will appear here and in the journal!! Cheer, Rodolfo M. Kurchan PUZZLE FUN Editor PUZZLE FUN Is it possible to make a rectangle that use the 12 pentominoes that have at least 1 single, 1 double, 1 triple and 1 cuadruple?. Michael Reid found a closer solution to this problem using 10 pentominoes:1 single, 5 doubles, 3 triples and 1 quadruple: 320 = 15 x 39. Can someone find a solution using more pentominoes? PUZZLE FUN Ramps pentominoes A ramp is a road of pieces between an horizontal line and a vertical line. Double and Triple Fence Probelms "Double fence" means that the fence should be double in all directions (i.a.d.: horizontal, vertical and diagonal). h.a.v cases will only requiere double horizontal and vertical directions. Find the biggest ramp with double fence h.a.v. symmetric (inside and outside border) Find the biggest ramp with triple fence h.a.v. symmetric (inside and outside border)

86. Sci.math FAQ: Unsolved Problems Subject sci.math FAQ unsolved problems; From alopezo@neumann.uwaterloo.ca (Alex Lopez-Ortiz); Date 17 Feb 2000 225551 GMT; Newsgroups sci.math, http://www.uni-giessen.de/faq/archiv/sci-math-faq.unsolved/msg00000.html

Index sci.math FAQ: Unsolved Problems Subject : sci.math FAQ: Unsolved Problems From alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) Date : 17 Feb 2000 22:55:51 GMT Newsgroups sci.math news.answers sci.answers Summary : Part 20 of 31, New version http://www.cs.unb.ca/~alopez-o Assistant Professor Faculty of Computer Science University of New Brunswick Index: Index sci-math-faq.unsolved

87. Sci.math FAQ: Unsolved Problems Subject sci.math FAQ unsolved problems; From alopezo@neumann.uwaterloo.ca (Alex Lopez-Ortiz); Date Fri, 17 Nov 1995 171513 GMT; Newsgroups sci.math, http://www.uni-giessen.de/faq/archiv/sci-math-faq.unsolvedproblems/msg00000.html

Index sci.math FAQ: Unsolved Problems Subject : sci.math FAQ: Unsolved Problems From alopez-o@neumann.uwaterloo.ca (Alex Lopez-Ortiz) Date : Fri, 17 Nov 1995 17:15:13 GMT Newsgroups sci.math sci.answers news.answers Sender news@undergrad.math.uwaterloo.ca (news spool owner) Summary : Part 18 of many, New version, Index: Index sci-math-faq.unsolvedproblems

88. FNF: UNSOLVED PROBLEMS - A NEGLECTED ISSUE?   2001-12-08 The Fascination of unsolved problems Excellent Reminder about Problem Neglect! formulating unsolved problems is not customary; !! http://www.hi.is/~joner/eaps/wh_pr65.htm

UNSOLVED PROBLEMS - A NEGLECTED ISSUE? FNF: UNSOLVED PROBLEMS - A NEGLECTED ISSUE? http://www.hi.is/~joner/eaps/wh_pr65.htm Jón Erlendsson WH GO ... Ný tækifæri INNOO It seems fairly obvious - actually crystal clear that: - what our main focus should be on are: unsolved problems and even undefined problems - knowledge gaps to be filled - important questions - not even yet asked BUT: - Our education is nearly exclusively focussed on disseminating what exists - while we know by experience that - our biggest opportunities almost always are linked to what does not yet exist new knowledge, products etc. We see here a major neglect - a major imbalance in todays education! C Jón Erlendsson See some supporting comments below. One of the first to mention this neglect was Francis Bacon ! LJ See Boyd LJ " William Boyd and Edmund King. The

89. STScI 1998 May Symposium unsolved problems in Stellar Evolution . May 4 7, 1998. The next STScI May Symposium, on the topic of unsolved problems in Stellar Evolution , http://www.stsci.edu/stsci/meetings/may98/

The Space Telescope Science Institute 1998 May Symposium "Unsolved Problems in Stellar Evolution" May 4 - 7, 1998 The next STScI May Symposium, on the topic of "Unsolved Problems in Stellar Evolution", will take place May 4 - 7, 1998. All aspects of stellar evolution, from birth to death, will be discussed, with an emphasis on important open questions. The deadline for registration is April 1, 1998. Detailed information is listed below. People interested in participating can register electronically (see below) or contact Cheryl Schmidt at STScI by mail (STScI, 3700 San Martin Drive, Baltimore, MD 21218, USA), e-mail ( schmidt@stsci.edu ), or phone (410-338-4404). The registration fee is $150 before April 1, 1998, and $170 thereafter. STScI is no longer accepting registrations for the May Symposium. 4:00 P.M. - 6:00 P.M. AT STScI FOR ALL REGISTERED PARTICIPANTS Symposium Agenda Poster Information Hotel Information Registration Fees ... Deadline is April 1, 1998 Last updated: April 24, 1998 schmidt@stsci.edu

90. Citations Unsolved Problems In Geometry - CROFT, FALCONER, GUY HT CROFT, KJ FALCONER, and RK GUY, unsolved problems in Geometry, SpringerVerlag, New York, 1991. http://citeseer.ist.psu.edu/context/85385/0

91. Distributed Data Management Unsolved Problems And New Issues Distributed database technology is expected to have a significant impact on data processing in the upcoming years. With the introduction of commercial http://citeseer.ist.psu.edu/ozsu94distributed.html

92. Unsolved Problems In Astrophysics, Ed. John N. Bahcall And Jeremiah P. Ostriker descriptions of the most important unsolved problems in astronomy and astrophysics by leading experts. http://www.sns.ias.edu/~jnb/Books/Unsolved/unsolved.html

Unsolved Problems in Astrophysics Overview Contents Preface Princeton University Catalog Listing ... Ordering Information Back to John Bahcall's Books Address questions and comments about this server to webmaster@sns.ias.edu

93. Unsolved Problems unsolved problems. unsolved problems. Since the discovery of RCrB itself, the mechanism that produces fadings has been elusive. http://star.arm.ac.uk/~csj/rcrb_rev/node15.html

Next: Bibliography Up: R Coronae Borealis Stars Previous: Other Hydrogen-Deficient Stars Unsolved Problems Since the discovery of RCrB itself, the mechanism that produces fadings has been elusive. Primary data connecting pulsation phase and the trigger for fadings exists for only two RCBs (V854Cen and RYSgr), and protracted photometry of several RCBs will be necessary to establish any connection firmly. A second difficulty is encountered by the physical conditions necessary for dust to condense above the surface of the star. The frequency and duration of fading events implies a geometry in which the dust clouds form within two stellar radii (2 R ). Under normal conditions, the local temperature would be too high for dust to condense at this distance, and a condensation distance of 20 R would be expected. Recent models treat the chemistry, energy balance and dust nucleation in pulsating star atmospheres in considerable detail. They show that excess cooling can occur during adiabatic expansion after the passage of a shock wave, reducing the local temperature to about 1500K within 1.5-3 R . It remains to be shown that pulsations in all RCB stars provide the necessary conditions for dust nucleation to occur at this distance. The RCB carbon abundance remains an enigma. If it is

94. SUP The Still Unsolved Problems Model SUP The Still unsolved problems Model To address problem mapping, I propose a new construction called SUP (Still unsolved problems). http://www.ceap.wcu.edu/Houghton/SUP/SUPdsgn.html

C ommunities R esolving O ur P roblems: the basic idea SUP: Sharing Problems THINK: Guidance LEAP: Solving Problems SUP - The Still Unsolved Problems Model This is a primer for creating structures that prioritize, track and manage the creation of problems (questions) and their eventual answers, that is, SUP models. The ideas below can be read in a linear fashion from beginning to end starting with the Introduction section, or you can jump to sections within this document by using the links below. Table of Contents Introduction to SUP Concept SUP Management What to collect How to collect ... A Class Time Assignment - Using Global Area Networks Critical Reflections SUP Research Questions Introduction to SUP Concept Image - child sucking single noodle from a plate of sphagetti. Conceptually the task is simple. Find something of interest and pursue it. The pursuit requires you to interact with the world around you. As you explore aspects of this interest, you inevitably find problems and create questions and from those problems you build collections of answers and more questions. Four steps are noteworthy here: problem discovery, problem mapping, solution discovery, and solution mapping. Of these, only problem mapping lacks a parallel more formal structure in computer networks. A possible solution to this missing structure within computer networks will be discussed. This essay is a primer for problem mapping, creating structures that stimulate, track and manage the creation of problems (questions) and their eventual answers. In turn, this engine for thought can be applied to any content area. To address problem mapping, I propose a new construction called SUP (Still Unsolved Problems).

95. Nat'l Academies Press: Prime Obsession: Bernhard Riemann And The Greatest Unsolv The Riemann Hypothesis is one of the deepest of all unsolved problems in mathematics. Unfortunately it is difficult to state exactly what the hypothesis is http://www.nap.edu/catalog/10532.html

Read more than 3,000 books online FREE! More than 900 PDFs now available for sale HOME ABOUT NAP CONTACT NAP HELP ... ORDERING INFO Items in cart [0] TRY OUR SPECIAL DISCOVERY ENGINE Questions? Call 888-624-8373 Read it Online - FREE! The views expressed in this book are solely those of the author(s) and do not necessarily reflect the views of the National Academies. SEARCH THIS BOOK Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics John Derbyshire 448 pages, 5.5 x.8.5, 2003 Purchase Options Web prices are provided only for orders placed online Online Orders 10% Off HARDBACK Reg: Web: isbn_elements.push('0309085497'); NEW! Purchase PDFs HARDBACK + PDF BEST VALUE isbn_elements.push('0-309-51259-x'); 0-309-51259-x PDF BOOK [13.8 MB] isbn_elements.push('0-309-51257-3'); PDF CHAPTERS $1.10 ea. isbn_elements.push('0-309-51258-1'); Show ISBNs About PDF Download Sample PDF Speed Related Links: Joseph Henry Press (JHP) More Titles from JHP Related Titles Press Release ... Dashboard NEW! Description In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false?

96. Wu :: Forums - Unsolved Problems In The Hard Forum This one is an unsolved problem in mathematics. Solve it and your name will be known There are unsolved problems in the Easy and Medium section too. http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action

97. Welcome To Mathsoft This evolving collection of unsolved mathematics problems is not systematic or complete; it is only an eclectic gathering of questions and partial answers http://www.mathsoft.com/mathsoft_resources/unsolved_problems/

Company Press Room Partners Events ... Math Resources Unsolved Problems 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 Links Sleeping Habits of Armadillos On a Generalized Fermat-Wiles Equation Zero Divisor Structure in Real Algebras ... Privacy

98. Open Problems For Undergraduates who is eager to think about interesting and unsolved mathematical problems. Some of these problems are quite hard and have been open for a long time. http://dimacs.rutgers.edu/~hochberg/undopen/

Open Problems for Undergraduates Open Problems by Area Graph Theory Combinatorial Geometry Geometry/Number theory Venn Diagrams Inequalities Polyominos This is a collection of open problems in Discrete Mathematics which are currently being researched by members of the DIMACS community. These problems are easily stated, require little mathematical background, and may readily be understood and worked on by anyone who is eager to think about interesting and unsolved mathematical problems. Some of these problems are quite hard and have been open for a long time. Others are newer. For further information on a particular problem, you may write to the associated researcher. Although these problems are intended for undergraduates, it is expected that high school students, teachers, graduate students and professional mathematicians will be drawn to this collection. This is not discouraged. Each of these problems is associated with some member of DIMACS. If you have any questions, comments, insights or solutions, please send email to the researcher who is listed with the problem. These pages are maintained by Robert Hochberg Last modified Feb. 5, 1997.

99. Mathematical Problems By David Hilbert Take any definite unsolved problem, such as the question as to the irrationality of the EulerMascheroni constant C, or the existence of an infinite number http://aleph0.clarku.edu/~djoyce/hilbert/problems.html

Mathematical Problems Lecture delivered before the International Congress of Mathematicians at Paris in 1900 By Professor David Hilbert Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries? What particular goals will there be toward which the leading mathematical spirits of coming generations will strive? What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose? History teaches the continuity of the development of science. We know that every age has its own problems, which the following age either solves or casts aside as profitless and replaces by new ones. If we would obtain an idea of the probable development of mathematical knowledge in the immediate future, we must let the unsettled questions pass before our minds and look over the problems which the science of today sets and whose solution we expect from the future. To such a review of problems the present day, lying at the meeting of the centuries, seems to me well adapted. For the close of a great epoch not only invites us to look back into the past but also directs our thoughts to the unknown future. The deep significance of certain problems for the advance of mathematical science in general and the important role which they play in the work of the individual investigator are not to be denied. As long as a branch of science offers an abundance of problems, so long is it alive; a lack of problems foreshadows extinction or the cessation of independent development. Just as every human undertaking pursues certain objects, so also mathematical research requires its problems. It is by the solution of problems that the investigator tests the temper of his steel; he finds new methods and new outlooks, and gains a wider and freer horizon.

100. Article About 3 Unsolved Math Problems Article about 3 unsolved math problems 2 is about graph theory. http://garsia.math.yorku.ca:16080/~zabrocki/math3260w03/article.html

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