21. Graph Theory I ve listed the unsolved problems from Appendix IV of Bondy and Murty. In Spring1997, I used West as the course text (and that now has a second edition). http://www.math.fau.edu/locke/GRAPHTHE.HTM

Graph Theory You can contact Stephen C. Locke at LockeS@fau.edu Why I don't want to talk about: Goldbach's Conjecture Index Brief History Basic Definitions If you have a graph theory page, let me know and I might include a link to it from my page for links to other people's files . I won't usually link to commercial pages. Please note also: I have received requests for assistance on problems that are standard undergraduate exercises. The most I will do in these situations is point out the exercise in a standard text (in case the writer doesn't realize that it is a standard problem) or refer the writer to a chapter in a standard textbook. Very Brief History The earliest paper on graph theory seems to be by Leonhard Euler, Solutio problematis ad geometriam situs pertinentis, Commetarii Academiae Scientiarum Imperialis Petropolitanae 8 (1736), 128-140. Euler discusses whether or not it is possible to stroll around Konigsberg (later called Kaliningrad) crossing each of its bridges across the Pregel (later called the Pregolya) exactly once. Euler gave the conditions which are necessary to permit such a stroll. Thomas Pennyngton Kirkman (1856) and William Rowan Hamilton (1856) studied trips which visited certain sites exactly once.

22. Mathematical Problems - Problem Solving - Mathematical Competitions The mathematical problems of David Hilbert by David E. Joyce unsolved problemsand Rewards by Clark Kimberling; Weekly math Contests by Dr. David Rock http://mathres.kevius.com/problem.html

Mathematical Problems - Problem Solving Mathematical Competitions not a complete list, only what I happened to see... The 3x+1 problem and its generalizations The 3x+1 problem, also known as the Collatz problem, the Syracuse problem, Kakutani's problem, Hasse's algorithm, and Ulam's problem by Jeff Lagarias 21st Century Problem Solving Solutions to solving word problems across the curriculum. (SureMath - hawaii.edu) MATHCOUNTS Foundation Algebra Story and Word Problems A collection of simple algebra word problems (SureMath: 21st Century Problem Solving) Algebrator - an Algebra Problem Solver for Students and Teachers Calculus Problems - Alvirne High School Problems of the Week site The Cereal Box Problem by George Reese A Collection of Math-Olympiad-Problems by Hans Vernaeve Competitions Canadian Mathematical Society (CMS) Countries with Mathematical Olympiad Websites - Links to Mathematical Olympiad Websites. CRUX Mathematicorium Online The Digital Supplement to the Canadian Mathematical Society's Problem Solving Journal Ken Duisenberg's Puzzle of the Week Elementary Problem of the Week by Ruth Carver (MathForum) Fermat's Last Theorem Flanders Mathematics Olympiad The Goal Angle Problem Hilbert ... 's Tenth Problem by Karlis Podnieks The Mathematical Problems of David Hilbert by David E. Joyce

23. Sci.math FAQ: Unsolved Problems Subject sci.math FAQ unsolved problems Summary Part 18 of many, New version, References unsolved problems in Number Theory. Richard K Guy. http://www.faqs.org/faqs/sci-math-faq/unsolvedproblems/

Usenet FAQs Search Web FAQs Documents ... RFC Index sci.math FAQ: Unsolved Problems There are reader questions on this topic! Help others by sharing your knowledge Newsgroups: sci.math alopez-o@neumann.uwaterloo.ca hv@cix.compulink.co.uk (Hugo van der Sanden): To the best of my knowledge, the House of Commons decided to adopt the US definition of billion quite a while ago - around 1970? - since which it has been official government policy. dik@cwi.nl (Dik T. Winter): The interesting thing about all this is that originally the French used billion to indicate 10^9, while much of the remainder of Europe used billion to indicate 10^12. I think the Americans have their usage from the French. And the French switched to common European usage in 1948. gonzo@ing.puc.cl alopez-o@barrow.uwaterloo.ca Rate this FAQ N/A Worst Weak OK Good Great Related questions and answers Usenet FAQs Search Web FAQs ... RFC Index Send corrections/additions to the FAQ Maintainer: alopez-o@neumann.uwaterloo.ca Last Update June 15 2004 @ 00:31 AM

24. Urban Legends Reference Pages: College (The Unsolvable Math Problem) Student mistakes examples of unsolvable math problems for homework and they were homework were in fact two famous unsolved problems in statistics. http://www.snopes.com/college/homework/unsolvable.asp

E-mail this Print this Advanced search Home ... Homework > The Unsolvable Math Problem The Unsolvable Math Problem Claim: Student mistakes examples of unsolvable math problems for homework assignment and solves them. Status: True. Example: [Brunvand, 1987] A young college student was working hard in an upper-level math course, for fear that he would be unable to pass. On the night before the final, he studied so long that he overslept the morning of the test. When he ran into the classroom several minutes late, he found three equations written on the blackboard. The first two went rather easily, but the third one seemed impossible. He worked frantically on it ten minutes short of the found a method that worked, and he finished the problems just as time was called. The student turned in his test paper and left. That evening he received a phone call from his professor. "Do you realize what you did on the test today?" he shouted at the student. "Oh, no," thought the student. I must not have gotten the problems right after all. "You were only supposed to do the first two problems," the professor explained. "That last one was an example of an equation that mathematicians since Einstein have been trying to solve without success. I discussed it with the class before starting the test. And you just solved it!"

25. AoPS Math Forum :: View Forum - Algebra Unsolved Problems English version Algebra unsolved problems, Change the language math Forum »Olympiad Section » Algebra » Algebra unsolved problems http://www.artofproblemsolving.com/Forum/forum-36.html

The AoPS Intermediate Trigonometry/Complex Numbers course begins Thursday, Sept 22. Enrollment deadline is October 2. Font Size: The time now is Fri Sep 23, 2005 2:20 pm English version Algebra Unsolved Problems Change the language View posts since last visit ... Algebra Unsolved Problems Moderators: Arne harazi Megus Myth ... pbornsztein Page of [1215 Topics] Goto page Next Topics Author Replies Views Last Post Indian IMOTC 73 Rushil Today, at 8:55 am Rushil Trig silouan Today, at 8:14 am Matnomi Indian IMOTC 72 Rushil Today, at 7:59 am Rushil Function [x] Gohan Today, at 7:30 am hardsoul Indian IMOTC 47 Rushil Today, at 6:51 am zhaoli Indian IMOTC 62 Rushil Today, at 5:52 am Rushil sum of squares task from teacher dondigo Today, at 5:45 am chuckywang Indian IMOTC 56 Rushil Today, at 5:33 am Rushil Indian IMOTC 54 Rushil Today, at 5:26 am Rushil Indian IMOTC 34 Rushil Yesterday, at 11:58 pm Rushil indian IMOTC 33 Rushil Yesterday, at 11:54 pm Rushil KMO Winter Progeram Test, 2001 vnmathboy Yesterday, at 11:39 pm vnmathboy system equations vnmathboy Yesterday, at 11:34 pm

26. MATH-abundance TUTORIAL Topics; Solved and unsolved problems; math links to links to math links Other solved and unsolved problems on the net. Many other math links http://ddart.net/science/mathmatics/mathtutorial/

MATH-abundance Main Purpose = MATH TUTORIAL TUTORIAL : Topics; Solved and unsolved problems Math links to links to math links ... Other Tutorials ... Many other math links J.C.'s Math Home Page = http://home.planetinternet.be/~ping1339 Last update: 12 jun 2001 Main Purpose = MATH TUTORIAL The main purpose of this site is to provide the net with a 'upper secondary' MATH TUTORIAL The order of the topics is not random. Most of them appeal on the properties and formulas stated in a preceding topic. You can find headword-links of the tutorial in the MATH-TUTORIAL INDEX Download Since each topic is in 1 file, it is easy to download the file and to study the subject off line. See Copying Conditions TUTORIAL : Topics; Solved and unsolved problems Trigonometry Vectors Lines - orthogonality ; distance (in a plane) Complex numbers ... Miscellaneous Problems about all topics Additionally, I can give a number of math links to math related links to math links... Math links to links to math links ... Other Tutorials Lessons, Tutorials and Lecture Notes

27. Internet Center For Mathematics Problems The following newsgroups are devoted to math problems or puzzles or contain a fair unsolved problems. Does there exist a number that is perfect and odd? http://www.mathpropress.com/mathCenter.html

Internet Center for Mathematics Problems On this page, we try to identify and list all sources of mathematics problems on the Internet and related information. Please advise us if you know of any sources that we are missing. Table of Contents Problem Columns from Mathematics Journals The Fibonacci Quarterly Mathematics and Informatics Quarterly (coming soon) Missouri Journal of Mathematical Sciences Problem Columns on the World Wide Web Mathematics Problems on the World Wide Web Newsgroups ... Sign-in We invite you to visit the MathPro Press home page Problem Columns from Mathematics Journals Many mathematics journals contain problem columns. They invite readers to send in solutions to the problems. The best solution submitted gets printed in a future issue along with the names of all the solvers. We list below only a few of the journals that are currently running problem columns. You are welcome to try your hand at solving these problems. Solutions should be sent to the appropriate problem column editor ( not to MathPro Press).

28. MathLinks Math Forum :: View Forum - Number Theory Unsolved Problems English version Number Theory unsolved problems, Change the language math Forum » Olympiad Section » Number Theory » Number Theory unsolved problems http://www.mathlinks.ro/Forum/forum-56.html

Art of Problem Solving News Links About ... Home Advanced Section College Playground IMO - Intl Math Olympiad National Forums Profile FAQ Search Members Usergroups Register Favorites Options Log in to check your messages Log in Photo Album Blogs The time now is Sat 24 Sep 2005, 00:20 English version Number Theory Unsolved Problems Change the language View posts since last visit ... Number Theory Unsolved Problems Moderators: amfulger Arne harazi Megus ... pbornsztein Page of [1258 Topics] Goto page Next Announcements Author Replies Views Last Post How to post problems Valentin Vornicu Wed 29 Dec 2004, 03:22 pigfly Topics Author Replies Views Last Post No idea dondigo Today, at 11:59 Diarmuid Indian IMOTC 6 Rushil Today, at 11:07 Kondr Indian IMOTC 35 Rushil Today, at 10:45 Arne Indian IMOTC 42 Rushil Today, at 08:35 pontios Indian IMOTC 10 Rushil Today, at 07:39 Arne Indian IMOTC 48 Rushil Today, at 07:14 Arne Indian IMOTC 63 Rushil Today, at 06:56 Arne Indian IMOTC 69 Rushil Today, at 06:08 Rushil Indian IMOTC 66 Rushil Today, at 06:00

29. MathLinks Math Forum :: View Forum - Algebra Unsolved Problems English version Algebra unsolved problems, Change the language Vojtech JarnikMath Competition, Problem 3, Category 1, 1997, Rafal, 3, 98, Sun Jul 24, http://www.mathlinks.ro/Forum/forum-36.html

Art of Problem Solving News Links About ... Home Advanced Section College Playground IMO - Intl Math Olympiad National Forums Profile FAQ Search Members Usergroups Register Favorites Options Log in to check your messages Log in Photo Album Blogs The time now is Sat 24 Sep 2005, 00:20 English version Algebra Unsolved Problems Change the language View posts since last visit ... Algebra Unsolved Problems Moderators: Arne harazi Megus Myth ... pbornsztein Page of [1215 Topics] Goto page Next Topics Author Replies Views Last Post Indian IMOTC 73 Rushil Today, at 08:55 Rushil Trig silouan Today, at 08:14 Matnomi Indian IMOTC 72 Rushil Today, at 07:59 Rushil Function [x] Gohan Today, at 07:30 hardsoul Indian IMOTC 47 Rushil Today, at 06:51 zhaoli Indian IMOTC 62 Rushil Today, at 05:52 Rushil sum of squares task from teacher dondigo Today, at 05:45 chuckywang Indian IMOTC 56 Rushil Today, at 05:33 Rushil Indian IMOTC 54 Rushil Today, at 05:26 Rushil Indian IMOTC 34 Rushil Yesterday, at 23:58 Rushil indian IMOTC 33 Rushil Yesterday, at 23:54 Rushil KMO Winter Progeram Test, 2001

30. Unsolved Problems Some Simple unsolved problems. One of the things that turned me on to math weresome simple sounding but unsolved problems that were easy for a high school http://www.math.utah.edu/~pa/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.

31. Understanding Mathematics That math courses are just hurdles one has to cross as an undergraduate student?Comments. Examples of simple but unsolved problems http://www.math.utah.edu/~alfeld/math.html

Peter Alfeld, Department of Mathematics, College of Science University of Utah Understanding Mathematics a study guide by Peter Alfeld. I wrote this page for students at the University of Utah. You may find it useful whoever you are, and you are welcome to use it, but I'm going to assume that you are such a student (probably an undergraduate), and I'll sometimes pretend I'm talking to you while you are taking a class from me. Let's start by me asking you some questions. If you are interested in some suggestions, comments, and elaborations, click on the Comments. Do so in particular if you answered "Yes!". (In making the comments I assume you did say "Yes!", so don't be offended if you didn't and are just curious.) Do you feel That being lost in mathematics is the natural state of things?

32. Full Text Online Of Blondel, V.D. And Megretski, A., Eds.: Unsolved Problems In Table of Contents for unsolved problems in Mathematical Systems and Control Theoryby Blondel, VD and Megretski, A., eds., published by Princeton University http://www.pupress.princeton.edu/math/blondel/

SEARCH: Keywords Author Title More Options Power Search Search Hints SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Unsolved Problems in Mathematical Systems and Control Theory Edited by Vincent D. Blondel and Alexandre Megretski Book Description Endorsements Table of Contents To Order ... Class Use and other Permissions . For more information, send e-mail to permissions@pupress.princeton.edu Full text online (PDF format): Entire book as one file (1.4 MB) (Separate files for each section follow below) Frontmatter Preface xiii Associate Editors xv Website xvii PART 1. LINEAR SYSTEMS Problem 1.1. Stability and composition of transfer functions Problem 1.2. The realization problem for Herglotz-Nevanlinna functions Seppo Hassi, Henk de Snoo, Eduard Tsekanovskii Problem 1.3. Does any analytic contractive operator function on the polydisk have a dissipative scattering nD realization? Dmitry S. Kalyuzhniy-Verbovetzky Problem 1.4. Partial disturbance decoupling with stability Problem 1.5. Is Monopoli's model reference adaptive controller correct?

33. Blondel, V.D. And Megretski, A., Eds.: Unsolved Problems In Mathematical Systems of the book unsolved problems in mathematical Systems and ControlTheory by Blondel, VD and Megretski, A., eds., VISIT OUR math WEBSITE...... http://www.pupress.princeton.edu/titles/7790.html

SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Unsolved Problems in Mathematical Systems and Control Theory Edited by Vincent D. Blondel and Alexandre Megretski Shopping Cart Endorsements Table of Contents Chapter 1 [in PDF format] ... How to submit a solution, partial solution, or comment This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here 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 consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed. Vincent D. Blondel

34. MATH-abundance TUTORIAL Topics; Solved and unsolved problems; math links to links to mathlinks Topics and problems mathabundance home page - tutorial http://www.ping.be/~ping1339/

MATH-abundance Main Purpose = MATH TUTORIAL TUTORIAL : Topics; Solved and unsolved problems Math links to links to math links ... Home Page = http://home.scarlet.be/~ping1339/ Last update: 18 apr 2004 Main Purpose = MATH TUTORIAL The main purpose of this site is to provide the net with a 'upper secondary' MATH TUTORIAL The order of the topics is not random. Most of them appeal on the properties and formulas stated in a preceding topic. You can find headword-links of the tutorial in the MATH-TUTORIAL INDEX Download Since each topic is in 1 file, it is easy to download the file and to study the subject off line. See Copying Conditions TUTORIAL : Topics; Solved and unsolved problems Trigonometry Vectors Lines - orthogonality ; distance (in a plane) Complex numbers ... Miscellaneous Problems about all topics Additionally, I can give a number of math links to math related links to math links... Math links to links to math links ... Lessons, Tutorials and Lecture Notes Tutorial about trigonometry Tutorial about algebra, calculus, geometry, statistics, trigonometry Linear Algebra ... Mathematics Archives Topics Searchable database. Mathematics Archives A very powerful search engine for math stuff S.O.S. MATHematics

35. Unsolved Problems unsolved problems. Next Does there exist a Up Famous problems in MathematicsPrevious Which are the. unsolved problems http://db.uwaterloo.ca/~alopez-o/math-faq/node59.html

Next: Does there exist a Up: Famous Problems in Mathematics Previous: Which are the Unsolved Problems Does there exist a number that is perfect and odd? Collatz Problem Goldbach's conjecture Twin primes conjecture Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

36. Unsolved Problems unsolved problems in Number Theory. Richard K Guy. Springer, Problem E16. GT Leavens and M. Vermeulen 3x+1 search programs Comput. math. Appl. http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node30.html

Next: Mathematical Games Up: Famous Problems in Mathematics Previous: Which are the 23 Unsolved Problems Does there exist a number that is perfect and odd? A given number is perfect if it is equal to the sum of all its proper divisors. This question was first posed by Euclid in ancient Greece. This question is still open. Euler proved that if N is an odd perfect number, then in the prime power decomposition of N , exactly one exponent is congruent to 1 mod 4 and all the other exponents are even. Furthermore, the prime occurring to an odd power must itself be congruent to 1 mod 4. A sketch of the proof appears in Exercise 87, page 203 of Underwood Dudley's Elementary Number Theory. It has been shown that there are no odd perfect numbers Collatz Problem Take any natural number n : = m; repeat n is odd) then n : = 3*n + 1 ; else n : = n/2 until ( n==1 Conjecture 1. For all positive integers m, the program above terminates. The conjecture has been verified for all numbers up to References Unsolved Problems in Number Theory.

37. Unsolved Problem Of The Week Archive Welcome to the archive for the unsolved math Problem of the Week. Each week, foryour edification, we publish a wellknown unsolved mathematics problem. http://cage.rug.ac.be/~hvernaev/problems/archive.html

Unsolved Problem of the Week Archive Welcome to the archive for the Unsolved Math Problem of the Week Each week, for your edification, we publish a well-known unsolved mathematics problem. These postings are intended to inform you of some of the difficult, yet interesting, problems that mathematicians are investigating. We give a reference so that you can get more information about the topic. These problems can be understood by the average person. Nevertheless, we do not suggest that you tackle these problems, since mathematicians have been unsuccessfully working on these problems for many years. Should you wish to discuss aspects of these problems with others, one of the newsgroups, such as sci.math , might be the appropriate forum. 3-Sep-1995 Problem 36 : Primes of the form n^n+1 27-Aug-1995 Problem 35 : Must one of n points lie on n/3 lines? 20-Aug-1995 Problem 34 : Squares with Two Different Decimal Digits 13-Aug-1995 Problem 33 : Unit Triangles in a Given Area 6-Aug-1995 Problem 32 : Can the Cube of a Sum Equal their Product 30-Jul-1995 Problem 31 : Different Number of Distances 23-Jul-1995 Problem 30 : Sum of Four Cubes 16-Jul-1995 Problem 29 : Fitting One Triangle Inside Another 9-Jul-1995 Problem 28 : Expressing 3 as the Sum of Three Cubes 2-Jul-1995 Problem 27 : Factorial that are one less than a Square 25-Jun-1995 Problem 26 : Inscribing a Square in a Curve 18-Jun-1995 Problem 25 : The Collatz Conjecture 11-Jun-1995 Problem 24 : Primes Between Consecutive Squares 4-Jun-1995 Problem 23 : Thirteen Points on a Sphere 28-May-1995

38. DoYourMath: A Friendly Place To Practice Math, Prepare For SAT Or AP Calculus, T Also, www.doyourmath.com links you to the greatest unsolved problems of 21stcentury math with the reward of $1million for solving any of them. http://www.doyourmath.com/

Interactive Practice Tests Pre-SAT SAT* AP* and Calculus SAT Test dates Check it out! DoYourMath.com recommends Books Meet the expert A math expert is here to answer to your questions Want some cool math? A bi-weekly section for all interested in mathematics. Puzzle Of the Week Includes puzzles and winners of previous week. Link Directory Links to various mathematical web pages, articles, academic research. Welcome to www.doyourmath.com where you can find everything about MATH from interactive SAT* math tests to amazing math puzzles $100 For A Problem. We are proud to present you the one hundred dollar problem sponsored by www.doyourmath.com Note: To receive the $100 prize you should be the first person to solve and send us the solution to the problem before July 31, 2005 (the solution should be mathematically correct) Click here: the $100 problem. Also, www.doyourmath.com links you to the greatest unsolved problems of 21-st century MATH with the reward of $1million for solving any of them. Announcements: New!

39. Hilbert's 23 Unsolved Problems Solve general Boundary Value problems. ? unsolved. 21. Prove that there alwaysexists a Fuchsian System with given singularities and a given Monodromy Group http://www.andrews.edu/~calkins/math/biograph/199899/tophilpr.htm

Back to the Table of Contents Topics - Hilbert's 23 Unsolved Problems In 1900, David Hilbert addressed the International Congress of Mathmaticians in Paris. In the address, he outlined 23 major mathematical problems that would be studied in the next century. The address was not only a collection of problems, it was also his philosophy of mathematics and problems important to that philosophy. Hilbert's Address Problem Proven True/False/? Comments 1a. Is there a transfinite number between that of a Denumerable Set and the numbers of the Continuum True/False 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 which was demonstrated in 1963 to be independent of all other axioms in Set Theory . There is no universally valid solution. 2. Can the axioms of logic be proven to be consistent? False Any formal system interesting enough to fomulate its own consistency can prove its own consistency if and only if it is inconsistent, derived from 3. Are there two tetrahedra which cannot be decomposed into congruent tetrahedra directly or by adjoining congruent tetrahedra.

40. Perplexus.info :: Just Math These problems are mostly mathrelated. That s not to say that they re allstraightforward. unsolved problems Top Rated problems This month s top http://perplexus.info/category/14/

All about flooble fun stuff Get a free chatterbox ... Avatars perplexus dot info Home Just Math These problems are mostly math-related. That's not to say that they're all straightforward. You'll still need to flex your noggin to figure them out! Sub-Categories All Problem Categories Latest: Buddy System Rating: 4.00 Miss Honey and Miss Wormwood were taking their classes out on an outing. The two classes were of different sizes, but in each class there were the same number of girls as boys. Miss Honey told the children in her class to form pairs, each consisting of a boy and a girl. For her own amusement, mentally calculated the number of different ways this could be done. Miss Wormwood also told her class to form into pairs, but with at least one single-sex pair. She also insisted that the girls Matilda and Susie did not pair up together as they were the most troublesome of her girls. She too calculated the number of different ways that this could be done. Both teachers arrived at the same answer. How many children were in each class?

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