61. Mudd Math Fun Facts: Riemann Hypothesis From the Fun Fact files, here is a Fun Fact at the advanced level The MathBehind the Fact Many other problems in number theory, http://www.math.hmc.edu/funfacts/ffiles/30002.5.shtml

hosted by the Harvey Mudd College Math Department Francis Su Any Easy Medium Advanced Search Tips List All Fun Facts Fun Facts Home About Math Fun Facts ... Other Fun Facts Features 1819325728.38792 Fun Facts viewed since 20 July 1999. Francis Edward Su From the Fun Fact files, here is a Fun Fact at the Advanced level: Riemann Hypothesis If you know about complex numbers, you will be able to appreciate one of the great unsolved problems of our time. The Riemann zeta function is defined by Zeta(z) = SUM k=1 to infinity (1/k z This is the harmonic series for z=1 and Sums of Reciprocal Powers if you set z equal to other positive integers. The function can be extended to the entire complex plane (with some poles) by a process called "analytic continuation", although what that is won't concern us here. It is of great interest to find the zeroes of this function. The function is trivially zero at the negative even integers, but where are all the other zeroes? To date, the only other zeroes known all lie on the line in the complex plane with real part equal to 1/2. This has been checked for several hundred million zeroes! No one knows, however, if

62. Frank Potter's Science Gems - Mathematics math by the SWAT TEAM S. Weimar S. Seastone at Swarthmore Elementary, Middle, unsolved mathematics problems - S. Finch at Wolfram Research This http://www.sciencegems.com/math.html

Frank Potter's Science Gems - Mathematics FYI: Check back weekly, for we will continue to add new resources to the more than 16000 WWW resources that we have located so far. Latest update: Wednesday, September 9, 2005. http://www.sciencegems.com Mathematics Categories Grades K - 3 Mathematics Grades 4 - 6 Mathematics Pre-Algebra Algebra I ... Return to Main Page Grades K - 3 Mathematics MONTESSORI MATH ALBUM - S.-C. J. Yen, University of Missouri Numerous lessons with beads, stamps, etc. on numeration, addition, subtraction, fractions, etc. FunBrain - P.M. Publishing Math Baseball and Change Maker: practice adding, subtracting, multiplying, and dividing in context. NANOWORLD HOME PAGE - D. Waddell @ Univ. of Queensland, Australia Electron microscope images in abundance: select Image Gallery If you have a slow connection, turn off auto-images and select later. ASK DR. MATH by the SWAT TEAM Elementary, Middle, High, and College levels: 100's of problems, favorite problems, and Problem of the Week, Problem of the Month. Grades 4 - 6 Mathematics ASK DR. MATH by the SWAT TEAM

63. CNN.com - Russian May Have Solved Great Math Mystery - Jan. 7, 2004 This is arguably the most famous unsolved problem in math and has been for sometime, Perelman s work has advanced the furthest without falling apart, http://www.cnn.com/2004/US/West/01/07/math.mystery.ap/

International Edition MEMBER SERVICES The Web CNN.com Home Page World U.S. Weather ... Autos SERVICES Video E-mail Newsletters Your E-mail Alerts RSS ... Contact Us SEARCH Web CNN.com Russian may have solved great math mystery The 100-year-old problem seeks to explain the geometry of three-dimensional space. Story Tools YOUR E-MAIL ALERTS Russia Research or Create your own Manage alerts What is this? SAN FRANCISCO, California (AP) A publicity-shy Russian researcher who labors in near-seclusion may have solved one of mathematics' oldest and most abstruse problems, the Poincare Conjecture. Evidence has been mounting since November 2002 that Grigori "Grisha" Perelman has cracked the 100-year-old problem, which seeks to explain the geometry of three-dimensional space. If Perelman succeeded, he could be eligible for a $1 million prize offered by the Cambridge, Massachusetts-based Clay Mathematics Institute, formed to identify the world's seven toughest math problems. Mathematicians around the world have been checking Perelman's work in search of the kind of flaws that have sunk the many other supposed solutions to a problem first presented by the French mathematician Henri Poincare in 1904. "This is arguably the most famous unsolved problem in math and has been for some time," said Bruce Kleiner, a University of Michigan math professor reviewing Perelman's work.

64. Mathematics Archives - Topics In Mathematics - Discrete Mathematics KEYWORDS Online Forums, Open problems, Topics, Search and Find, Software, Markov System Simulation math Forum advanced Discrete mathematics http://archives.math.utk.edu/topics/discreteMath.html

Topics in Mathematics Discrete Mathematics Constructive Theory of Discrete Structures ADD. KEYWORDS: Software, SYMMETRICA, List of Large Designs, Finite Group Actions, Group Theory, Coding Theory, Finite Geometries, Mathematical Chemistry, MOLGEN Counting problems ADD. KEYWORDS: Permutations, Combinations, Binomial Theorem Discrete Applied Mathematics ADD. KEYWORDS: Journal Discrete Mathematics ADD. KEYWORDS: Journal Discrete Mathematics ADD. KEYWORDS: Course Materials, Lecture Notes Discrete Mathematics ADD. KEYWORDS: Course Materials, Lecture Notes, Exams SOURCE: Robin John Chapman, University of Exeter TECHNOLOGY: TeX DVI Discrete Mathematics Project ADD. KEYWORDS: Lesson Plans, Definitions, Glossary, Bibliography, People, Standards Discrete Structures in Computer Science ADD. KEYWORDS: Lecture Notes, Logic Elements, Boolean Algebra, Techniques of Proof and Problem Solving, Mathematical Induction, Graph Theory Discussiones Mathematicae Graph Theory ADD. KEYWORDS: Published Journal SOURCE: DIMACS - Center for Discrete Mathematics and Theoretical Computer Science ADD. KEYWORDS:

65. The Telson Spur: Field Nodes -- Ground (8): Mathematics Best Information on the Net math and Computer Science (O Keefe Library) unsolved problems (Frank Wikstrom) unsolved problems (mathSoft) http://www.snark.org/~pjhughes/math.htm

Contents Jump Search Gopher ... Index Ground DESCRIPTION : The eighth of nine pages on Ground (the first of the Field Nodes comprising the subject tree of The Telson Spur ), this page is a list of links to on-line resources in mathematics. The coordinate pages, with a common header and List of Contents KEYWORDS : algebra; analysis; foundations; geometry; logic; mathematics; number; order; proof; world If you have built castles in the air, your work need not be lost; that is where they should be. Now put the foundations under them. Henry David Thoreau List of Contents Science Resources Science and Technology Science Centres and Organizations Science Education Science Forums and Periodicals Scientific Equipment and Exploration Chaos and Complexity Mathematics Mathematics Education Physical Sciences Astronomy Earth Sciences Life Sciences ... Science News Science Resources (cont.) Science Mathematics Mathematics Mathematics Education Mathematics takes us still further from what is human into the region of absolute necessity, to which not only the actual world, but every possible world, must conform. Bertrand Russell Search only in Mathematics For history and foundations, see

66. Gallileus - Prime Obsession: Berhhard Riemann And The Greatest Unsolved Problem Prime Obsession Berhhard Riemann and the Greatest unsolved Problem in mathematicsNew advanced math, and perhaps might even suffer from math anxiety. http://www.gallileus.info/search/amazon_detail_ca?asin=0452285259

67. Mathematics Department Courses and become acquainted with several solved and unsolved problems in number theory . BASIC MATHEMATICS SKILLS WORKSHOP FOR advanced PLACEMENT http://www.hostos.cuny.edu/oaa/mat/courses.htm

Mathematics Department Courses MAT 1604 BASIC MATHEMATICS SKILLS FOR SCIENCE STUDENTS 1 credit (6 equated), 4 hours Prerequisites: ESL 1320, for English sections only Corequisites: ESL 1325, for English sections only This course provides the basic arithmetic skills that will be utilized in all subsequent mathematics and science courses. Topics: operations with whole numbers, fractions, decimals, ratio, proportion and percent, scientific notation, the metric system, word problems, and applications. MAT 1612 ELEMENTARY ALGEBRA FOR NON-SCIENCE STUDENTS 2 credits (6 equated), 4 hours

68. Department Of Mathematics And Statistics, Cal Poly Pomona MAT 391 Elementary Mathematics from an advanced Viewpoint (4) FWSpSu Please send comments or report problems to Dr. Hoon Kim or Dr.Weiqing Xie. http://www.csupomona.edu/~math/students/courses/300.shtml

Undergraduate Graduate Test -ELM -MDPT Online Registration -PMP ... -Links 300 Level Mathematics Courses Course Descriptions F, W, Sp, Su notations indicate the quarter(s) each course is normally offered. Unless otherwise specified, the course is offered this year during the indicated quarter(s). Students subject to the CSU system required Entry Level Mathematics test (ELM) are required to take the ELM prior to enrolling in any math and statistics course. Any course listed as a prerequisite must be passed with a C or better grade. MAT 306: History of Mathematics (4) F Development of mathematics over four millennia. Recommended for students preparing to teach mathematics. 4 lectures. Prerequisite: C or better in MAT 215, or consent of instructor. MAT 310: Basic Set Theory and Logic (4) FSp Basic set theory and logic, relations, functions, mathematical induction, countable and uncountable sets. Emphasis on how to present and understand mathematical proof. 4 lecture/problems. Prerequisite: C or better in MAT 116, or consent of instructor. MAT 314, 315: Intermediate Analysis (4) (4)

69. Complex Polynomials - Cambridge University Press Series Cambridge Studies in advanced Mathematics (No. These ideas are usedto study a number of unsolved problems, bearing in mind that such problems http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521400686

70. Integer Partitions - Cambridge University Press 12.4, Are there any unsolved problems left? They have all contributed to thedevelopment of an advanced theory of these simple mathematical objects. http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521600901&ss=fro

71. TeacherSource . Recommended Books . Math | PBS Intended for advanced math students, high school or older, Millennium ProblemsThe Seven Greatest unsolved mathematical Puzzles of Our Time , The http://www.pbs.org/teachersource/recommended/math/bk_9-12.shtm

search options Monday, September 26, 2005 Archived Recommendations Grades 9-12 (Mis) Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, The By Benoit Mandelbrot and Richard L. Hudson Published August 2004 Financial markets are even riskier than past theory predicts. Mathematician Mandelbrot employs fractal models to understand stock prices, commodities trading, and currency exchange rates. He assesses the old theory, describes the new, and looks to the future. By Ivan Moscovich and Tim Robinson Published October 2001 If you own only one puzzle book, this should be the one. This magnum opus organizes brightly illustrated puzzles under fourteen headings, including geometry, points and lines, graphs and networks, curves and circles, shapes and polygons, patterns, dissections, numbers, logic and probability, topology, science, perception, and a bonus collection. Solutions are provided in a separate section at the back, as well as references and a difficulty index. All puzzles are rated on a scale 1-10, from beginner to challenging. 57 Great Math Stories and the Problems They Represent By Debbie Haver Published January 1998 Young adult readers will love these engaging, brain-teasing math problems and will strengthen their math skills as they puzzle through to the solutions.

72. Snarkout: Big Numbers the most important unsolved problem in number theory (and one worth a million education or understanding of math more advanced than arithmatic. http://www.snarkout.org/archives/2003/12/12/

If all is mobility, mathematics won't do Main December 12, 2003 Big numbers Last week, a 26-year-old engineering grad student at the University of Michigan got back from a meeting, sat down at his computer, and discovered that he had earned his own footnote in the history of mathematics. Michael Shafer did a victory dance, then called his wife to let her know that he had found the largest known prime number Prime numbers are those, like 7 and 101, that have no divisors other than 1 and themselves. Although there are an infinite number of primes, it's impossible to predict precisely where they will show up. The prime number theorem gives a rough estimate of how many primes exist below a given number the degree of error in this estimate is intimately tied to the Riemann Hypothesis , the most important unsolved problem in number theory (and one worth a million bucks to the mathematician who solves it) but there's generally no easy way to tell if a given number is prime. The type of prime that Shafer discovered, mersenne primes , are an exception. Mersenne primes are primes of the form 2

73. Other Sites Geometry problem of the week. math Magic. Geometry project of the Month. Known also as Erdös for Kids this site offers unsolved problems. http://www.cut-the-knot.org/collection.shtml

Username: Password: Other sites of interest Art of Problem Solving A site for gifted math students, especially those planning to participate in various math olympiads. Created by former olympiad winners, the site offers an online school, a variety of forums and improvisational problem solving sessions guided by Art of Problem Solving instructors. Stella - Polyhedron Navigator Great Stella is by far the most comprehensive tool around for exploring the fascinating world of polyhedra. Select from over 200 built-in models (including Platonic Archimedean Kepler-Poinsot and all other uniform polyhedra Johnson solids and Stewart toroids ), or create endless new ones using advanced tools such as duality, stellation, faceting, and augmentation. Also comes with a library containing hundreds of additional models so you can take advantage of the power without learning all the ins and outs. Nets can be printed for any polyhedron created, allowing you to build your own physical models with a bit of cutting, folding and gluing. Photos of many models built using the program also appear on the site, as well as a

74. ENC Online: Curriculum Resources: Browse: Mathematics> History> Famous Problems This book, suitable for college and advanced secondary students, Prime obsession Bernhard Riemann and the greatest unsolved problems in mathematics http://www.enc.org/resources/browse/0,,0-100-295-4493_1_0-0-0,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Browse Search the Site More Options Don't lose access to ENC's web site! Beginning in August, goENC.com will showcase the best of ENC Online combined with useful new tools to save you time. Take action todaypurchase a school subscription through goENC.com Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse Frequently Asked Questions Resource of the Day ... About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. 53 Records Sorted by Date Use these menus to limit browse results using specific criteria Grade: All Grade Levels Pre-K to 2 3 to 5 6 to 8 9 to 12 Post Sec. Media Type: All Media Types Only Web Sites Excluding Web Sites Cost: All Costs Low Cost (Less than $50) Free Return to Subject Tree Modify using Advanced Search Convergence, a magazine of the Mathematical Association of America ENC Digital Dozen Site Date: Grade(s): 9 - Post Sec.

75. Admissions - Graduate Studies - Advising - Baskin School Of Engineering, UCSC We generally do not accept students who have not had any advanced mathematics . If you like working on unsolved problems in computing and/or teaching http://www.soe.ucsc.edu/advising/graduate/admissions.html

Home Advising Graduate Studies Admissions Graduate Studies - Admissions UCSC Graduate Admissions Graduate Division International Applicants Questions Regarding Applications Admissions FAQ Financial Aid International Students Applications ... General Info Graduate Programs Bioinformatics Program CE Program CS Program EE Program Useful Links GRE Web site TOEFL Web site Grad Housing Campus Information ... Campus Recreation Please be advised that we will only accept admissions in the Fall quarter. Applications for the 2006-2007 academic year will be available online in October 2005. Deadlines are as follows: -December 15, 2005. Computer Science -January 15, 2006 For more information on how to apply online, please go to http://www.grad.ucsc.edu/PSapplicationfiling.html A pplicants to the Network Engineering distance-learning program do not use the on-line application. Instead please follow the application instructions for the Network Engineering program. See below for frequently asked questions regarding the School of Engineering graduate program: Admissions FAQ Which program should I apply to?

76. Mathematics 1995 Publications - Cardiff University math. Soc. (Series A) 59 (1995) 384398 ISSN 0263-6115 Khoukhro EI and MazurovVD (Editors) - unsolved problems in Group Theory. http://www.cardiff.ac.uk/research/publications/pubs/year1995/maths.html

Search: Contact Us A-Z Index Cymraeg Home ... Publications Research Mathematics 1995 Publications Baker R C and Harman G - Numbers with a large prime factor, Acta Arithmetica 73 (1995) 119-145 ISSN 0065-1036 Baker R C, Harman G and Rivat J - Primes of the Form [nc], J. Number Theory 50 (1995) 261-277 ISSN 0022-314X Barker L - Block of endomorphism algebras, Journal of Algebra 168 (1994) 728-740 ISSN 0021-8693 Barker L - Induction, restriction, and G-algebras , Communications in Algebra 22 (1994) 6349-6383 ISSN 0092-7872 Barker L - Modules with simple multiplicity modules, Journal of Algebra 172 (1995) 152-158 ISSN 0021-8693 Barker L - G-algebras, Clifford Theory, and the Green correspondence, Journal of Algebra 172 (1995) 335-353 ISSN 0021-8693 Bishop J C, Dunstan F, Nix B and Reynold T - The effects of gestation dating on the calculation of patient specific risks in Down Syndrome screening , Annals of Clin. Biochem . 32 (1995) 464-477 ISSN 0004-5632 Buckley J T, Lennox J C, Neumann B H, Smith H and Wiegold J - Groups with all subgroups normal-by-finite, J. Austral. Math. Soc. (Series A)

77. Mathematical Problems By David Hilbert The deep significance of certain problems for the advance of mathematical science in Take any definite unsolved problem, such as the question as to the 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.

78. The Riemann Hypothesis: The Most Important Unsolved Problem In Mathematics the most important unsolved problem of mathematics now is the Riemann Hypothesis.This hypothesis involves concepts of advanced mathematics but connects http://www.wolfram.com/products/explorer/topics/riemann.html

PreloadImages('/common/images2003/btn_products_over.gif','/common/images2003/btn_purchasing_over.gif','/common/images2003/btn_services_over.gif','/common/images2003/btn_new_over.gif','/common/images2003/btn_company_over.gif','/common/images2003/btn_webresource_over.gif'); Products The Mathematical Explorer What Is The Mathematical Explorer ... Give us feedback Sign up for our newsletter: Part of the glamour, mystery, and excitement of mathematics involves finding solutions to famous problems. The Four-Color Problem and Fermat's Last Theorem have been solved in the past 30 years to great public acclaim. Both of these long-standing problems are easy to state even though their solutions baffled the best minds in mathematics for centuries. There is general agreement in the mathematical community that the most important unsolved problem of mathematics now is the Riemann Hypothesis. This hypothesis involves concepts of advanced mathematics but connects to elementary notions such as prime numbers. A proper understanding of the Riemann Hypothesis requires some advanced mathematics, but you will see how The Mathematical Explorer allows us to understand some of the functions related to the Riemann function and to examine some of the evidence for the truth of the Riemann Hypothesis.

79. Calculus@Internet Webprimitives Calculus@Internet advanced Mathematics unsolved MathematicsProblems Welcome! This evolving collection of unsolved mathematics http://www.calculus.net/ci2/search/?request=category&code=C&off=0&tag=9200438920

80. Clay Public Lecture: Are The Unsolved Problems In Mathematics — Barry Mazur This lecture by Barry Mazur fill focus on one of the great unsolved problemsthe Riemann hypothesis. Are there unsolved problems about numbers? http://www.claymath.org/public_lectures/lenstra.php

Clay Mathematics Institute Dedicated to increasing and disseminating mathematical knowledge HOME ABOUT CMI PROGRAMS AWARDS ... PUBLICATIONS Escher and the Droste effect A public lecture Hendrik Lenstra, Mathematics Institute, Leiden University October 25, 2005 at 7pm Science Center, Harvard University One Oxford Street, Cambridge In 1956, the Dutch graphic artist M.C. Escher made an unusual lithograph with the title `Print Gallery'. It shows a young man viewing a print in an exhibition gallery. Amongst the buildings depicted on the print, he sees paradoxically the very same gallery that he is standing in. A lot is known about the way in which Escher made his lithograph. It is not nearly as well known that it contains a hidden `Droste effect', or infinite repetition; but this is brought to light by a mathematical analysis of the studies used by Escher. On the basis of this discovery, a team of mathematicians at Leiden produced a series of hallucinating computer animations. These show, among others, what happens inside the mysterious spot in the middle of the lithograph that Escher left blank. Clay Public Lectures Upcoming Lectures Escher and the Droste effect

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