61. UW Math: Milliman Lectures Archive will state some of the main unsolved problems on the Robert MacPherson Institute for advanced Study. applications of algebra to some problems in combinatorics http://www.math.washington.edu/~sheetz/Milliman/milliman-archives.html

2002-2003 Milliman Lectures Princeton University Lecture I: What is the biggest multiplicity of a root of a degree d polynomial? Lecture II: What are the simplest algebraic varieties? Lecture III: Rationally connected varieties over finite fields 2001-2002 Milliman Lectures Peter Sarnak Institute for Advanced Study, Princeton and New York University A series of three lectures entitled Families of L-functions and applications Abstract L-functions, starting from Riemann's zeta function and continuing to the modern automorphic L-function have played a central role in number theory. These lectures will focus on recent developments in the analytic theory of such functions. A key technique which is at the heart of these advances is based on the formation and analysis of families of L-functions. There are numerous applications of these developments to number theory, combinatorics and mathematical physics. We will describe two in detail. One is the solution of Hilbert's eleventh problem which asks about the representability of integers in a number field by an integral quadratic form. The other is to eigenfunctions on an arithmetic surface and in particular problems in quantum chaos. 2000-2001 Milliman Lectures Charles Fefferman Princeton University A series of three lectures entitled Unsolved problems of fluid mechanics Abstract The talks will state some of the main unsolved problems on the Euler and Navier-Stokes equations for incompressible fluids, and sketch the proofs of some of the main results known so far on these and related equations. I hope to get through the main ideas in the proofs of the Beale-Kato-Majda theorem and results of Constantin, Majda and me on breakdown of Euler solutions, the work of Sheffer, Caffarelli-Kohn-Nirenberg and F. H. Lin on Navier-Stokes, and recent results by D. Cordoba and me on breakdown scenarios. Also, I hope to state precisely some problems arising from Kolmogorov's ideas on turbulence.

62. ScienceDaily -- Browse Topics: Science/Math/Analysis See Also Science math Calculus. Some unsolved problems Mainly in analysis advanced Calculus and Analysis - Lecture notes from the University of Aberdeen for http://www.sciencedaily.com/directory/Science/Math/Analysis

Match: sort by: relevance date Free Services Subscribe by email RSS newsfeeds PDA-friendly format loc="/images/" A A A Find Jobs In: Healthcare Engineering Accounting College Contract / Freelance Customer Service Diversity Engineering Executive Healthcare Hospitality Human Resources Information Tech International Manufacturing Nonprofit Retail All Jobs by Job Type All Jobs by Industry Relocating? Visit: Moving Resources Moving Companies Mortgage Information Mortgage Calculator Real Estate Lookup Front Page Today's Digest Week in Review Email Updates ... Math Analysis (156 links) Complex Variable Events Functional Analysis Journals ... Transform Calculus See Also: Science: Math: Calculus News about Analysis How Brain Gives Special Resonance To Emotional Memories (June 10, 2004) full story Scientists Find Cancer's Genetic Core: 67 Genes Universally Activated In Human Cancer (June 9, 2004) full story Gene Expression Ratio Identifies Risk Of Recurrence In Breast Cancer Patients Receiving Tamoxifen (June 8, 2004) full story A "Swarm" Of Satellites For A Unique Look Inside The Earth (June 7, 2004) full story Nearly One-third Of The Calories In The US Diet Comprised Of Junk Food, Researcher Finds

63. ZapMeta Directory > Science > Math > Analysis . advanced Calculus and Analysis open this site http//www.math.ucdavis.edu/~emsilvia/math127/math127.html. . Favorite unsolved problems open this site in a http://www.zapmeta.com/search/meta/db.pl?dir=391044

64. Selected Number Theory References Written with a target audience of nonmath majors. Publ, 1991 Good text, best suited for either advanced undergraduate or Guy94 unsolved problems in Number http://www.math.umbc.edu/~campbell/NumbThy/Class/References.html

Selected Number Theory References General - Elementary Level Elementary Number Theory A good general text. Written at a fairly simple level, but covers a broad range of topics in elementary number theory. ($35, UMBC library) A Friendly Introduction to Number Theory , Silverman, Prentice-Hall, 1997 A good, if somewhat sparse, introduction to number theory. Gives short shrift to some classical topics in order to provide a coverage of elliptic curves. Written with a target audience of non-math majors. ($72) General - Advanced Level A Course in Number Theory nd Ed, by H. E. Rose, Oxford Univ Press, 1996 Good general text, best suited for either advanced undergraduate or first graduate course. ($45, UMCP library) The Theory of Numbers Good text, best suited for either advanced undergraduate or first graduate course. Classical approach with recently added sections having some computational flavor. Previously used as a text for this class. ($95, UMBC library) A Classical Introduction to Modern Number Theory One of the best general number theory books at a graduate level. Little computational coverage but good coverage from a modern algebraic viewpoint. Contains a short introduction to the theory of finite fields. ($60, UMCP library)

65. Directory - Science: Math: Operations Research Search only in Operations Research (advanced). The math Forum math Library - Operations Research unsolved problems in OR · cached · A good collection. http://www.incywincy.com/default?p=26930

66. BSU 96-98 Graduate Math Course Descriptions LCM s, the Euclidean Algorithm, famous unsolved problems, and congruences. modeling to real world problem situations. 552 advanced EUCLIDEAN GEOMETRY (4 credits http://www.bemidjistate.edu/BSUCatalog/GRADCATALOG/MATH/Courses.html

BSU Catalog Home Undergraduate Math Program All-University Courses and Descriptions Mathematics Graduate Course Offerings (MATH) College-Program Codes: 17-10 Unless otherwise specified, the prerequisite for the graduate courses in mathematics is an undergraduate major in mathematics or MATH 520 or equivalent. 500 MATH MODELS, GAMES, AND ACTIVITIES FOR THE PRIMARY GRADES (2 credits). For teachers of grades K-3. Mathematical background including teaching-aids, games, projects and activities that relate to the primary level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint. 501 MATH MODELS, GAMES, AND ACTIVITIES FOR THE INTERMEDIATE GRADES (2 credits). For teachers for grades 3-6. Mathematical background including teaching-aids, games, projects, and activities that relate to the intermediate level will be presented. The basic mathematical operations will be presented from a "concrete" standpoint. 502 MATH MODELS, GAMES, AND ACTIVITIES FOR ELEMENTARY CLASSROOMS (4 credits). An intensive introduction to activities, models, projects, and ideas needed to effectively teach using contemporary text materials. Materials usable at every ability level will be included. Prerequisite: Teaching experience or consent of instructor.

67. Wu :: Forums - Unsolved Problems In The Hard Forum A math puzzler from Barukh, Random Exponentiation, is solved this one is diving into some advanced number theory. This one is an unsolved problem in mathematics http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action

68. Frank Potter's Science Gems - Mathematics and engineering at the advanced undergraduate level Ocean Models, Bioelectric Field problems, Monte Carlo unsolved Mathematics problems S. Finch at Wolfram 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: Tuesday, April 20, 2004. 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

69. Alexa Web Search - Subjects > Science > Math > Analysis Favorite unsolved problems Alexandre Eremenko (Purdue University). front.math.ucdavis.edu/math.CA Site Info. advanced Calculus and Analysis Lecture notes from http://www.alexa.com/browse/general?catid=391044&mode=general

70. Undergraduate Studies Course Listing Emphasis on examples, applications, and unsolved problems in contemporary areas such as elliptic curves, geometric surfaces math 4431 advanced Calculus, J http://talon.stockton.edu/eyos/page.cfm?siteID=14&pageID=86&program=MATH

71. The Math Forum - Math Library - Problems/Puzzles math Forum's Internet math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating to problems_puzzles. more advanced http://mathforum.com/library/selected_sites/problems_puzzles.high.html

Browse and Search the Library Home Resource Types Ed. Materials : Problems/Puzzles : High Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites 20,000 Problems Under the Sea - MathPro Press An online reference to mathematical problems, comprising a searchable database of 20,000+ math problems from journals and contests including the American Mathematical Monthly, Journal of Recreational Mathematics, Mathematical Questions and Solutions from the Educational Times, and several national and international mathematical olympiads. Search for problems by subject, keyword, source, problem number (requires publication source), year, proposer, solver, or author; or request a randomly-served problem. Search or view comments, search commenters, and post your own comments on problems. Contribute problems through the Web site or by email. The site also outlines technical details of database publishing with TeX. Compiled by MathPro Press and located in the Department of Mathematics and Statistics at the University of Missouri - Rolla. more>> AIMS Education Foundation "Activities Integrating Mathematics and Science." A non-profit, independent organization established to develop integrated math/science materials for grades K-9. See, in particular, the

72. Unsolved Problems Check out the NEW Hotbot. Tell me when this page is updated. Hi! We're E and Pi, here to introduce you to Jon Bettencourt's web page on unsolved math problems. It's his final project for COSMOS, the http://members.tripod.com/kopylefted2002/cosmos

var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Check out the NEW Hotbot Tell me when this page is updated Hi! We're E and Pi, here to introduce you to Jon Bettencourt's web page on unsolved math problems. It's his final project for COSMOS, the math and science program he's in. Is he going to be surprised when he sees what we've done! Our favorite problem is the one about e (pi* n) being close to integers, since it involves us! Although Pi says she likes the formula for any digit of pi better (of course). To which Jon responds... I'm gonna get them for this! If E and Pi keep messing with this page, I'll have to get Bromine to get them off my back, and I know they don't want that! More information on E and Pi (the characters, not the numbers) Anyway, I have been gathering information on unsolved problems from the Internet and other sources. Here are a few of the problems I have found and some information on some of them. Some of these problems seem very simple, but end up with no simple proof or solution to them. As an example, Fermat's Last Theorem was very simple, but it took hundreds of years and some parts from very advanced branches of mathematics to solve it. So if one seems simple, don't try to solve it unless you know a lot of math. More information about unsolved problems can be found with a search for unsolved problems on Google.com

73. CNN.com - Russian May Have Solved Great Math Mystery - Jan. 7, 2004 This is arguably the most famous unsolved problem in math a University of Michigan math professor reviewing Perelman s work has advanced the furthest without 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 ... Special Reports SERVICES Video E-mail Services CNNtoGO 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.

74. Math: Research: Open Problems Most Wanted List Elementary unsolved problems in mathematics, listed at the MathPages archive. unsolved Mathematics problems - Compiled by Steven Finch. http://www.spacetransportation.org/Math/Research/Open_Problems/

Science Directory - Open Problems Home Search Add a Site Modify a Site ... Links SEARCH ADVANCED SEARCH RANDOM LINK Find this: CUSTOM LINKS Yoursite Another Area Somewhere else Home ... Research : Open Problems Mathematical Problems - In various subjects, compiled by Torsten Sillke. Millennium Prize Problems - The seven problems proposed by the Clay Mathematics Institute: P versus NP; Hodge Conjecture; Poincar© Conjecture; Riemann Hypothesis; Yang-Mills Existence and Mass Gap; Navier-Stokes Existence and Smoothness; Birch and Swinnerton-Dyer Conjecture. Resources include articles on each problem by leading researchers. Most Wanted List - Elementary unsolved problems in mathematics, listed at the MathPages archive. Some Unsolved Problems with Elementary Formulation - Satements of some famous problems compiled by Frank Wikstrom, Ume¥ University. Unsolved Mathematics Problems - Compiled by Steven Finch. Descriptions of some unsolved problems and numerous links to other collections. Unsolved Problem of the Week Archive - A list of unsolved problems published by MathPro Press during 1995. Open Problems Spacetransportation.org - Science Directory - Last Update: Sun May 23 2004

75. Math: Number Theory: Open Problems Maintained at AIM. Mathematician s Secret Room unsolved problems in Number Theory. unsolved problems and Rewards - By Clark Kimberling. http://www.spacetransportation.org/Math/Number_Theory/Open_Problems/

Science Directory - Open Problems Home Search Add a Site Modify a Site ... Links SEARCH ADVANCED SEARCH RANDOM LINK Find this: CUSTOM LINKS Yoursite Another Area Somewhere else Home ... Number Theory : Open Problems ABC Conjecture Catalan Conjecture Collatz Problem Goldbach Conjecture ... Advice to Research Students - Some tips for solving problems in number theory, collected by the Cardiff University group. L-functions and Random Matrix Theory - Conjectures and open problems concerning L-functions, focussing on the areas in which there has been recent progress using results from Random Matrix Theory. Maintained at AIM. Mathematician's Secret Room - Unsolved problems in Number Theory. English and Japanese text by Hisanori Mishima. Number Theory Conjectures - A collection of easily stated conjectures which are still open. Each conjecture is stated along with a collection of references. Open Problems - Some questions compiled by Jon Perry. Seva Lev's Problem Page - A collection of research problems. Unsolved Problems and Conjectures - Regarding equal sums of like powers, compiled by Chen Shuwen. Unsolved Problems and Rewards - By Clark Kimberling. Offers prizes for solutions of some problems in number theory.

76. MSNBC - Publicity-shy Whiz Rocks The Math World is arguably the most famous unsolved problem in math and Kleiner, a University of Michigan math professor reviewing Perelman’s work has advanced the furthest http://www.msnbc.msn.com/id/3899479/

MSN Home My MSN Hotmail Shopping ... Money document.write('') Web Search: document.write(''); logoImg("http://sc.msn.com"); MSNBC News Alerts Newsletters Help ... MSNBC Shopping Search MSNBC: Advanced Search   RESOURCE GUIDE Buy Life Insurance Yellow pages expedia.com Shopping ... Small Business Tips Science Publicity-shy whiz rocks the math world Million-dollar solution to age-old problem is holding up By Paul Elias The Associated Press Updated: 3:13 p.m. ET Jan.07, 2004 SAN FRANCISCO - A publicity-shy Russian researcher who labors in near-seclusion may have solved one of mathematics’ oldest and most abstruse problems, the Poincare Conjecture. advertisement 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, Mass.-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.

77. Mudd Math Fun Facts: Fermat's Last Theorem is a Fun Fact at the advanced level that mathematics, like other disciplines, has unsolved questions that Behind the Fact Pursuit of this problem and related http://www.math.hmc.edu/funfacts/ffiles/30004.5.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 1561017 Fun Facts viewed since 20 July 1999. Francis Edward Su From the Fun Fact files, here is a Fun Fact at the Advanced level: Fermat's Last Theorem There are lots of Pythagorean triples ; triples of whole numbers which satisfy: x + y = z But are there any which satisfy x n + y n = z n for integer powers n greater than 2? The French jurist and mathematician Pierre de Fermat claimed the answer was "no", and in 1637 scribbled in the margins of a book he was reading (by Diophantus) that he had "a truly marvelous demonstration of this proposition which the margin is too narrow to contain". This tantalizing statement (that there are no such triples) came to be known as Fermat's Last Theorem even though it was still only a conjecture, since Fermat never disclosed his "proof" to anyone. Many special cases were established, such as for specific powers, families of powers in special cases. But the general problem remained unsolved for centuries. Many of the best minds have sought a proof of this conjecture without success. Finally, in the 1993, Andrew Wiles, a mathematician who had been working on the problem for many years, discovered a proof that is based on a connection with the theory of

78. Prime Obsession: Bernhard Riemann And The Greatest Unsolved Problem In Mathemati great clarity to many aspects of advanced mathematics Bernhard Riemann and the Greatest unsolved Problem in mathematics who are more skilled in math, this book http://www.sciencesbookreview.com/Prime_Obsession_Bernhard_Riemann_and_the_Great

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Authors: John Derbyshire Released: 23 April, 2003 ISBN: 0309085497 Hardcover Sales Rank: List price: Our price: You save: Book > Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics > Customer Reviews: Average Customer Rating: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics > Customer Review #1: Its got that certain "cant put it down" feel This is a fascinating and very well-written book about a singular problem in mathematics history. Derbyshire presents a look at the history of the Riemann hypothesis (or is it "conjecture"? Derbyshire asks, as an aside, what the real difference is between the two, in mathematical terminology) the people and their political context as well as the equation and efforts to prove it. As a blessing to those of us who are not hard-core mathematicians, Derbyshire takes the approach of alternating chapters between (even numbered chapters) math and (odd chapters) people and context. This gives the effect of telling two intimately linked stories simultaneously, and keeping the reader in just a bit of suspense in each while telling the other. I found myself enjoying each of the two tales, yet impatient to see where the other was going next.

79. MathLinks EveryOne Index Forum, Topics, Posts, Last Post. advanced Section, Tell Us About Your Country Your impressions on how math is done in your country. Post only files with problems. http://www.tg-mures.roedu.net/index.php

80. Prime Obsession: Bernhard Riemann And The Greatest Unsolved Problem In Mathemati clarity to many aspects of advanced mathematics Bernhard Riemann and the Greatest unsolved Problem in mathematics Excellent Reading for math and Nonmath Types http://www.biography-reviews.com/Prime_Obsession_Bernhard_Riemann_and_the_Greate

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Authors: John Derbyshire Released: 23 April, 2003 ISBN: 0309085497 Hardcover Sales Rank: List price: Our price: You save: Book > Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics > Customer Reviews: Average Customer Rating: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics > Customer Review #1: Its got that certain "cant put it down" feel This is a fascinating and very well-written book about a singular problem in mathematics history. Derbyshire presents a look at the history of the Riemann hypothesis (or is it "conjecture"? Derbyshire asks, as an aside, what the real difference is between the two, in mathematical terminology) the people and their political context as well as the equation and efforts to prove it. As a blessing to those of us who are not hard-core mathematicians, Derbyshire takes the approach of alternating chapters between (even numbered chapters) math and (odd chapters) people and context. This gives the effect of telling two intimately linked stories simultaneously, and keeping the reader in just a bit of suspense in each while telling the other. I found myself enjoying each of the two tales, yet impatient to see where the other was going next.

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