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         Unsolved Problems Advanced Math:     more detail
  1. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire, 2004-05-25

21. Math Links
among a small group of mathematicians as a popular unsolved problem. Week A site providing links to problems for students from elementary to advanced.
http://www.district10.nbed.nb.ca/Links/Math.htm

First Page

Up

Information

Curriculum
...
Experiment and Explore Mathematics
Interactive mathematics site that includes several java applets to help you explore mathematical, pre-calculus concepts and topics, and some calculus topics. GraphCalc GraphCalc is an all-in-one solution to everything from everyday arithmetic to statistical analysis, from betas to Booleans, from cubes to calculus, from decimals to derivatives. RHS Math Portal This website was created by the Electronic Commerce class of Rothesay High School. In cooperation with the enriched grade 11 mathematics class, this unique resource was created. This site contains many resources that relate to mathematics and in particular, to the grade 11 math curriculum here in New Brunswick. The Mathematics Behind Maps How many different colors must you have available if you want to color a map so that countries that share a boundary line are not colored the same color? In the mid-1800's this problem became known among a small group of mathematicians as a popular unsolved problem. Even at that time, it was common knowledge among map-makers that 4 colors seemed to be sufficient to color a map. This wasn't actually proved, however, until 1976. What's Special About This Number?

22. Curriculum Links
flashcards, games, a homework helper and help on advanced math problems. Ping math math tutorials and topics on solved and unsolved problems for upper
http://www.kingcluster.phila.k12.pa.us/curriculumlinks.html

23. Finest Image Search Page
url www.math.purdue.edu/~eremenko/uns advanced Calculus and Analysis Lecture notes from the Favorite unsolved problems - Alexandre Eremenko (Purdue University
http://www.finestimage.com/cgi-bin/odp/index.cgi?base=/Science/Math/Analysis/

24. Mudd Math Fun Facts: Riemann Hypothesis
here is a Fun Fact at the advanced level find it fascinating that a great unsolved problem amounts to The math Behind the Fact Many other problems in number
http://www.math.hmc.edu/funfacts/ffiles/30002.5.shtml
hosted by the Harvey Mudd College Math Department Francis Su
Any Easy Medium Advanced
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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

25. Research
What about more advanced recent topics in mathematics? Although some of Hilbert s problems are vague is considered the most outstanding unsolved problem in pure
http://www.math.wustl.edu/~nweaver/research.html
Research in pure mathematics
What is pure mathematics?
    Pure mathematics is the study of a priori truth - facts that hold because they must hold, because logic mandates them. You could also say that these are things which are tautologically true, or true "by definition." But that does not mean they are necessarily simple or trivial. Is it obvious that there are infinitely many prime numbers? Not if you've never seen the proof . And yet this is true solely as a consequence of the definition of prime numbers.

Why is advanced mathematics so hard to explain to laymen, and even to other scientists?
    The infinitude of primes has been known for over two thousand years. Mathematics extends as far back as written history.
    Mathematical truths are tautological - so they can never be falsified. Because of this, the discipline of mathematics is fundamentally cumulative. It keeps building on itself, creating more and more elaborate structures. All of the "easy" things in math were discovered very long ago and are now known to every educated person. More advanced topics are hard to explain if one has to jump over intermediate material, as if you tried to explain division to someone who did not already know multiplication. Actually, much advanced math logically cannot be explained to laymen: once you had covered all of the necessary intermediate material, the listener would be an expert himself!

26. Math
unsolved mathematics problems. Virtual mathematics Center. math Forum Selected math Resources by Subject kindergarten through advanced math.
http://www.rbls.lib.il.us/dpl/about/hmwrk/schmath.htm
School Assignments: Math Gen eral Sites Armadillo's Math Resources annotated directory of links Cornell University Mathematics Library A Dictionary of Units Eric's Treasure Trove of Mathematics Figure This! Math Challenges for Families ... Math Forum fun activities to celebrate Pi Day (March 14 or 3.14) Math Help Topics Math in Daily Life Mathematical Web Sites links Mathematics Archives Mathematics Center Mathematics Information Servers Mathematics Lessons ... MathSearch search over 90,000 documents Measurements Converter MegaMathematics! Problem Solving Resources for Mathematics ... Smallshop: Math veriety of math resources Unsolved Mathematics Problems Virtual Mathematics Center K-12 A Plus Math Arabcsq.com Ask Dr. Math Elementary School Level Middle School Level High School Level Captain Zoom's Math Adventure basic math Dave's Math Tables Favorite Mathematical Constants Flashcards for Kids For Teachers Everyday Mathematics Resource Guide for teachers Math Resources for Teachers MathEd: Mathematics Education Resources GoMath!

27. Resource Links -- Math
interactive flashcards, games, a homework helper and help on advanced math problems. math tutorials and topics on solved and unsolved problems for upper
http://www.sau35.org/resource-math.htm
You are
here:
White Mountains School Administrative Unit 35 Home District Links School Boards SAU Staff/Resources ... In the News Internet Resources Webmaster K-12 Mathematics http://www.pbs.org/teachersource/math.htm Teacher Source site. http://www.mathprojects.com The Math Projects Journal offers tips, lesson plans for interactive projects, and advice from educators around the globe. http://www.funbrain.com/math Batter up! Play a little Math Baseball and test your math smarts at all levels with this mind-exercising site. http://www.aplusmath.com http://www.mathgoodies.com Offers math lessons and resources designed to meet NCTM Standards for Teaching Math. http://www.c3.lanl.gov/mega-math/index.html Mega Math authors at Los Alamos National Laboratory. They go on to provide activities and explanations for some high-level mathematical concepts. What is infinity plus one? Why does a map never need to contain more than four colors? http://www.hbschool.com/glossary/math/glossary8.html Use the Harcourt Multimedia Math Glossary to help elementary and middle school students visualize challenging math ideas. Illustrations and animations of concepts such as sums, ordinal numbers, and telling time are available for young students, while items such as alternate interior angles and congruency are depicted for older students. Descriptions are categorized by grade level.

28. Great Math Sites
students work on open (unsolved) problems in mathematics a math question having a problem check out Dr statistics, calculus, and general and advanced math.
http://www.colchesterhs.k12.vt.us/math_sites.htm
CHS Home Page Great Math Sites GPS Tutorial Sites: www.corvus.com/con-page/con-12.htm amazing-space.stsci.edu/ hubble.stsci.edu/ www.aero.org/publications/GPSPRIMER/index.html ... Pi Math Page
The concept of Pi, an irrational number, has been calculated and explored throughout history from biblical times to the present. The Chinese calculated Pi and their value was used for a thousand years. One mathematician calculated pi
to 35 places and had it inscribed on his epitaph. With the advent of the computer, pi has been calculated to over six billion decimal places. Whether it is of historical significance, mathematical importance or a personal goal, pi has universal appeal.
Join us in an adventure of exploring the concept of pi.
Manipula Math with Java

MacTutor History of Mathematics

Archives contains the biographies of more than 1100 mathematicians. All the mathematicians now have individual biographies and have extensive references. You can access them from a selection of Alphabetical or Chronological Biographical indexes.
Mathmania
is dedicated to helping students work on open (unsolved) problems in mathematics and getting more people involved in live math research.

29. Math
Plot Gallery, Favorite mathematical Constants, unsolved mathematics problems help as well as math problems to solve and include K12, college and advanced math.
http://www.pthsd.k12.nj.us/SCH/PHHS/MediaCenter/math.htm
MATH SITES ON THE INTERNET
Parsippany Hills High School Media Center Return Home
General Math Sites
This Gateway is maintained by the Cornell Department of Education and provides links to resources in mathematics and science for educators and students in grades 9-12. Math In Action This site is developed by Mathsoft and has interesting links to math related sites. Contents feature Math 3D Plot Gallery, Favorite Mathematical Constants, Unsolved Mathematics Problems, Math Puzzle Page, Math Animation Gallery, Math and Statistics Links and MathCAD Files Around the World. Mathematics Resources on the World Wide Web Links to a variety of math sites.. Math Homework Help Ask Dr. Math Staffed by math teachers, mathematicians, college professors and students from around the country, this site provides a question-and-answer service for students and teachers. Part of the Math Form site. Discovery School's Webmath Math homework help as well as math problems to solve are the focus of this site.

30. Ten Ways To Use Puzzles In Math Education
Unlike advanced mathematical topics, most puzzles require no special background, yet are rich with unsolved challenging problems.
http://www.scottkim.com/education/tenways.html
Ten Ways to Use Puzzles in Math Education
Puzzles make math fun
Chances are that you already use puzzles in your classroom. After all, a puzzle is nothing but a problem that is fun to solve. Primary level teachers commonly use puzzle manipulatives like tangrams to teach concepts like sahpe, fractions and area. Secondary and high school teachers often use puzzles to introduce concepts and spice up homework. College entrance exams and math competitions are mostly collections of puzzles.
As a professional puzzle designer and math educator, I would like to see puzzles used more widely at all levels of math education. Here are ten ways you can use puzzles in your math classrooms, with links to web resources. Most of the products mentioned work with upper elementary through high school students.
1. Classroom Resource
Rush Hour Hoppers , and Lunar Lockout from Binary Arts , each of which include a graded series of 40 puzzles.
The Problem of the Week book and posters from Dale Seymour Publications (part of Pearson Learning) is a colorful collection of entertaining puzzles that you can hang on your wall. I plan to create similar puzzles on the web.
Having students build puzzles themselves both saves money and involves them in a creative crafts activity.

31. Science, Math: Analysis
ScienceMathCalculus. advanced Calculus and Analysis Lecture notes from the University of Favorite unsolved problems - Alexandre Eremenko (Purdue University
http://www.combose.com/Science/Math/Analysis/
Top Science Math Analysis ... Transform Calculus Related links of interest:

32. WebGuest Directory - Math : Analysis
Related categories Science/math/Calculus. Sites advanced Calculus and Analysis Favorite unsolved problems Alexandre Eremenko (Purdue University).
http://directory.webguest.com/Science/Math/Analysis
Science Math : Analysis
Related categories:
Sites:

33. Frequently Asked Questions In Mathematics
Topics range from trivia and the trivial to advanced subjects such as Wiles Information about the International math Olympiad home page. unsolved problems.
http://db.uwaterloo.ca/~alopez-o/math-faq/math-faq.html
Frequently Asked Questions in Mathematics
The Sci.Math FAQ Team.
Editor:
(C) 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997.
This is a compilation of Frequently Asked Questions (and their answers) about Mathematics. Topics range from trivia and the trivial to advanced subjects such as Wiles recent proof of Fermat's Last Theorem. There are several formats available for the table of contents, mostly because HTML does not handle math symbols well. At this time pretty much all versions are in synchrony. (See list of updates ). The available formats are: Note: The FAQ in dvi format contains an Encapsulated PostScript drawing which cannot be read directly from your local dvi browser. Any ideas?
  • Text Based Browsers such as Lynx should browse the Text Table of Contents . This link is also great for low bandwith (aka slow) connections.
  • Graphic Browsers Table of Contents
  • Dvi (TeX) Format is available for on-screen browsing. This dvi version has small pages, so that users with 14" monitors may read each page without scrolling. (245KB)
  • Dvi (TeX) Format This is a printer ready dvi version
  • New Acrobat (PDF) Format This is a printer ready pdf version
  • PostScript Format . The dvi file above is also available in PostScript
  • Compressed PostScript Format . The PS file above is also available in *.ps.Z

34. Math
interactive flashcards, games, a homework helper and help on advanced math problems. math Tutorials and topics on solved and unsolved problems for upper
http://www.olc.edu/library/math.htm
MATH 24 Game Math Club A+ Math - interactive flashcards, games, a homework helper and help on advanced math problems. Ask Dr. Math Calculus - includes detailed graphics and explanations, as well as formal breakdowns of terms and applications. Calculus Reference Page Camosun College - Carpentry Math Finite mathematics and applied calculus. Funbrain - Play a little math baseball and test your math smarts at all levels with this mind-exercising site. Geometry Center Los Alamos National Laboratory MATH site - hands-on exploration of all things math. Math Archives - This comprehensive source covers a wide range of different topics in mathematics, software and teaching materials. Math Dictionary for kids Mathematics - clear, straightforward site where you can access materials on modules, projects, and texts for calculus, linear algebra, engineering mathematics and more. Math Goodies - Offers math lessons and resources designed to meet NCTM Standards for Teaching Math.

35. Web Sites For 1115
Egyptian fractions; unsolved problems; naming large numbers; this site assumes greater math background; Indiana proof; Mersenne Primes and more advanced extensions;
http://www.css.edu/users/aguckin/WebSites1115.htm
Web sites for Mathematics for Teachers Web sites can be very useful. However, any list will need to be modified frequently. These are some good sites for getting started. You will find other sites that you like and some of these sites will become inaccessible. Start keeping your own mathematics bookmarks and record a brief dedscription of them. You will be expected to have your modified list in your portfolio. PBS Mathline site periodically lists Web resources for teachers. Check out the following site for incorporating math ideas into activities for elementary students . This will change regularly which can be a very useful! Web sites arranged by topic
  • i deas for younger children Texas Instrument; a commercial site; contains helpful links TI calculators
  • Calendar
  • Compute the day of week for a given date Calendar activities and Algebra
  • Card Games
  • Links to card games Alphametric site Cryptarithmetic and hints for solving Cryptography some basic ideas License coding Public Key Encrytion Links to more on Encrytion
  • Combinatorics
  • Includes creating subsets, combinations and permutations
  • 36. Lukol Directory - Science Math Analysis
    advanced Calculus and Analysis Lecture notes from the University of http//www.math.vanderbilt.edu/~schectex/ccc/ga Some unsolved problems Mainly in analysis
    http://www.lukol.com/Top/Science/Math/Analysis/

    Lukol Directory -
    Science Math Analysis ... Front for the Mathematics ArXiv
    Classical Analysis papers and preprints available in pdf, ps, and abs formats from UC Davis.
    http://front.math.ucdavis.edu/math.CA
    Handbook of Analysis and its Foundations (HAF)

    Eric Schechter (AP, 1996) available in printed and CR-ROM editions. Preface, table of contents and other excerpts.
    http://www.math.vanderbilt.edu/~schectex/ccc/
    Harmonic Analysis

    Maintained by Terence Tao, UCLA. Lists events, personal pages, preprints, research groups, other links.
    http://www.math.ucla.edu/~tao/harmonic/
    Computability and Complexity in Analysis Network
    CCA Net aims to provide a central location for collecting information useful to researchers working in the field. http://www.informatik.fernuni-hagen.de/import/c... Advanced Calculus and Analysis Lecture notes from the University of Aberdeen for a first course in Analysis. http://www.maths.abdn.ac.uk/~igc/tch/ma2001/not... An Introduction to the Gauge Integral Discusses the properties of an alternative integration theory, and its relationship with the Riemann and Lebesgue integrals. http://www.math.vanderbilt.edu/~schectex/ccc/ga...

    37. Problem Solving Resources
    www.mcrel.org/csmp/mtindex.asp Medieval Adventure In Problem Solving http//tqjunior.advanced.org/4471 K2 unsolved Mathematics problems http//www
    http://www.asd.wednet.edu/pioneer/barnard/sites/Math/ProblemSolving.htm
    Problem Solving Resources
    AIMS Puzzle Corner http://www.aimsedu.org/puzzle/puzzleList.html
    The goal of the AIMS Puzzle Corner is to provide teachers with a variety of interesting puzzles that can be used to create a learning environment where students engage in doing mathematics just for the fun of it! With the proper encouragement and enthusiasm on the part of the teacher, students can learn to enjoy puzzles and the mathematics behind them. Solutions appear the month following the puzzle's introduction.
    Aunty Math http://www.dupagechildrensmuseum.org/aunty/index.html
    DuPage Children's Museum presents Aunty Math, otherwise known as Mathilda Mathews, poses challenges to students on this web site. She presents a math problem, and then students can email their answers to her. Past challenges are posted so that students may solve them if they want to. Teachers can receive ideas on how to modify the math challenge to fit the needs of students.
    Brain Teasers-Math Problem of the Week http://www.eduplace.com/math/brain/index.html

    38. 1Up Science > Links Directory > Math: Analysis
    Science math Calculus. advanced Calculus and Analysis Lecture notes from the University of Favorite unsolved problems Alexandre Eremenko (Purdue University).
    http://www.1upscience.com/links/math-analysis.html
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    39. Science Math Analysis
    advanced Calculus and Analysis, advanced Calculus and Analysis problems in Function Theory, unsolved problems in Function Some web results for math Analysis
    http://world.ammissione.it/browse_/Science/Math/Analysis/

    40. :: Ez2Find :: Analysis
    advanced Calculus and Analysis Site Info - Translate URL http//www.math.ucdavis.edu/~emsilvia CA_problems.html; Favorite unsolved problems - Site Info
    http://ez2find.com/cgi-bin/directory/meta/search.pl/Science/Math/Analysis/
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