Universe

Mersenne Primes

International Year of Physics

1, 3, 8, 120, ... http://www.weburbia.demon.co.uk/pg/diophant.htm
Sets of numbers such that the product of any two is one less than a square. Diophantus found the rational set 1/16, 33/16, 17/4, 105/16; Fermat the integer set 1, 3, 8, 120.

Bibliography on Hilbert's Tenth Problem http://liinwww.ira.uka.de/bibliography/Math/Hilbert10.html
Searchable, ~400 items.

Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n http://www.biochem.okstate.edu/OAS/OJAS/thiendo.htm
Methods to solve these equations.

Diagonal Quartic Surfaces http://www.boojum.org.uk/maths/quartic-surfaces/
Articles, computations and software in Magma and GP by Martin Bright.

Diophantine Equations http://www.math.niu.edu/~rusin/papers/known-math/index/11DXX.html
Dave Rusin's guide to Diophantine equations.




Diophantine Geometry in Characteristic p http://www.ma.utexas.edu/users/voloch/surveylatex/surveylatex.html
A survey by Jos� Felipe Voloch.

Diophantine m-tuples http://www.math.hr/~duje/dtuples.html
Sets with the property that the product of any two distinct elements is one less than a square. Notes and bibliography by Andrej Dujella.

Diophantus Quadraticus http://www.bioinfo.rpi.edu/~zukerm/cgi-bin/dq.html
On-line Pell Equation solver by Michael Zuker.

Egyptian Fractions http://www.ics.uci.edu/~eppstein/numth/egypt/
Lots of information about Egyptian fractions collected by David Eppstein.

Fermat's Method of Infinite Descent http://sweb.uky.edu/~jrbail01/fermat.htm
Notes by Jamie Bailey and Brian Oberg. Illustrates the method on FLT with exponent 4.




Hilbert's Tenth Problem http://www.ltn.lv/~podnieks/gt4.html
Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could determine by a finite number of operations whether the equation is solvable in rational integers.

Hilbert's Tenth Problem http://logic.pdmi.ras.ru/Hilbert10/
Statement of the problem in several languages, history of the problem, bibliography and links to related WWW sites.

Linear Diophantine Equations http://www.thoralf.uwaterloo.ca/htdocs/linear.html
A web tool for solving Diophantine equations of the form ax + by = c.

MAGMA program http://www.math.leidenuniv.nl/~tengely/main2.html
MAGMA code to solve Diophantine equations of the form F(x)=G(y), for which Runge's condition is satisfied. Created by Szabolcs Tengely.
On the Psixyology of Diophantine Equations http://web.inter.NL.net/hcc/J.Moree/linkind2.htm
PhD thesis, Pieter Moree, Leiden, 1993.




Pell's Equation http://www.ieeta.pt/~tos/pell.html
Record solutions.

Pythagorean Triples in JAVA http://home.foni.net/~heinzbecker/pythagoras.html
A JavaScript applet which reads a and gives integer solutions of a^2+b^2 = c^2.

Pythagorean Triplets http://www.faust.fr.bw.schule.de/mhb/pythagen.htm
A Javascript calculator for pythagorean triplets.

Quadratic Diophantine Equation Solver http://www.alpertron.com.ar/QUAD.HTM
Dario Alpern's Java/JavaScript code that solves Diophantine equations of the form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 in two selectable modes: "solution only" and "step by step" (or "teach") mode. There is also a link to his description of the solving methods.

Rational and Integral Points on Higher-dimensional Varieties http://aimath.org/WWN/qptsurface2/
Some of conjectures and open problems, compiled at AIM.




Rational Triangles http://grail.cba.csuohio.edu/~somos/rattri.html
Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.

Solving General Pell Equations http://hometown.aol.com/jpr2718/pelleqns.html
John Robertson's treatise on how to solve Diophantine equations of the form x^2 - dy^2 = N.

The Erdos-Strauss Conjecture http://math.uindy.edu/swett/esc.htm
The conjecture states that for any integer n > 1 there are integers a, b, and c with 4/n = 1/a + 1/b + 1/c, a > 0, b > 0, c > 0. The page establishes that the conjecture is true for all integers n, 1 < n <= 10^14. Tables and software by Allan Swett.

Thue Equations http://finanz.math.tu-graz.ac.at/~cheub/thue.html
Definition of the problem and a list of special cases that have been solved, by Clemens Heuberger.





computing equal sums of like powers


Computing Minimal Equal Sums Of Like Powers http://euler.free.fr/
Jean-Charles Meyrignac's distributed-computing project on equal sums of like powers and the place to look for the current status of the problem.
Equations Involving Sums of Powers http://www.glasgowg43.freeserve.co.uk/sumintro.htm
Joseph McLean's investigations into those equations.
On Equal Sums of Like Powers and Related Problems http://www.cs.man.ac.uk/cnc/EqualSums/
Classification of problems related to equal sums of like powers.
Overview of Mathematician Secret Room http://www.asahi-net.or.jp/~KC2H-MSM/mathland/overview.htm
Page keeping track of solutions of x^3+y^3+z^3 < 1000 and x^3+y^3+2*z^3 < 1000.
Power Page http://www.uwgb.edu/dutchs/RECMATH/rmpowers.htm
Steve Dutch's page about powers of numbers.



Sortedsums http://cr.yp.to/sortedsums.html
D. J. Bernstein's collection of tools for enumerating small solutions to certain types of equal sums of like powers.
Taxicab Numbers http://pi.lacim.uqam.ca/eng/problem_en.html
David W. Wilson's list of the smallest number that can be expressed as a sum of two positive cubes in n different ways, for n = 1 through 5.
The Fifth Taxicab Number is 48988659276962496 http://www.cs.uwaterloo.ca/journals/JIS/wilson10.html
David W. Wilson's article on his search for the smallest integer that can be expressed as a sum of two positive cubes in 5 distinct ways, up to order of summands.
Tom's Mathematical Things http://tom.womack.net/maths/dissert_abstract.htm
Dissertation about equal sums of like powers by Tom Womack.



Algebraic Geometry events



Activities in Algebraic Geometry and Related Areas http://www.math.ist.utl.pt/galg/
A list maintained at Instituto Superior T�cnico, Lisbon.

Calf http://www.maths.bath.ac.uk/~mapamk/Calf.html
UK Junior Algebraic Geometry Seminar (an offshoot of COW). Occasional meetings, mailing list.

Conferences in Algebraic Geometry and Related Fields http://www-euclid.mathematik.uni-kl.de/conferences/
A list maintained by the EAGER node at Kaiserslautern, Germany.

COW Seminar http://www.dpmms.cam.ac.uk/Seminars/COW.html
UK peripatetic algebraic geometry seminar. Programmes, mailing list, resources.

EAGER Activities http://euclid.mathematik.uni-kl.de/activities/
European Algebraic Geometry Research Training Network. Activities of or related to the network.




Equivariant Intersection Theory http://www.mimuw.edu.pl/~alan/html/Lukecin05.html
28th Autumn School in Algebraic Geometry. Lukecin, Poland; 11--17 September 2005.

GAEL - G�ometrie Alg�brique En Libert� http://euclid.mathematik.uni-kl.de/~gael/
A series of conferences particularly designed for researchers in Algebraic Geometry at the beginning of their scientific career.

GAEL XIII http://www-euclid.mathematik.uni-kl.de/~gael/GaelXIII/GaelXIII.html
CIRM (Centre International de Rencontres Math�matiques), Luminy, Marseille, France; 21--25 March 2005.

G�om�trie Alg�brique en Libert� http://www-euclid.mathematik.uni-kl.de/~gael/
A series of conferences aimed at researchers in Algebraic Geometry at the beginning of their scientific career.

MEGA 2005 http://www.dm.unipi.it/MEGA05/
The Eighth International Symposium on Effective Methods in Algebraic Geometry. Computing in and with algebraic geometry: Theory, Algorithms, Implementations, Applications. Porto Conte, Alghero, Sardinia,Italy; 26 May -- 2 June 2005.


Summer Institute in Algebraic Geometry http://www.math.princeton.edu/~rahulp/seattle05.html
Three one-week sessions: Interactions with physics; Classical geometry; Arithmetic geometry. University of Washington, Seattle, WA, USA; 25 July -- 12 August 2005.

Trento Schools http://euclid.mathematik.uni-kl.de/activities/trento.html
Intended for European doctoral students and post-doctoral fellows in algebraic geometry.

VBAC Meetings http://www.mi.uni-erlangen.de/~forkel/vbac/meetings.html
Past and future meetings on Vector Bundles on Algebraic Curves.



Key Curriculum Press

 More Mersenne Primes!

Algorithms and Ancient Machines

Website Design Update ....... Chaos Update ...... Mathematics Ed Sites ...... Math Lessons


GRADES 1-2 Flash Site Counting
Dynamical Systems



English Spanish German French Dutch Italian Swedish Portuguese Danish Norwegian Finnish Russian Japanese American English Brazilian Portuguese






eXTReMe Tracker ART/ARMS © 1991-2005









basic science


Dynamic Systems - Information Technology

Nanotechnology - Internet
...........










Make your own free website on Tripod.com