History of mathematics presented through famous problems, with some exercises and their solutions. Done in conjunction with the Math Forum, the home of Ask Dr. Math.

The Four Color Theorem This page gives a brief summary of a new proof of the Four Color Theorem and a four-coloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas. Table of Contents: History. Why a new proof Outline of the proof. Main features of our proof. Configurations. Discharging rules. Pointers. A quadratic algorithm. Discussion. References. History.

NOVA Online presents The Proof, including an interview with Andrew Wiles, an essay on Sophie Germain, and the Pythagorean theorem.

Fermat's last theorem Number theory index History Topics Index Pierre de Fermat died in 1665. Today we think of Fermat as a number theorist, in fact as perhaps the most famous number theorist who ever lived. It is therefore surprising to find that Fermat was in fact a lawyer and only an amateur mathematician. Also surprising is the fact that he published only one mathematical paper in his life, ...

The Mathematical Problems of David Hilbert About Hilbert's address and his 23 mathematical problems Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics. In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century.

Stanford Encyclopedia of Philosophy A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z Russell's Paradox Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if ...

The four colour theorem Geometry and topology index History Topics Index The Four Colour Conjecture first seems to have been made by Francis Guthrie. He was a student at University College London where he studied under De Morgan. After graduating from London he studied law but by this time his brother Frederick Guthrie had become a student of De Morgan. Francis Guthrie showed his brother some ...

Biography of Edouard Lucas (1842-1891) ...

Plus Online Maths Magazine: Regular Item ...

The ultimate Knight's Tour page of Links ...

How many moves will it take to transfer n disks from the left post to the right post

A fast unique solution for the travelling salesman problem using genetic algorithms.

The Infamous Monty Hall Problem The Setup you are presented with 3 doors (A, B, C) only one of which has something valuable to you behind it (the others are bogus) you do not know what is behind any of the doors You choose a door Monty then counters by showing you what is behind one of the other doors (which is a bogus prize), and asks you if you would like to stick with the door you have, or ...

Navigation Panel: Go backward to The Tower of Hanoi Go up to Mathematically Interesting Games Go down to first subsection The Mathematics Behind the Game Switch to text-only version (no graphics) Go to University of Toronto Mathematics Network Home Page The Car and the Goats You are a contestant on a television game show. Before you are three closed doors. One of them hides a car, which you want ...

Navigation Panel: (These buttons explained below) Question Corner and Discussion Area Patterns in the Towers of Hanoi Solution Asked by Alex Doskey on May 7, 1997: I first encountered the Towers of Hanoi puzzle when I was 8 years old. With an eager mind a attacked the puzzle and quickly discovered a pattern to its solution. This recursive solution is the one described in you web page discussion ...

Welcome to Monty Hall The so-called Monty Hall Problem is an ancient net.chestnut which, every time it appears on the net ignites mega-flame wars and consumes enormous bandwidth as folks wrangle (once again) over the problem and its solution. The following is an attempt to supply an introduction to the problem (in case you haven't seen it before) and provide a reasonable and clear explanation of ...

Information about, an analysis of, and simulation of the Monty Hall Problem.

The WWW Tackles The Monty Hall Problem Discourse on the Monty Hall Problem: The following sites all pose the problem and discuss the solution and the conflict the solution has with our intuition. Monty Hall, Let's Make a Deal, Problem http://www.nadn.navy.mil/MathDept/courses/sm230/montyhal.htm The Infamous Monty Hall Problem http://www.comedia.com/Hot/monty.html Monty Hall Problem http://129.

Navigation Panel: Go up to The Tower of Hanoi Go forward to Discovering the Mathematics, Continued Switch to text-only version (no graphics) Go to University of Toronto Mathematics Network Home Page Discovering the Mathematics Behind the Game If you've played the game as well as possible, you should have discovered that the minimum number of turns it takes to win (for 1, 2, 3, and 4 disks, ...

A new approach to the Monty Hall problem Reams and reams have been written about the Monty Hall problem, but no-one seems to have mentioned a simple fact which, once realised, makes the whole thing seem intuitive. The Monty Hall show is a (possibly fictional, I'm not sure) TV gameshow. One couple have beaten all the others to the final round with their incredible skill at answering questions on ...

Simulation for the Monty Hall Dilemma ...

From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/ Education Queensland, 1997 Monty Hall Puzzle - Explanations of the Solution One interesting aspect of this puzzle is that no one explanation seems to satisfy everybody. If you want to convince an entire class of skeptical students, you will need all of the solutions below, at least. Explanation 1 - my favourite The ...

TOWER OF HANOI Please note that the material on this website is not intended to be exhaustive. This is intended as a summary and supplementary material to the required textbook. Given: 3 pegs labelled A , B, C n disks labelled 1, 2, 3, ..., N where 1 is the smallest disk and N is the largest disk Initially, all n disks are piled in peg A according to size with the smallest on top Objective: To ...