The Art of Complex Problem Solving. Khan Academy. Pauls Online Math Notes. Hammack Home. This book is an introduction to the standard methods of proving mathematical theorems.

It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews. Mathematical Atlas: A gateway to Mathematics. Welcome!

This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) Questions. The material is arranged in a hierarchy of disciplines, each with its own index page ("blue pages"). To reach the best page for your interests, use whichever of these navigation tools ("purple pages") you prefer: IntegralCALC. PatrickJMT. Unsolved Problems. There are many unsolved problems in mathematics.

Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture. 2. Prime Time - Mathematicians have tried in vain to this day to discover some oreder inthe sequence of prime numbers... 6174 (number) 6174 is known as Kaprekar's constant[1][2][3] after the Indian mathematician D.

R. Kaprekar. This number is notable for the following property: Take any four-digit number, using at least two different digits. (Leading zeros are allowed.)Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.Subtract the smaller number from the bigger number.Go back to step 2. Fibonacci in Nature. The Fibonacci numbers play a significant role in nature and in art and architecture.

We will first use the rectangle to lead us to some interesting applications in these areas. We will construct a set of rectangles using the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, and 34 which will lead us to a design found in nature. Wolfram MathWorld: The Web's Most Extensive Mathematics Resource. Mathematica Online Integrator.