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Mathematics Articles
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The Method of Eigenfunction Expansion
Author: David Mcmahon
 Added: 03/19/2005
 Type: Tutorial
 Average visitor rating of 8/10Average visitor rating of 8/10Average visitor rating of 8/10Average visitor rating of 8/10Average visitor rating of 8/10Average visitor rating of 8/10Average visitor rating of 8/10Average visitor rating of 8/10Average visitor rating of 8/10Average visitor rating of 8/10

In this article we explore a technique used to solve partial differential equations called the method of eigenfunction expansion.
Neural networks
Author: Guest Writer
 Added: 03/05/2004
 Type: Review
 Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10

An artificial neural network, more commonly known as a neural network or neural net for short, is a mathematical model for information processing based on a connectionist approach to computation.
René Descartes
Author: Tab Stevens
 Added: 01/23/2004
 Type: Review
 Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10

We may consider Descartes as the first of the modern school of mathematics. René Descartes was born near Tours on March 31, 1596, and died at Stockholm on February 11, 1650; thus he was a contemporary of Galileo and Desargues.
Questioning the Proof
Author: Christian Ottem
 Added: 12/24/2003
 Type: Summary
 Average visitor rating of 7.7/10Average visitor rating of 7.7/10Average visitor rating of 7.7/10Average visitor rating of 7.7/10Average visitor rating of 7.7/10Average visitor rating of 7.7/10Average visitor rating of 7.7/10Average visitor rating of 7.7/10Average visitor rating of 7.7/10Average visitor rating of 7.7/10

Science has the problem of induction, we can not really know anything to be ultimately true, thus a perfect 'proof' in the mathematical sense is unattainable. Proof is however, in mathematics the essence. But what are the simliarities between the types of proof? Read on!
Introduction to Cryptology - Part 1
Author: Paul Hancock
 Added: 10/26/2003
 Type: Tutorial
 Average visitor rating of 9.6/10Average visitor rating of 9.6/10Average visitor rating of 9.6/10Average visitor rating of 9.6/10Average visitor rating of 9.6/10Average visitor rating of 9.6/10Average visitor rating of 9.6/10Average visitor rating of 9.6/10Average visitor rating of 9.6/10Average visitor rating of 9.6/10

This series of articles will introduce readers to the ancient art and science of cryptology. No high tech wizardry here, it's all simple, and dare I say fun.
Geometry in Space
Author: Sridhar Narayanan
 Added: 10/18/2003
 Type: Tutorial
 Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10Average visitor rating of 8.3/10

Geometry is how Nature displays itself to us. Geometry is the language of Nature. We have only been exposed to Geometry inside Earth. How beautiful is the Geometry of Outer Space...?
Matrix Algebra...This one's new...
Author: Sridhar Narayanan
 Added: 10/17/2003
 Type: Review
 Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10

This is a fundamental discovery on the existence of circulants. Circulants are Matrices, which have a sequence of arrangements of the elements. The article deals with a new Algebra developed on Matrices..

An Introduction to Kramer's Rule
Author: Philip Mathew
 Added: 05/10/2003
 Type: Tutorial
 Average visitor rating of 8.4/10Average visitor rating of 8.4/10Average visitor rating of 8.4/10Average visitor rating of 8.4/10Average visitor rating of 8.4/10Average visitor rating of 8.4/10Average visitor rating of 8.4/10Average visitor rating of 8.4/10Average visitor rating of 8.4/10Average visitor rating of 8.4/10

I always thought this was handy in those inevitable cases where I would have to solve n unknowns in n equations.
At Heart, I am Irrational, and Demonstrate this with Elegant Absurdity.
Author: Kelvin Corlett
 Added: 05/03/2003
 Type: Tutorial
 Average visitor rating of 8.2/10Average visitor rating of 8.2/10Average visitor rating of 8.2/10Average visitor rating of 8.2/10Average visitor rating of 8.2/10Average visitor rating of 8.2/10Average visitor rating of 8.2/10Average visitor rating of 8.2/10Average visitor rating of 8.2/10Average visitor rating of 8.2/10

Archimedes, irrationality, absurdity, and the usual smutty insinuation. Come, drink from my cyber mouth. (No lengthy introduction today, I have embedded my rambling, for your pleasure).
Proof by Induction, the Power Rule, and a Moderate Snipe at Engineers
Author: Kelvin Corlett
 Added: 05/01/2003
 Type: Tutorial
 Average visitor rating of 8.7/10Average visitor rating of 8.7/10Average visitor rating of 8.7/10Average visitor rating of 8.7/10Average visitor rating of 8.7/10Average visitor rating of 8.7/10Average visitor rating of 8.7/10Average visitor rating of 8.7/10Average visitor rating of 8.7/10Average visitor rating of 8.7/10

Hey, you! You want to be certain about the truth of mathematical statements? You better had, or I'm going to be mightily angry. Here's a brief example of how you can be (in certain cases). Note: Go straight to page 2 if you want the good stuff.
Book Review: Mathematical Techniques, an Introduction...
Author: Kelvin Corlett
 Added: 04/29/2003
 Type: Review
 Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10Average visitor rating of 9/10

Hey, you want an introduction to Mathematical Techniques? You're in luck, my friend, it just so happens that I can fix you up... Just make sure you use protection. Note: You may not want to read this if you happen to hate the rambling, self-indulgent style adopted by Dj Sneaky Whiskers in his Physicsforum book reviews. My similarity to him is almost sinister.
Linear Independence and Wronskian Determinants
Author: Philip Mathew
 Added: 03/28/2003
 Type: Tutorial
 Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10Average visitor rating of 8.9/10

Linear Algebra and Calculus: distinct from one another? Read on and find out.

An Introduction to Linear Algebra
Author: Paul Hancock
 Added: 03/26/2003
 Type: Tutorial
 Average visitor rating of 9.2/10Average visitor rating of 9.2/10Average visitor rating of 9.2/10Average visitor rating of 9.2/10Average visitor rating of 9.2/10Average visitor rating of 9.2/10Average visitor rating of 9.2/10Average visitor rating of 9.2/10Average visitor rating of 9.2/10Average visitor rating of 9.2/10

A brief introduction to linear algebra. This tutorial can be thought of as a precursor to the article "An Introduction to Eigenvalues and Eigenvectors".

Complex Numbers- The Other Side of Algebra
Author: Jennifer Barlow
 Added: 03/22/2003
 Type: Tutorial
 Average visitor rating of 6.8/10Average visitor rating of 6.8/10Average visitor rating of 6.8/10Average visitor rating of 6.8/10Average visitor rating of 6.8/10Average visitor rating of 6.8/10Average visitor rating of 6.8/10Average visitor rating of 6.8/10Average visitor rating of 6.8/10Average visitor rating of 6.8/10

We all have worked with the real number system for as long as we can remember. The set of imaginary numbers are a mystery that many of us have never explored. You can't take the square root of -81! Or can you???
The Newton-Raphson Method for the Approximation of Polynomial and Monomial Roots
Author: Philip Mathew
 Added: 03/20/2003
 Type: Tutorial
 Average visitor rating of 8.8/10Average visitor rating of 8.8/10Average visitor rating of 8.8/10Average visitor rating of 8.8/10Average visitor rating of 8.8/10Average visitor rating of 8.8/10Average visitor rating of 8.8/10Average visitor rating of 8.8/10Average visitor rating of 8.8/10Average visitor rating of 8.8/10

There are other Calculus-based methods for finding the roots of a function. Find out more in this article...
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