Computational Science Resources
Unit 2.3.2: Topic Research (Mathematics)

Summary
This page has links to professional mathematical organizations; project ideas; and sections on algorithms, chaos, cryptography, geometry and statistics. There are also links to other links.


Professional Organizations

American Mathematical Society
The AMS was founded in 1888 to further mathematical research and scholarship. The Society has approximately 30,000 members throughout the United States and around the world. On this E-math site, you will find articles, news and other links.

Mathematical Association of America
MAA is the world's largest organization devoted to the interests of collegiate mathematics. MAA Online has news and features, journals, columns and links.

National Council of Teachers of Mathematics
NCTM is dedicated to improving the teaching and learning of mathematics. On this site, you will find things of interest to math education: standards, links, and discussions.


Project ideas

21st Century Problem Solving
This site offers a variety of math problems over a wide range of ability levels.

MathSoft
MathSoft is a company that produces the mathematical software Mathcad. There are many on-line pages that have project ideas, including Unsolved Math problems, The Puzzle Page, and Math in Action.

This is Mega Mathematics!
Project ideas include topics in cartography, geometry and paradoxes (complete with resources).

Fun With Numbers
Fun? Numbers? Me?? This page has a number of mathematical and computational puzzles including factorials and primes.


Algorithms

History of the Monte Carlo Method
The Monte Carlo method provides approximate solutions to a variety of mathematical problems by performing statistical sampling experiments on a computer.

The Pi Page
More algorithms than you can imagine to find the value of pi.

Eric's Treasure Trove of Life
It's hard to know if the game of Life should be classified as math or biology. You decide.


Chaos and fractals

The Non-linear Lab
An excellent introduction to non-linear dynamical systems and questions related to chaotic behavior. Available in Spanish, too.

In a World of Order, Chaos Reigns
Devoted to the Chaos Theory, this colorful page offers information on the theory's history, real life examples, a glossary of chaos terminology, diagrams, fractals... all the CHAOS you could want.

Chaos Theory
A great explanation of chaos theory. Definitely check out the "Brief Intro" which is understandable with examples and history. Another paper, "Fractional Dementia" is also included.

Mandelbrot and Julia Set Explorer
Enter your parameters and create fractals on-line.


Cryptography

A-Z Cryptography This site has information about everything in cryptology, many links to more resources, and many examples.

Beginner's Guide to Cryptography
This site starts at the very beginning with examples, history and uses.

CryptoWeb
This site features an introduction to cryptography, reviewed links and current news.

ISAAC: a fast cryptographic random number generator
Contains good internal pointers to hash functions and block ciphers.


Geometry and Topology

The Geometry Center
"The Geometry Center Web at a Glance" will help you to navigate this site, which details the work of the Geometry Center, a National Science Foundation Center at the University of Minnesota. You'll find interactive Web and Java applications, geometry reference archives, software, video, and teaching materials.

Geometric and Surface Modeling
This page demonstrates Java graphics, and has tutorials on geometric modeling -- the fundamentals of computer graphics and computer aided design. There are also some practical applications.

The KnotPlot Site
Here you will find a collection of knots and links, viewed from a mathematical perspective. Has images created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions.

A Gallery of Interactive On-Line Geometry
This on-line site allows you to draw geometric shapes right on your screen.

Virtual Reality Polyhedra
A collection of over 1000 virtual reality polyhedra for you to explore.


Statistics

Basic Principles in Statistical Analysis
A textbook on statistical methods.

InStat Guide to Choosing and Interpreting Statistical Tests
InStat is a commercial software company, and has produced this 154 page textbook on statistical analysis.

Statistical Inference on the TI-82/83
Tutorials on using a graphing calculator for statistical analysis, including distributions, confidence intervals and hypothesis tests. Also has several projects.

AP Statistics
This page is primarily devoted to statistics on a TI-83 graphing calculator, but you will find a textbook and projects here.

The Prob and Stat Page
A collection of resources that includes news, links, topics and more.

WWW Resources for Teaching Statistics
This unassuming page contains a wealth links to on-line statistical resources (courses, algorithms, etc).


References and links

The CRC Concise Encyclopedia of Mathematics
Yikes!! Zillions of entries. You can find information by keyword or by browsing alphabetically.

Fibonacci Numbers and the Golden Section
Has explanations and problems based on these regularities in nature.

Artificial Intelligence
Artificial Intelligence (AI) is the area of computer science focusing on creating machines that can engage on behaviors that humans consider intelligent. This pages serves as a comprehensive introduction to the subject.

The Prime Page
Way more than you ever wanted to know about prime numbers: history, algorithms, software and discussions.

History of Mathematics
The title pretty much explains it all. You can find information by subject, region, or timeline. Site also includes reference to related online and print resources.

Ask Dr. Math
Dr. Math has a list of math questions and their answers. If you can't find an answer here, submit your question.

The Math Forum
This extensive site has news, categorized links, ideas, and much more.

S.O.S. Mathematics
A very helpful page--with tutorials--on subjects that include Algebra, complex variables, trigonometry and calculus.

GraphPad Software
There are some nice links on this page to specific topics: radioactive decay, statistical analysis and biostatistics.

Math Virtual Library
Florida State University's list of links, categorized by field (numerical analysis, statistics, topology, etc).

Martindale's: Mathematics
Every link in the universe--by topic, location, you name it. Don't get too lost.

Yahoo: Mathematics
More links