Anthony Beckwith's Website - Advanced Topics in Math Course (covers topology, knot theory, chaos theory, barcodes, number theory, and other interesting topics)

Ask Dr. Math - Ask Dr. Math is a question and answer service for math students and their teachers. A searchable archive is available by level and topic, as well as summaries of Frequently Asked Questions (the Dr. Math FAQ).
Calculus Help - A professor in the Department of Mathematics at the University of Hawaii, authored these notes to help students learn how to use, not just understand, the concepts of calculus. A total of fifteen topics are covered and include max-min problems, exponential growth, and the derivation of Kepler's second law.

eCYBERMISSION is a web-based science, math and technology competition that allows students in grades six through nine to compete for regional and national awards, while working to solve problems in their community.  The competition encourages and rewards students from a diverse range of proficiency levels, interests and backgrounds. 
Flash Cards for Kids - This is an interactive flash card site. You can choose among addition, subtraction, multiplication, and division; simple or complicated problems; and how many digits the numbers will have. While this isn't exactly high school material, it's a nice site, so we're including it anyway. Enjoy, and show it to your kid sister or brother!

InvenTeams - High School Invention Grants
Graphics for the Calculus Classroom - This is a collection of graphical demonstrations developed for first year calculus, but suitable and interesting for high school students as well. From Douglas Arnold at Penn State.
Lessons and Appetizers for Math and Reason - Several puzzles and short discussions to help students understand algebra and proofs. If you don't like the first one you look at, try another; they're all quite different. From books by Alan Selby.
Math.com - Students can find free homework help and lessons. Teachers can find lesson plans and classroom resources. Tons of free math reference materials. From elementary and everyday math to algebra and beyond.
Math Goodies - A site featuring interactive math lessons. It also contains chat boards that can be used to help with homework and other areas.
The Math Forum - helps students learn mathematics through the use of the Internet and innovative technologies. It also gives advanced students an opportunity to pursue their interests as well as use their skills to help others.
Math Help (From The Math Leaque) - This is a help resource for 4th through 8th grades. It contains help on whole numbers, decimals, data statistics, fractions, geometry, ratio proportion, percentages, integers, metric units measurements, intro to algebra, and positive negative numbers, all in an easy to follow format (with examples).
Math Homework Help - A collection of links to sites that provide help with math homework, mostly by email.

Math is Fun - Math concepts explained in easy language, plus puzzles and games and worksheets
MathMagic - Math problem challenges on the net. Enjoy the challenges on your own, or register to submit your answers along with other participants.
MegaMath - An absolutely wonderful collection of creative and imaginative ideas, exercises, and fun things to do. For all ages. From the Computer Research and Applications Group at Los Alamos National Laboratory.

Math and Reading Help for Kids! - Only the very best  educational resources available for children of all ages, skill levels, and geographic locations.

Mathematics Archives: K-12 Teaching Materials - An excellent list of sites that contain significant collections of materials which can be used in the teaching of mathematics at the K-12 level. This is the K-12 section of Mathematics Archives WWW Server, which primarily contains links to materials for mathematics educators at the community college, college and university level.
Mathematics Experiences Through Image Processing (METIP) - The goal of the METIP project is to use digital image processing to motivate students to stay interested in mathematics
Maths Online - A project based at the University of Vienna, Austria, and is running since March 1998. Its goal is the construction of a modern mathematics learning site on the web. It has a large variety of interactive math tutorial applets which are interesting. 
Math Projects Journal - A bimonthly electronic publication offering tips and lesson plans for interactive math projects, discussions of relevant topics, and contributions from teachers around the country.
Math Puzzles - A mixed bag of interactive math puzzles and philosophy. Many of these require Java and/or JavaScript.
Miscellaneous Math Utilities - The site includes utilities for solving N Equations in N Unknowns, Eigenvalues and Eigenvectors, Kepler's Equation, Optimization, Root-finding, Numerical Integration, and more.
Nick's Mathematical Puzzles - A collection of puzzles ranging over geometry, probability, number theory, algebra, calculus, and logic. Hints are provided (wherever possible), along with answers, fully worked solutions, and links to relevant mathematical topics. Many of the puzzles are elementary in their statement, yet quite challenging. New puzzles are added on a regular basis.
Numeroscope - The Numeroscope is a multi-media, interactive laboratory for exploring the the number systems which form the basis for today's cryptography, Along the way, we will use the exploration ofthese somewhat exotic number systems to illuminate the meaning of familiar algebraic operations (like +, -, ?, ÷, Log).
Probability Tutorials - This is a full advanced class in probability. It covers measure theory, lebesgue integration and probability.
Puzzles with Polyhedra and Numbers - At this site one can print copies of polyhedron puzzles and read several mathematical articles on the subject.
Step by Step Integrals and Derivatives - Calc101 does derivatives and integrals with each step explained, automatically, in seconds.
Visual Math For Java - A graphing calculator and equation solver. You can specify a function, plot it, solve it, and more. (Requires Java).
WebMath - Tutorials and games for all levels of math. It has everything from simple adding to calculus.
Zona Land - In Zona Land you will find educational and entertaining items pertaining to physics, to the mathematical sciences, and to mathematics in general. This site is heavily loaded with Java, VRML and JavaScript so be prepared!
The Institute for Mathematics and Computer Science - IMACS is a research and teaching institute based in South Florida. Through its distance learning division, IMACS offers a series of high quality interactive mathematics courses (not free however) designed for talented secondary school students.
Calculus-Help.com - This website, founded in 1998, began as a resource for high school calculus students who needed additional practice and detailed solutions to the types of problem they saw everyday in class but had trouble understanding
The Fifth Arithmetical Operation - web page on new arithmetical methods for roots solving, new generalized continued fractions and many other new concepts
Purplemath - Your Algebra Resource.

 

Geometry
Non-Euclidean Geometry - Description of non-Euclidean geometry, along with a software package, NonEuclid, an interactive simulation of the Poincare Model of Hyperbolic Geometry.
The Diamond 16 Puzzle - Online puzzle illustrating principles of symmetry and permutation groups in geometry.

The Fine Structure Constant - The question of how to calculate the numerical value of the fine structure constant from theory was one of the most outstandingly difficult problems in mathematical physics for the greater part of the 20th century.

Geometry Step by Step from the Land of the Incas - This interactive web site uses a variety of techniques to introduce geometry to the user. Mathematics, music, visual displays, quizzes, puzzles, science, history, and geography are integrated in this web site. A very visual and engaging site which brings geometry to life.

Fractals
A Fractals Lesson - Draw your own fractal patterns, and more. This is intended for younger students, but I think that high school students would enjoy it, too.
INTERFACE Project - Dedicated to explaining and demonstrating the science behind chaos theory and fractal images. This site has lessons, games, activities, demonstrations and software, all related to fractals and chaos. The site caters for all - even if you know nothing about fractals and chaos.
Mandelbrot Explorer - An interactive web page to let you investigate the Mandelbrot set by zooming and setting the drawing area.

 

History of Mathematics
Biographies of Women Mathematicians
History of Mathematics Archive - Lots of information, including the biographies of more than 1000 mathematicians. From the University of St Andrews in Scotland.

 

Tables, Constants, and Definitions
Math Tables - A collection of mathematical tables, theorems, and proofs, covering algebra to advanced calculus.
Online Mathematics Dictionary
Statistics for Everyone - Excellent explanation of basic terms in statistics, including mean, median, percent change, and per capita.

Funny, Irrational Pages about Pi and Other Numbers
The Uselessness of Pi - There's something about pi that makes people really bizarre in a lovely sort of a way.
The Pi Page - Serious and silly information about pi.
Fun With Numbers - Who said numbers and "the first n digits" can't be funny?

Favorite Mathematical Constants - Archimedes' Constant, pi,  The Golden Mean, The Natural Logarithmic Base, e. Most of the rest of what's here is even more advanced.

 

Mathematics Software
This list of math software is growing very rapidly. Please let us know if you find that these descriptions are no longer applicable, or if software is under the wrong heading (free/commercial). Thanks.

 

Free Software (listed alphabetically)
Click-n - Click-n is a visual way to do calculations, design work and programming. You click on the operations such as sin, cos, and square root to put them together. It runs on Windows, and is distributed for free.
MathPad Graphing Scientific Calculator - MathPad is a general purpose graphing scientific calculator. It uses text input which allows you to see and edit your entire calculation. It runs on a Macintosh and is distributed for free. Developed by Mark Widholm at the University of New Hampshire.
NuCALC - The Graphing Calculator for Windows features powerful symbolic and numeric methods for visualizing two and three dimensional mathematical objects. NuCalc is a tool for quickly visualizing math. You type an equation and NuCalc draws it for you without complicated dialogs or commands. Offers a free demo!
Guide to Available Mathematical Software - A comprehensive list of math and statistics software packages. This is not specifically geared to secondary schools. SolvOpt - For use with MATLAB. The program SolvOpt (Solver for local optimization problems) handles minimization/maximization of nonlinear, possibly non-smooth objective functions. SolvOpt was written by Dr. Alexei Kuntsevich and Professor Franz Kappel, from the Institute for Mathematics, University of Graz in Austria.
StarLogo - A programmable modeling environment for exploring the behaviors of decentralized systems, such as bird flocks, traffic jams, and ant colonies. The software runs on a Macintosh, and is designed especially for use by students.

Commercial Software (listed alphabetically)
Boxer Learning, Inc. - Interactive, self-paced, instructional software. Topics include algebra and trigonometry.
Cognitive Technologies Corporation Software - Math software for middle and high school. Topics include pre-algebra and trigonometry. For Windows and Macintosh.
Geometry Expressions - the world's first Interactive Symbolic Geometry System, and the missing link between Geometry and Algebra software

Howe-Two Software - A large collection of software that helps with learning many topics including Pre-Algebra, Algebra, Geometry and more.
GrafEq Software - GrafEq is an easy-to-use program for graphing equations encountered in the secondary pre-calculus mathematics curriculum: linear, polynomial, conics, trigonometric, exponential, absolute value, and so on. GrafEq is available for Windows and the Mac; a demo version may be downloaded for free.
Maple Software - Waterloo Maple Software includes products for symbolic, numeric, and algebraic calculations. It also includes 2-D and 3-D graphing and plotting tools. Two of their products are Maple V and Theorist/MathPlus.
Math Applets -  This site contains two applets for learning math. One applet, IntegerZone, teaches about arithmetic and number theory using a number grid. The other applet, TenBlocks, turns the times table into a series of simple puzzles.
Mathematica - Mathematica is a software system for numerical, symbolic, and graphical computations and visualization. It includes an interactive calculation tool and versatile programming language, and is available for over 20 computer platforms. The company offers special products specifically aimed for the high school level. Also check out The Integrator, which runs interactively using Mathematica 3.0 to perform integrals for anyone with a web browser. By simply typing in any integral or choosing a random sample, The Integrator sends a Mathematica Link message to a Mathematica kernel, which then does the integral using its built-in Integrate function. The result is sent back within seconds to the Integrator Web Page for you to see.

MathSoft - MathSoft offers a full range of calculation software tools for students and educators. StudyWorks serves the high school and general studies college market, while Mathcad, S-PLUS, and Axum are geared to college level technical students, researchers, and educators.
MathWorks Home Page - The MathWorks is the company that produces MATLAB, a popular scientific and engineering software tool. MATLAB is a technical computing environment for high-performance numeric computation and visualization. MATLAB integrates numerical analysis, matrix computation, signal processing, and graphics in an easy-to-use environment.
SureMath - Problem solving and graphing software for students and educators. Topics cover a wide range, including algebra, trigonometry, and calculus. SureMath is available for the Macintosh. There is a teacher's edition and a personal edition.

 

Last updated 3/29/07