 3Blue1Brown  Grant Sanderson
Video explanations that elucidate with computer animations, changes in perspective, humor, and — occasionally — rhyming voiceover: Euler's formula, circle division (disjoint regions obtained by joining n points around a circle), and complex
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 5 Numbers  Simon Singh and Marcus du Sautoy, BBC Radio 4
Web pages and Real Audio Music downloads of fifteen minutelong radio broadcasts that take a "quirky look" at zero, pi, the golden ratio, i, and infinity. "Hear about the stark reality behind the imaginary number, try a slice of pi, find out about the
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 Algebra for Athletes.com  Cameron Bauer
Excerpts from the Nova Science Publishers, Inc., book Algebra for Athletes: algebraic laws illustrated in a variety of sports scenarios; exponents and weight room mechanics; linear equations and speed; vectors and golf; quadratic equations and parabolas;
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 Appetizers and Lessons for Math and Reason  Alan Selby
Logic Appetizers to test or or improve reading, writing and thinking skills, with definitions, concepts and proofs in many subjects (Chains of Reason; One or TwoWay Implications; Islands & Divisions of Knowledge; Deception); Advice (How to Study
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 Applications of Imaginary Numbers in the Real World  Bradley Chung
An exploration of typical questions about imaginary numbers, such as "Can you show me examples of imaginary numbers in the real world?" and "Are there any practical applications of imaginary numbers?" Lessons include "Mapping Imaginary to Physical"; "Complex
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 The Art of Calculating Real 2D Vectors  Hero van Jindelt
Freeware: Print the text for pupils. Numerical 2Dcalculator. We don't need
words like imaginary, complex number, or Argand Diagram any moresave them
for a history lesson. Ordinary vectorcalculation with a "new" (centuriesold) multiplication,
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 Basic Ideas in Greek Mathematics  Michael Fowler; University of Virginia
Lecture notes from a course entitled "Galileo and Einstein." Nailing down the square root of 2. Zeno's paradoxes: Achilles and the tortoise. Proving an arrow can never move  analyzing motion, the beginning of calculus. How Archimedes calculated Pi to
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 The Basics of MRI  Joseph P. Hornak; Rochester Institute of Technology
An introduction to magnetic resonance imagining, which is based on the principles of nuclear magnetic resonance (NMR), a spectroscopic technique used by scientists to obtain microscopic chemical and physical information about molecules. See, in particular,
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 Bytes of Science: An Internet Magazine  David S. Mazel, Ed.
An Internet magazine on science and engineering, with tutorials and introductory articles on various areas of science, math, or engineering. Articles include: A Basis for Functions: The Fourier Series; The Fourier Transform: The Frequency in a Waveform;
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 Calc 3D
Calculators for Windows 95/98/NT/XP designed to handle vectors, matrices, complex numbers, quaternions and coordinates. For point, line, plane, sphere, circle Calc 3D calculates distances, intersections, and some additional
information like volume and
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 Calc3D  Andreas Greuer
Calc 3D is a free program for calculating 3dimensional vectors, matrices and
complex numbers with Windows 95/98/NT. Cartesian coordinates, spherical coordinates und cylindrical coordinates can be transformed into each other.
Distances, intersections,
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 Calculators OnLine Center: Part II  Mathematics  Martindale's Reference Desk
Over 7,420 calculators for: Unit Conversion (Time, Distance, Length, Speed, Weight, etc.); Abacus; Basic Math; Complex Mathematics; Complex Math Education; Complex Math Calculators by Specialty: Algebra and Linear Algebra; Algorithms; Calculus; Central
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 College Math Prep for High School Students  C. J. Kentler and V. S. Manoranjan, Washington State University
Selfscoring problems, new with every click, to gauge a student's preparedness for college level math: operations, solving for a variable, solving linear equations, word problems, solving absolute value equations, solving inequalities, distance between
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 Complex Numbers  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A series of articles on the algebraic structure of complex numbers and their application to solving various problems in algebra and geometry. Several of the discussed features, for example, real and complex products, are drawn from very recent literature
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 Complex Numbers (Manipula Math)  International Education Software (IES)
Java applets to investigate complex numbers, their reciprocals, powers, and other selected functions. (One function leads to a fractal.)
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 Complex Numbers & Trig  Alan Selby
Complex Numbers and the Distributive Law for Complex Numbers, offering a short way to reach and explain trigonometry, the Pythagorean theorem, trig formulas for dot and crossproducts, the cosine law, and a converse to the Pythagorean theorem. A geometric
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 Complex number to a complex power may be real  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A proof using Euler's formula.
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 Complex Variables (S.O.S. Mathematics)  Dept. of Mathematical Sciences, Univ. of Texas at El Paso
An online course: learning units presented in worksheet format review the most important results, techniques and formulas in college and precollege complex variables. Complex Numbers: Basic Definitions and Arithmetic, The Complex Plane, The Polar Form
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 Conception of the Good  Naveen Rizvi
"Insights into our current education system" by a UK classroom teacher. Rizvi, a selfdescribed "believer in teaching via direct instruction," blogs to "share ideas and model how I have implemented these ideas and then discuss the impact of the number
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 De Moivre's Theorem  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about de Moivre's theorem, including its usefulness and proofs.
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 Doug's Home Page  Douglas J. Ingalls
Includes mathematical interests such as images of fractal applications of Newton's Method and Gibb's Phenomena, with related programs in FORTRAN and BASIC, a discussion of the apparent depth problem in optics, and how multiple decisions can be reduced
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 Extreme Optimization: Numerical Linear Algebra Library for C# and VB.NET  Jeffrey Sax, Extreme Optimization
Objectoriented classes for linear algebra and a broad range of numerical techniques for the Microsoft .NET framework. Topics covered: solving equations, mathematical curves, approximation, numerical integration and differentiation, complex numbers.
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 Fractal Explorer Kit  Tom Harrington
Java applets show fractals based on the Mandelbrot Set, the Julia Set, and Newton's method. Pictures grow more detailed in a series of iterations; zoom in to see a closeup of the center. A brief FAQ explains the methods behind these different types
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 Fundamental Theorem of Algebra  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Some of the history of complex numbers, perfect numbers, irrational numbers, imaginary numbers, and the first proof of the Fundamental Theorem of Algebra (statement and significance), given by Carl Friedrich Gauss (17771855) in his Ph.D. Thesis (1799).
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 The FUNKtion  Appreciating Math through Art  ThinkQuest 1996
How to do really hard graphic stuff. Tilings, Fractals, Sierpinski Gaskets, animations, pictures, links. Math "crash courses" on Complex Numbers; Magnitude and the Pythagorean Theorum; Functions; and 3D.
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 Gateways to Advanced Mathematical Thinking (GAMT)  Michelle Manes; Education Development Center, Inc. (EDC)
The goal of this project is to research the ways in which high school and college mathematics students come to acquire flexible understandings of essential concepts needed for analytic and algebraic thinking. Integral to this research effort is the development
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 The house of Mathematics software  Akihiro Akitsu
Math '98 for Windows, free software to download. Topics include the Mandelbrot set; Complex numbers; Dragon curve; Tree curve; Koch curve; Peano curve; Pascal's triangle; and the Sierpinski gasket. In English and Japanese.
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 Imaginary Exponents and Euler's Equation  Math Forum, Ask Dr. Math FAQ
What does it mean to have an imaginary exponent? Two different proofs, a consequence, and an application of Euler's Equation.
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 Imaginary Numbers in Real Life  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about imaginary numbers in real life, such as where imaginary numbers are used today in real life and who uses them.
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 Interactive Mathematics  Murray Bourne, Ngee Ann Polytechnic, Singapore
Flash Tutorials for PreCalculus (Algebra, Trigonometry, Logarithms, Complex Number Systems, Graphs); Calculus (Differentiation  The Derivative, its Applications, Deriving Transcendental Functions; Integration, its Applications and Methods), and Advanced
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 Introduction to the Mandelbrot Set  David Dewey
Images of the Mandelbrot set, with information on complex numbers and on graphing Mandelbrot sets.
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 Java Fractals  James Henstridge
Java applets to draw different kinds of fractals: Iterated Function Systems (Sierpinski Triangle, fern, etc.), complex number fractals, and orbit fractals. Includes explanations of the algorithms used, and code for each applet.
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 Making Order Out of Chaos  Andrew Davenport, Shane Kraynak, and Brian Timko  ThinkQuest 97
An introduction to chaos and fractals: history, theory, and a gallery of fractal images. Includes a review of complex numbers and a Java applet to investigate sensitive dependence on initial conditions.
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 Manipula Math with Java  International Education Software (IES)
Hundreds of interactive Java applets for middle school through early college years on subjects such as geometry, calculus, trigonometry, linear transformations, vectors, complex numbers, and conics. Applets and animations often include introductions to
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 Maple Application Center  Waterloo Maple, Inc.
Software you can order to explore, share, and publish math on the Internet. Interactive media for exploring and exchanging mathematical ideas, with content on a variety of subjects at the high school, university, and graduate level. (There are high school
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 MATHabundance  Johan Claeys
An uppersecondary math tutorial, with topics in order, each building on the previous topic. Includes solved and unsolved problems and links to other tutorials, problems, and math sites.
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 Mathematics Curriculum Notes  Alan Selby
A model for mathematics instruction from primary school to college. The first part describes Pattern Based Reason, its origins, benefits and limitations in many subjects. In mathematics education there are two barriers to comprehension to be lowered or
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 Mathematics  John Savard
A collection of essays and illustrations: pentagonal tilings, infinity (Cantor's theory of transfinite numbers), rotations of the dodecahedron, Archimedean solids, the fourth dimension (regular polytopes), Gödel's proof and the halting problem, and
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 Math Explorers' Club  Cornell Department of Mathematics
Selfcontained modules of activities and other materials for middle and high school teachers to give their students experience with more advanced topics in mathematics, such as combinatorics and cryptology, graph theory, probability and applications,
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 Math for Morons Like Us  ThinkQuest 1998
Students talk to students about math: a site designed to help you understand math concepts better. Tutorials, sample problems, and quizzes for PreAlgebra, Algebra, Geometry, Algebra II, and PreCalc/Calculus, designed assuming you know some of the basic
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 Mathématique du secondaire  Xavier Hubaut, l'Université Libre de Bruxelles
A collection of lessons for advanced high school students. Includes: linear algebra, geometric concepts, complex numbers, polyhedrons, and applications. In French.
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 Math Motivation  Michael Sakowski
Answers to the question "Where will I ever use algebra?" Examples of how "the process of learning higher mathematics provides valuable skills in deductive reasoning and symbolic reasoning, in addition to math skills used directly in science and engineering
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 Math Quiz
Hundreds of free tests suitable offering instant feedback to prepare students for GCSE and ALevel examinations. Register to see more than five questions per test and access your profile, which tracks your past assessments; purchase to see a full solution
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 The Medians  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Interactive proofs (elementary geometry, barycentric coordinates, complex numbers, Ceva's theorem, affine geometry) of the fact that the three medians of a triangle meet at a point called the centroid. See also The medians, contributed by Scott Brodie.
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 Morley's Pursuit of Incidence  Cut the Knot!, Alexander Bogomolny
With all the geometric context of his theory (applets are provided for explorations), Morley's method is purely algebraic, founded on the theory of complex numbers. Curves are mappings x = f(t) from the unit circle. x = X + iY, where X and Y are the plane
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 National Centre for Excellence in Mathematics and Science Teaching and Learning  University of Limerick
Ireland's NCEMSTL researches, coordinates, supports, develops and implements programmes to enhance Irish science and mathematics teaching and learning at all levels. Read Centre publications and reports; learn about its courses and other events. Register
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 Newton Basins  David Joyce; Dept. of Mathematics & Computer Science, Clark University
Newton's method for finding solutions to equations leads to some fantastic images when applied to complex functions. This program colors the complex plane according to where an initial guess will eventually take you, and gives each solution a different
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 Online Math Center  Whatcom Community College, Bellingham, WA
Resources for mathematics students and teachers, including answers to Frequently Asked Questions and online Live Math applications demonstrating algebra, calculus, and linear algebra topics.
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 OpsResearch  DRA Systems
A collection of Java classes for developing operations research programs and other mathematical applications. The site includes documentation and tutorials, and software download is free. Also features a bookstore and related links.
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 Paul's Online Math Notes and Tutorials  Paul Dawkins, Lamar University
Online notes and tutorials on algebra, calculus, and differential equations. Also, PDFs, some reduced to fit onto one printed page, offering a review of algebra and trigonometry, a primer of complex numbers, listing common math errors, suggesting how
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