 Function Basics  David Eger; Interactive Mathematics Online (IMO)
Functions are mathematical ideas that take one or more variables and produce a variable. In an abstract mathematical sense, a function is a mapping of some domain onto some range. For each item in the domain, there is a corresponding item in the range
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 Functions of a Complex Variable  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to complex variables, studying the effect of assuming differentiability of functions defined on complex
numbers. The effect is markedly different than for real functions; these functions are much more
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 Function Squashing  David Eger; Interactive Mathematics Online (IMO)
Exploring things you can do with periodic functions like sine and cosine; translation, and vertical and horizontal scaling.
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 Functor  Jordan Touzsouzov  Mordred
Math software for the graphical analysis and display of one and twoargument functions z = f(x, y), using OpenGL. A beta version is available for Win95/98 and WinNT.
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 Fundamentals of Geometry  Oleg A. Belyaev
A work in progress to create a free online book on geometryfrom exposition of elementary absolute geometry based on Hilbert's axioms to more advanced topics. The site contains a current draft of the book. This text is also intended to provide math background
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 The Fundamental Theorem of Algebra  B. Fine, Fairfield Univ., CT; G. Rosenberger, Univ. of Dortmund, Germany
The Fundamental Theorem of Algebra states that any complex polynomial must have a complex root. This basic result, whose first accepted proof was given by Gauss, lies at the intersection of the theory of numbers and the theory of equations, and arises
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 The Fundamental Theorem of Algebra  MacTutor Math History Archives
Linked essay covering from Cardan in the 1500's to the Euler and Argand proofs through the 1800's, with 8 references (books/articles).
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 The Fundamental Theorem of Projective Geometry  Maska Law; Dept. of Mathematics, University of Western Australia
A brief definition of projective geometry, by the author of an honours dissertation covering ideas from the areas of projective geometry and group theory.
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 Funforms: a New Math Learning System  Joel S. Steinberg
An abacus or sliderulelike notation system, essentially binary (though a trinary system also exists). The web site includes a description of how to use it, and suggests that it might be taught to preschoolers as a game, or used to teach math concepts
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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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 Fun, Puzzles, Travel  Paul Bourke
Brain twisters, arranged by approximate level, and designed for the most part to require no particularly advanced mathematical skills. Illusions include impossible triangle, MullerLyer, bad box, and Colours.
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 Fun with Cellular Automata  Mathilde Rufenacht
Java applets such as "pattern calculators" for exploring onedimensional cellular automata, Conway's game of life, and the skins and furs of animals. Also, use the site to run your own screen savers.
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 Fun with Fractals  Keith Gabryelski
Click in the fractal image to select the area of the fractal you would like to examine; select a location and style for the fractal image by modifing the values in the form.
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 Fun With Num3ers
A blog of mathematical puzzles, mostly in number theory. Posts, which date back to January, 2012, have included "Using digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 only once (Part Two)," "Pythagorean triple – Digits Reversed," "Concatenation puzzle: when (A 
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 Furman University Wylie Mathematics Tournament  Furman University, Greenville, South Carolina
A page with links to annual Furman University mathematics tournament exams for 19961999, and to postscript or PDF files of Senior and Junior Written Problems, with answer sheets. The date of the 2000 Furman University Wylie Mathematics Tournament is
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 Futility Closet  Greg Ross
"An idler's miscellany of compendious amusements." Math posts, which date back to January, 2005, have included puzzles, curios, and trivia from the lives of famous mathematicians  all "selfcontained and written as concisely as possible"  such as
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 Future of Leap Seconds  Steve Allen
Allen, an astronomer, discusses leap years, leap seconds  and how to avoid their use when redefining Coordinated Universal Time (UTC): three pictures that show the situation; elapsed time (JavaScript that shows POSIX's inability to provide an interface
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 Fuzzy Logic  Quadralay Corporation
A departure from classical twovalued sets and logic, Fuzzy Logic uses "soft" linguistic (e.g. large, hot, tall) system variables and a continuous range of truth values in the interval [0,1], rather than strict binary (True or False) decisions and assignments.
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 Fuzzy sets for Ada  Dmitry A. Kazakov
A free (GPL) implementation of fuzzy sets, intuitionistic fuzzy sets, fuzzy
numbers, linguistic variables and sets of linguistic variables.
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 fxsolver  Equanalysis UG
Free equation solver with a formula database for quick calculations on tables and data input "without messing around with programming languages or spreadsheet software." Browse the hundreds of math formulas, then click the gray "Add to Solver" button
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 g3d 3Dimensional Graphing Applet  Eugene Agichtein
Currently available functions: sin, cos, tan, acos, asin, atan arguments in radians; Hyperbolic Functions  sinc, ctan, actan; sqrt, sqr, exp, log, ln. Operators: +, , /, *, ^ . Graphs are highlighted in red to show contours, and can be rotated by dragging
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 GalaxyGoo
An interdisciplinary, volunteer thinktank dedicated to exploring expressions of science and math with online technologies, for public benefit. Read interviews of scientists; explore math such as the sine curve with Flash, participate in forums and blogs,
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 The Galileoscope™  International Year of Astronomy
Highquality, lowcost, easytoassemble telescope kits developed for the International Year of Astronomy (2009) in celebration of "... the celestial wonders that Galileo Galilei first glimpsed 400 years ago and that still delight stargazers today. These
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 Gallery of Data Visualization  Michael Friendly, York University
Examples of the best and worst of statistical graphics, from what is arguably the best statistical graphic ever drawn, to the current recordholder for the worst.
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 Gallery of Fluid Mechanics  M. S. Cramer
An image/movie gallery illustrating a wide variety of phenomena, including aurora, vortices, supersonic flow, supersonic cars, water drops, water waves, and shock waves. Accompanying each image or movie is a brief physical explanation. Students and teachers
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 Gallery of Interactive OnLine Geometry  The Geometry Center
Twelve interactive online geometry programs: WebPisces (compute implicitly defined curves in the plane); Build a Rainbow (a lab that examines a mathematical model of light passing through a water droplet); QuasiTiler (generate Penrose tilings or design
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 Gallery of Mathematical Images  Dept. of Mathematical Sciences, Loughborough University, UK
The Mandelbrot Set (frames from an animation); Quaternionic Fractals (an extension of the complex numbers  Mandelbrot and Julia sets); Hyperspace (4dimensional structures projected into 3dimensional space); Molecular Dynamics (images from simulations,
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 Gallery of Mathematical Models  Arthur Sherman
"Gold standard" versions of published models, given as input files for xpp but also humanreadable ASCII files adaptable for use with other programs. BetaCell Models: Generic, CRAC Models I and II, SmolenKeizer, KeizerSmolen, ShermanKeizerRinzel
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 Gallery of Pseudospheres  Robert McLachlan
A short version of an article by Robert McLachlan, "A gallery of constantnegativecurvature surfaces," (Mathematical Intelligencer, Fall 1994, 3137) about "pseudospherical" surfaces, equally "saddleshaped" at each point, extensively studied in the
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 Gallica  Bibliothèque nationale de France
Une sélection de documents numérisés qui montrent la diversité des collections manuscrites de la Bibliothèque nationale de France: les oeuvres de Joseph Liouville, Augustin Cauchy, Joseph Fourier, Henri Poincaré, Janos
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 Galois Field Package for Mathematica  Ryoh FujiHara; University of Tsukuba
An explanation of the concept and design of the Galois field package. Start Up and Declarations; Variables; Mixed operations with integers or constants of the base field; Implemented functions; How to get the Package and its Manual.
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 The Galois Story  Ivars Peterson (MathTrek)
The life and death, myth and reality, of Evariste Galois, with a short bibliography.
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 Gambit  Theodore Turocy, Director
An opensource collection of tools for doing computation in game theory. Gambit lets you build, analyze, and explore game models.
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 Gamelan  The Official Java Directory  EarthWeb, Inc.
Gamelan's primary mission is to serve as a central registry and directory of Java resources. Much like Yahoo!, Gamelan collects links to resources stored on other sites across the Web. However, unlike Yahoo!, Gamelan's mission is specific  Gamelan collects
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 The Game of Chaos  Juergen Giesen
This applet performs the following game at varying speeds: Choose a random starting point (o) within the triangle ABC. Roll a die. Connect the point with point A, when you roll 1 or 2; with point B, when you roll 3 or 4; with point C, when you roll 5
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 The Game of Go  JeanClaude Chetrit
A page for Go players interested in mathematics or abstract reasoning. How many static positions exist and how many are legal? This is purely an exercise in counting (combinatorics). See also Chetrit's conjectures about playing Go on a 2 by 2 board and
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 The Game of Life: (Serendip: Complex Systems)  Bryn Mawr College
Order without a planner: play a Java game about a world consisting of locations that may or may not be occupied by life. At each step, life persists in any location where it is also present in two or three of the eight neighboring locations, and otherwise
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 The Game of Nim Explained  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A Java simulation of the famous game, with a theoretical explanation and extension to other similar games: see also similar Java games: Nimble, Northcott's game, Plainim, the Scoring game, and Turning Turtles.
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 gamepuzzles: for the joy of thinking  Kadon Enterprises, Inc.
Board games and the like: Combinatorial puzzles, tessellations, math manipulatives for all grades. Handson sets and some online exemplars of polyominoes, polyforms, color tilings. Source for classics like Archimedes' Square (Stomachion), Penrose tiles,
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 Games: Analysis and Simulation  Dave Rusin; The Mathematical Atlas
Pointers to games on Rusin's site, including analyses, posts from usenet, PC executable versions, source codes, and documents with descriptions of some of the games, with rules. Also pointers to general information on games on the Web.
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 Games Conceived  Leroy Quet
Quet's blog, begun in September, 2008, describes his "simple games," which include Triangle Grid Of Coprimality; LineSegments In Circle; Turn It Around  Multiply/Add Grid; Up And Up, Grid Solitaire; Vertex/Intersection Polygon Game; Diagonal/Straight:
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 GAMES Group  The University of Alberta
GAMES is a research group for Gameplaying, Analytical methods, Minimax search and Empirical Studies. It produces realtime programs for strategic game such as Amazons, Awari, Checkers, Chess, Domineering, Go, Hex, Lines of Action, Othello, Poker, RoShamBo,
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 Games Mathematicians Play  Gregory McColm; Dept. of Mathematics, Univ. of South Florida
Mathematical games from a logical point of view: strategies for games and using games in descriptive complexity. Contents include Bisimulation; Foundations; Game Theoretic Semantics; and Guarded Quantifiers. With an outline of the problem of what it means
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 Game Theory in the News  Mike Shor
A regularly updated archive of news articles about game theory or probability. Hundreds of articles currently archived are indexed by mathematical theme or by area of application, including evolutionary biology, computer science, politics, and economics.
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 Game Theory, Linear/NonLinear Programming  Math Forum
Links to some of the best Internet resources for game theory and linear or nonlinear programming: Web sites, software, Internet projects, publications, and public forums for discussion.
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 Game Theory .net  Mike Shor
Lecture notes, text book reviews, and interactive applets and games, print and online tests and quizzes, a section on game theory in pop culture, and links to other resources on the web.
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 A Gamma Process  Charlie Geyer
An applet that draws a Gamma process, a stochastic process with independent increments.
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 GAMS : Guide to Available Mathematical Software  National Institute of Standards and Technology (NIST)
A crossindex and virtual repository of mathematical software available to staff of the National Institute of Standards and Technology (NIST). Provides centralized access to abstracts, documentation, and source code of software modules that it catalogs.
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 GANG Discrete Library  Ian McIntosh; Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
A library of discrete conformal maps as discrete integrable systems. A discrete conformal map is a map z : z^2 > p^1 with the property that the
crossratio of four adjacent points is constant... Illustrations show how a Riemann surface arises, considering
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 GANG Knot Library  Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
A library of Energy Minimizing Knots and Links. Select a knotimage or category to see more members of the knot's family. The catalog contains knots up to 8 crossings. 2,q torus knots and links; Rational link with two, three, and fourterm continued
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