 Leonardo, Water, and Math  Ivars Peterson (MathLand)
Leonardo da Vinci had a special interest in water, both practical and theoretical. Between the years 1506 and 1510, as he shuttled between projects in Milan and Florence, Leonardo jotted down his thoughts in a scientific notebook. His intention was to
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 Life in the Frequency Domain  J. Paul Giolma
A paper that complements standard college textbooks' coverage of time and frequency domain analysis. Includes sections entitled The Continuous Fourier Transform; A View of the Transform; The Inverse Transform; The Impulse Function; Convolution; Fourier
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 Linear Mathematics in Infinite Dimensions: Signals Boundary Value Problems and Special Functions  Ulrich Gerlach, The Ohio State University
An online text for learning about the nature of waves, signals, and fields, with extensions and applications to several wellknown ideas from finite dimensional linear algebra to infinite dimensions. The book has six major chapter topics: Infinite Dimensional
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 Linear Methods of Applied Mathematics  Evans M. Harrell II and James V. Herod
An online textbook suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. Organized into nineteen chapters: Linearity, The geometry of functions, Fourier series, Calculating Fourier
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 The Living Mathematics Project  Mathematics Department, Univ. of British Columbia
A project that is working to apply recent advances in computer programming languages and the technology of the World Wide Web to construct a new medium for creative visualization and the communication of mathematics. Applets on this site include: Copycat
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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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 Math2.org (formerly Dave's Math Tables)  David Manura
A collection of useful searchable math reference tables, formatted especially for the Web. Tables cover topics in general math (number notation), algebra (identities, polynomials, exponents, etc.), geometry (areas, volumes, surface areas), trigonometry
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 Mathematical Science  IOS Press, Amsterdam
Abstracts of books in the mathematical sciences: Symmetry and Physical Properties of Matter; Singular Perturbations in Elasticity Theory; Edgar Krahn, a Centenary Volume; Applied Fourier Transform; Analysis of Random Walks; Passage Times for Markov Chains;
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 Mathematical Tables and Formulas (S.O.S. Mathematics)  Dept. of Mathematical Sciences, Univ. of Texas at El Paso
A place for students and educators to access mathematical formulas. The tables are organized by topics: The First 1000 Prime Numbers; The Prime Factorization of the First 1000 Integers; Math for the Toolbox  SAE to Metric Conversion; Some Important Constants;
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 Mathematics Illuminated  Annenberg Media
A video course for adult learners, high school and college teachers; 13 halfhour video programs, online text, course guide, and Web site; graduate credit available. "Rather than a series of problems to be solved, mathematics is presented as play we engage
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 Mathematics Journals: Electronic and Printed  Mathematics Dept., Penn State University
Links to dozens of journals, from the Academic press electronic journal library to the Ulam Quarterly, and spanning printed journals from Abstract and Applied Analysis to the Zentralblatt für Mathematik. A link to the Bibliothèque Mathématique
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 MathGifs
"Illuminating mathematics through animations." This blog, which dates back to September, 2013, has included illustrated posts such as "Reflective Property of the Ellipse," "Rotations Through Translations," "Fourier Pumpkins," "Sonic Booms," and "The Mandelbrot
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 Math  PhET Simulations  University of Colorado
Dozens of free interactive, researchbased simulations of mathematical phenomena, from arithmetic, estimation, graphing lines, and Plinko probability, to projectile motion, wave on a string, Fourier (making waves), and blackbody spectrum. PhET's Java
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 maths online  University of Vienna, Austria
A modern mathematics learning site on the Web: details of the project, persons and institutions participating, or project proposals (only in German). The Gallery consists of interactive multimedia learning units (Java applets), each of which includes
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 MathSource  Wolfram Research
An extensive electronic library of Mathematica material and notebooks, with over 100,000 pages of immediately accessible Mathematica programs, documents, examples, and more. You may browse the archive or search by author, title, keyword, or item number.
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 MathsTools  Carlos Toro
Online apps for the Simplex algorithm, Runge Kutta methods, Fourier series, linear algebra, and more. Read the theory behind linear programming, numerical methods, Fourier analysis, special relativity, nonlinear programming, differential geometry, and
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 MathWizards  MathWizards, Inc.
Software applications and components (ActiveX, Java, TCL) for digital signal Processing (DSP), data analysis, visualization, and application development: MathViews, WaveXplorer, MathXplorer.
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 The MathWorks, Inc.
From the makers of MATLAB, a technical computing environment for highperformance numeric computation and visualization, and Simulink, an interactive environment for modeling, analyzing, and simulating a wide variety of dynamic systems, including discrete,
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 Math WWW VL: Specialized Fields  Dept. of Mathematics, Florida State University
Links to sites for resources in specialized fields in collegelevel mathematics.
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 Multigrid Algorithm Library  Ulrich Ruede; German Scientific Computing Pages
Multigrid (MG) methods are fast linear iterative solvers based on the multilevel or multiscale paradigm. The typical application for multigrid is in the numerical solution of elliptic partial differential equations in two or more dimensions. MG can be
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 Multirate Signal Processing Group  Univ. of Wisconsin  Madison
Members' research, software developed by the group, references; people, publications, other links.
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 MultiRes Modeling Group  California Institute of Technology
The Caltech MultiRes Modeling Group is a research group within the Computer Science Department under the leadership of Prof. Peter Schröder, working closely with the Graphics Group. Its research touches on many areas of computer graphics, but the
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 Multiresolution Signal Processing Group  University of Minnesota
The group's research consists of developing and applying multiscale signal processing techniques and wavelets in the design of high quality interactive audio, image and video multimedia databases and coders, optimal data acquisition schemes for radar,
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 Musemath  Bob O'Rourke
Videos on the mathematics and physics of the Western Traditional Music Scale.
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 Numerical Methods  Douglas N. Arnold; Mathematics Dept., Penn State University
An extensive list of centers (including online services and search engines), individual libraries, other sites (general and specific), journals, books, online publications, and other resources for numerical methods.
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 Numerical Recipes in C: The Art of Scientific Computing  Books OnLine  Press, Teukolsky, Vetterling, Flannery; Cambridge University Press
An online book available in Adobe Acrobat or PostScript formats that outlines the method of organizing a program, and then provides the methodology and (copyrighted) source code in the C programming language for: linear algebraic equations, interpolation
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 Poles and Zeros of a Causal LTI System  Manfred Thole
A Java applet that shows the domain of a system whose transfer function has two poles and two zeros. Poles and zeros can be dragged with the mouse. The amplitude response and the phase response are shown along the side. Plot: H(s) may take a while.
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 A Practical Guide to Wavelet Analysis  Christopher Torrence and Gilbert P. Compo
Read an introduction to wavelet analysis and Monte Carlo methods, or download it in PDF or PostScript format. Use an interactive wavelet plotting form to investigate sample time series or your own data. Download wavelet software in Fortran, IDL, or
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 Prof. Kuo's Research Group  University of Southern California
Prof. Kuo's research group is devoted to theoretical issues and practical applications of multimedia information processing, including image, video, graphics, audio and speech signals. Research projects cover multimedia information compression, communication
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 The Ramanujan Journal  Frank Garvan
This journal publishes research articles in the areas of mathematics influenced by Srinivasa Ramanujan, specifically number theory. Potential topics include the circle method and asymptotic formulae, diophantine analysis including irrationality and transcendence,
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 A Really Friendly Guide to Wavelets  C. Valens
A tutorial in wavelet transforms and their applications to signal theory and image compression, aimed at engineers. The tutorial may be read online, or downloaded as a PDF or zipped PostScript file.
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 Realtime Fourier synthesis  Sound generation  Erich Neuwirth
An Excel application that will allow you to synthesize sounds. Mathematically speaking the sliders control the amplitudes of the overtones of the base frequency. Excel workbooks for different versions of Excel to download for Microsoft Windows. Realtime
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 Rice Computational Mathematics Laboratory  R. O. Wells, Jr., Director; Rice Univ., Houston, TX
A mathematics laboratory collaboration. CML's current research efforts concern wavelet theory and its application in a variety of areas of numerical analysis and signal processing, especially the Automatic Target Recognition (ATR) program.
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 RockandRoll Bridge  Ivars Peterson (MathTrek)
Startling scenes of rippling pavement, featured in a classic film that captured the 1940 destruction of the Tacoma Narrows suspension bridge in Washington state, rank among the most dramatic and widely known images in science and engineering. This old
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 Short Signal Harmonic Spectra and Approximation  Dmitriev E.V.
The author writes: "Presently traditional ways to determine signal spectra are based on the expansion of functions in Fourier series or on their representation by Fourier integrals with applying a system of basis ORTHOGONAL functions. For the first time,
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 Signal Processing Laboratory  Thomas W. Parks, Director; Cornell University, Ithaca, NY
People; wavelets and multiresolution analysis research.
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 Sines and Cosines, Part 1 (Periodic functions)  Project MATHEMATICS!, California Institute of Technology
A videotapeandworkbook module that explores a basic topic in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. Sines and cosines occur as rectangular coordinates of a point moving on a unit circle, as graphs related
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 Software for Graphics and Data Analysis  S. Baum; Dept. of Oceanography, Texas A&M University
Links to software with descriptions, features, and where to find it, in (mostly) the following categories (or check out the complete alphabetical list): mostly graphics; mostly numerical analysis and number crunching; mostly data formats; commercial packages;
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 splib/wavelets  Rice University
Rice Digital Signal Processing (DSP) wavelet resources: links to wavelet research groups around the world.
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 The Stony Brook Algorithm Repository  Steven S. Skiena; Dept. of Computer Science, SUNYStony Brook
A comprehensive collection of algorithm implementations for over seventy of the most fundamental problems in combinatorial algorithms. The problem taxonomy, implementations, and supporting material are drawn from Skiena's book The Algorithm Design Manual.
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 Tides and Tide Prediction  Tony Phillips; Dept. of Mathematics, SUNYStony Brook
General information about tides and tide prediction: Priming/Lagging: a calculus with calculators exercise demonstrating the priming and lagging of the tides at Stony Brook. Samples of current tide predictions from the National Ocean Service. TideSounds:
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 UC Berkeley Wavelet Group  Univ. of California at Berkeley
People, papers and publications.
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 The Virtual Mathematics Center  Martindale's Graduate & Undergraduate Center
Preprints and online journals from a wide variety of math and science organizations; Online math dictionaries and encylopedias; mathematics courses, tutorials and databases; courses by subject; related mathematics information and databases.
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 A Virtual SpaceTime Travel Machine  JeanFrançois Colonna, École Polytechnique
Still Pictures and MPEG Animations (Images Fixes et Animations MPEG): Art and Science, Artistic Creation, Astrophysics, Celestial Mechanics, Deterministic Chaos, Deterministic Fractal Geometry, Fluid Mechanics, From the Infinitely Small to the Infinitely
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 WAVELAB 802 for Matlab5.x  Donoho, Duncan, Huo, Levi
WaveLab is a collection of Matlab functions that have been used by the authors and collaborators to implement a variety of computational algorithms related to wavelet analysis. A partial list of the techniques available includes orthogonal wavelet transforms,
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 Wavelet Cascade Applet  Wim Sweldens
Cascading (or subdivision) is one of the standard methods to build wavelets and scaling functions. With this Applet you can graph all scaling functions and wavelets with two parameters, even and odd, which satisfy refinement relations with four coefficients.
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 Wavelet Forum  Daniel Lemire, Ondelette.com
A friendly posting board on wavelets, spectral analysis, and signal processing.
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 Wavelet NetCare  Ben Nicholson; Dept. of Mathematics, Washington Univ., St. Louis
Wavelet links.
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 Wavelet Resources  Mathematics Dept., Yale University
Preprints and software for wavelets available from the Yale Mathematics Department.
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