MARTINDALE'S CALCULATORS ON-LINE CENTER MATHEMATICS CENTER: I-M (Calculators, Applets, Spreadsheets, and where Applicable includes: Courses, Manuals, Handbooks, Simulations, Animations, Videos, etc.)

US/Pacific: Saturday, July 4, 2009 Sydney, Australia: Sunday, July 5, 2009 File Download Time Calculator Author, E-Mail, Privacy Policy & Disclaimer Currently the Calculators On-Line Center contains over "23,730" Calculators & Spreadsheets, over "3,545" Courses, Lectures, Manuals, Handbooks, & "1,000's" of Movies, Videos, Simulations & Animations

COMPLEX MATH: I-M Image Processing ~ Integers & Integer Sequences ~ Integrals Interval Arithmetic Knots, Knot Theory, Vectors, Vector Analysis, Topology, Algebraic Topology, Computational Topology, etc. Lambda ~ Lattices ~ Lebesgue Integration & Measure Theory Level Set Methods ~ Limits of Mathematics & Information Theory Linear & Nonlinear Programming & Simplex Logarithms Logic & Abstract Mathematics ~ Math Animations ~ Math Music Math Video Lectures NSF Mathematical Sciences Institutes Multidisciplinary Math Workshops Mathematical Player Mathematical Constants, Functions & Symbols (Pi, Stieltjes, etc.) Mathematical Cognitive Tools Mathematical Methods for Engineers ~ Mathematical Physics Mathematica JavaView & LiveGraphics3D Mathematics of Plant Patern Formation ~ Maximum Entropy Mathematics Center Calculators On-Line Center

Image Processing IMAGE PROCESSING COURSES, CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS IMAGE PROCESSING: ALL OPERATOR EXPERIMENTATION (JAVA APPLETS) - R. Fisher, S. Perkins, A. Walker and E. Wolfart, School of Informatics, University of Edinburgh, Edinburgh, Scotland, U.K. Multimedia Image Processing Course, Lessons, Calculators, Applets (Text & Images). VERY VERY VERY...EXTENSIVE. "...provides on-line reference and tutorial information on a wide range of image processing operations, extensively illustrated with actual digitized images, and bound together in a hypermedia format for easy browsing, searching and cross-referencing. Amongst the features offered by HIPR are: Reference information on around 50 of the most common classes of image processing operations in use today; Detailed descriptions of how each operation works; A JAVA demonstration of each operator, with online JAVA code for the core of the algorithm; An interactive tableau where multiple operators can be linked together to demonstrate sequences of operations; etc..." Examples of "Image Processing" Subject Categories include "...Image Arithmetic; Point Operations; Geometric Operations; Image Analysis; Morphology; Digital Filters; Feature Detectors; Image Transforms; Image Synthesis; Convolution..." For more information see Robert Fisher's Home Page or the School of Informatics Some examples from over "50" Image Processing Applets include Image Arithmetic: Image AND Experimentation Point Operations: Contrast Stretching Experimentation Geometric Operations: Rotation Experimentation Morphology: Thinning Experimentation Image Transforms: Interactive Fourier Transform Experimentation Image Processing Concepts DIGITAL IMAGE PROCESSING - Wolfram Research Inc. Digital Image Processing Calculator "...This example uses webMathematica to demonstrate the action of a number of image processing filters contained in the Digital Image Processing application package for Mathematica..." For more information see webMathematica; webMathematica: The Way The Web Calculates or Wolfram Research Inc. IMAGE LINE PROFILES - Wolfram Research Inc. Image Line Profiles Calculator "...This example uses webMathematica and the application package Digital Image Processing to plot a brightness profile along a specified line for a given image..." For more information see webMathematica; webMathematica: The Way The Web Calculates or Wolfram Research Inc. Integers & Integer Sequences INTEGERS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS INTEGER SEQUENCES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ENCYCLOPEDIA OF INTEGER SEQUENCES SLOANE'S ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES - N.J.A. Sloane, AT&T Shannon Lab, AT&T Labs, AT&T VERY VERY VERY...EXTENSIVE. What comes next after 1, 2, 4, 9, 20, 48, 115, 286, 719, ...? "...This is the place to find out!..." Sloane's On-Line Encyclopedia of Integer Sequences is available in Arabic, Chinese, Czech, Danish, Dutch, English, Esperanto, Finnish, French, German, Hebrew, Hindi, Hungarian, Italian, Japanese, Korean, Polish, Portuguese, Romanian, Russian, Serbian, Spanish, Swedish, Turkish, etc. For more information see Neil J.A. Sloane's Home Page INTEGER CALCULATORS & APPLETS ARBITARY-PRECISION INTEGER CALCULATORS - R.R. Howell, Department of Computing and Information Sciences, Kansas State University VERY VERY EXTENSIVE. Arbitrary-Precision Integer Calculators "...Both calculators use RPN (Reverse Polish Notation) data entry. The computational model is stack-based, with operations taking their arguments from the top of the stack and replacing them with their results. The value in the display is always the value at the top of the stack. The size of the stack is bounded only by the available memory..." For more information see Java; Rodney R. Howell's Home Page or the Department of Computing and Information Sciences LARGE INTEGER CALCULATOR - U. Sondermann VERY VERY EXTENSIVE. Integer Calculator "...operates on Integers only, in any base up to 36. The shift operations operate at the binary bit level of any number regardless of base..." For more information see Binary, Primes, and Factors or Ulrich (Ulie) Sondermann's Home Page INTEGER FACTORIZATION CALCULATORS & APPLETS GAUSSIAN INTEGER FACTORIZATION CALCULATORS & APPLETS GAUSSIAN INTEGER FACTORIZATION APPLET - D.A. Alpern, Buenos Aires, Argentina VERY VERY VERY...EXTENSIVE. Gaussian Integer Factorization Calculator "...finds the factors of complex numbers of the form a+bi where a and b are integers. It also includes a complete calculator with operators and functions using gaussian integers...You can enter numbers of up to 500 digits,..." For more information see Number Theory; Calculators or Darío A. Alpern's Home Page Integrals INTEGRALS CALCULATORS & APPLETS INTEGRALS: THE INTEGRATOR - Wolfram Research, Inc VERY VERY VERY...EXTENSIVE. Wolfram Mathematica Online Integrator "...The Power To Do Integrals As The World Has Never Seen Before..." Wolfram Mathematica Online Integrator "...is powered by webMathematica, so it expects input to be in Mathematica syntax. It can also parse many expressions when they are not in exactly the right form, so people who are unfamiliar with Mathematica syntax details will not usually encounter problems..." For more information see Wolfram Research, Inc Interval Arithmetic INTERVAL CALCULATORS & APPLETS INTERVAL ARITHMETIC CALCULATORS & APPLETS JAVA-INTERVAL CALCULATOR - A. Pereira & E. Alicea, Computer Architecture & Arithmetic Research (CAAR), Lehigh University VERY VERY EXTENSIVE. Interval Calculator "...performs interval arithmetic operations and computers interval version of mathematical functions..." For more information see Undergraduate Research; Research or Computer Architecture & Arithmetic Research (CAAR) INTERVAL ARITHMETIC CALCULATORS - T.J. Hickey, Department of Computer Science, Brandeis University VERY VERY EXTENSIVE. Examples of "Interval Arithmetic" Calculators include IA-Solver "...a solver for non-linear constraints...." IA-Eval "...a simple Interval Arithmetic Evaluator..." GIA-Eval "...A General Interval Arithmetic Evaluator..." For more information see JScheme Applications; JScheme or Timothy J. Hickey's Home Page INTERVAL ARITHMETIC CONSTRAINT SOLVER - T.J. Hickey, Department of Computer Science, Brandeis University VERY VERY EXTENSIVE. For more information see Timothy J. Hickey's Home Page or the Department of Computer Science

Knots, Knot Theory, Vectors, Vector Analysis, Topology, Algebraic Topology, Computational Topology, etc. KNOT CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS KNOT THEORY S COURSES, TEXTBOOKS, LECTURES, LESSONS, CALCULATORS, ETC. KNOTS COURSES, TEXTBOOKS, LECTURES, LESSONS, ETC. MATHEMATICS AND KNOTS - Designed by: R. Brown , N. Gilbert, & T. Porter; W.W.W. Production by: C. Quinton, Schools of Electronics and Computer Science, Department of Mathematics, University of Wales, Bangor Multimedia Mathematics and Knots Lessons (Text & Images). Mathematics and Knots "...For mathematicians, the first object of study is the form of a knot..." For more information see Sculpture & Mathematics or the Centre for the Popularisation of Mathematics THE KNOTPLOT SITE - R.G. Scharein VERY VERY VERY...EXTENSIVE. The KnotPlot Site "...Here you will find a collection of knots and links, viewed from a (partly) mathematical perspective. The images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions..." For more information see Hypnagogic Software KNOT CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS HYPERBOLIC KNOT CENSUS: 3D INTERACTIVE VIEWER (JAVA APPLETS) - - R.G. Scharein VERY VERY VERY...EXTENSIVE. Hyperbolic Knot Census "...Click on an image to bring up a 3D interactive viewer... change the model parameters..." For more information see The Knotplot Site or Hypnagogic Software KNOT SIMPLIFIER (JAVAVIEW) - M. Andreeva, I. Dynnikov, S. Koval, K. Polthier & I. Taimanov, The JavaView Project, Germany VERY VERY EXTENSIVE. For more information see JavaView TORUS KNOTS 2D & 3D: CREATE 2D & 3D TORUS KNOTS - CALCULATOR - Wolfram Research Inc. VERY EXTENSIVE. Torus Knots "...The torus is the mathematical figure that looks like the surface of a doughnut..." For more information see webMathematica; webMathematica: The Way The Web Calculates or Wolfram Research Inc. TOPOLOGY COURSES & TEXTBOOKS ALGEBRAIC TOPOLOGY - A. Hatcher, Department of Mathematics, Cornell University, and Published by: Cambridge University Press Multimedia Algebraic Topology Textbook, PDF (Text & Images). VERY VERY VERY...EXTENSIVE. Algebraic Topology "...This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in spirit, and stays well within the confines of pure algebraic topology..." Examples of Algebraic Topology Textbook Chapters include "...The Fundamental Group; Homology; Cohomology; Homotopy Theory; etc..." For more information see Algebraic Topology Book Home Page; Allen Hatcher's Home Page or the Department of Mathematics ALGEBRAIC TOPOLOGY II - M. Behrens, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Algebraic Topology Course (Text & Images). VERY VERY EXTENSIVE. Algebraic Topology "...topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and..." Examples of Algebraic Topology Course Lectures include "...Compactly Generated Spaces; Pointed Spaces and Homotopy Groups; Cofibers; Puppe Sequences; Fibrations; The Hurewicz Homomorphism; The Spectral Sequence of a Filtered Complex; Line Bundles; etc..." For more information see the Mathematics Courses; Courses by Departments; MIT OpenCourseWare or the Department of Mathematics GENERAL TOPOLOGY AND REAL ANALYSIS - D.R. Wilkins, School of Mathematics, Faculty of Science, Trinity College, University of Dublin, Ireland Multimedia General Topology and Real Analysis Course, PDF (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of General Topology and Real Analysis Course Lectures include "...Sets, functions and countability; Complete metric spaces, normed vector spaces, and Banach spaces; Topological spaces; Compact spaces; The Lebesgue integral; Signed measures and the Radon-Nikodym Theorem; etc..." For more information see Courses & Lecture Notes; David R. Wilkins Home Page or the School of Mathematics SPECTRAL SEQUENCES IN ALGEBRAIC TOPOLOGY - A. Hatcher, Department of Mathematics, Cornell Universitys Multimedia Spectral Sequences in Algebraic Topology Textbook, PDF (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Spectral Sequences in Algebraic Topology Textbook Chapters include "...Introduction to the Serre Spectral Sequence; Adams Spectral Sequence; Eilenberg-Moore Spectral Sequences..." For more information see Allen Hatcher's Home Page or the Department of Mathematics VECTOR BUNDLES & K-THEORY - A. Hatcher, Department of Mathematics, Cornell University Multimedia Bundles & K-Theory Textbook - PDF, 115 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Vector Bundles & K-Theory "...The primary goal of the course is to present basic concepts from topology to enable a non-specialist to grasp and participate in current research in computational topology. As such, this course will not be a readings course in computational topology. Rather, it will present mathematics from a computer scientist's point of view..." Examples of Vector Bundles & K-Theory Textbook Chapters & Subchapters include Vector Bundles "...Basic Definitions and Constructions; Classifying Vector Bundles..." K-Theory "...The Functor K(X), Bott Periodicity; Division Algebras and Parallelizable Spheres; etc..." Characteristic Classes "...Stiefel-Whitney and Chern Classes; Euler and Pontryagin Classes; etc..." The J-Homomorphism "...Lower Bounds on Im J; Upper Bounds on Im J..." For more information see Vector Bundles & K-Theory Home Page; Allen Hatcher's Home Page or the Department of Mathematics Computational Topology INTRODUCTION TO COMPUTATIONAL TOPOLOGY - A. Zomorodian, Computer Graphics, Stanford University Multimedia Introduction to Computational Topology Course (Text & Images). VERY VERY VERY...EXTENSIVE. Introduction to Computational Topology "...primary goal of the course is to present basic concepts from topology to enable a non-specialist to grasp and participate in current research in computational topology..." Examples of Computational Topology Course Lectures include "...Point Set Topology; Surface Topology; Simplicial Complexes; Group Theory; Homotopy; Isosurface Topology Simplification; Topology Matching for fully Automatic Similarity Estimation of 3D Shapes; etc..." For more information see Computer Graphics TOPOLOGY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS SURFACE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ALGEBRAIC SURFACE SOLVER (JAVAVIEW) - The JavaView Project, Germany VERY VERY EXTENSIVE. Algebraic Surface Solver "...Algebraic surfaces are level sets of a scalar valued function F(x,y,z) from R3 to R where..." For more information see JavaView GALLERY OF SURFACES (JAVA APPLETS) - I. McIntosh, Department of Mathematics, University of York, U.K. VERY EXTENSIVE. Surface Applets include: "...Round Sphere; Delaunay Unduloid; Delaunay Nodoid; Smyth Surface; Smyth-Delaunay; Generalized Smyth Surface; Triunduloid, etc..." For more information see Ian McIntosh's Home Page or the Department of Mathematics JAVAVIEW - INTERACTIVE 3D GEOMETRY AND VISUALIZATION (JAVA APPLETS) - The JavaView Project, Germany VERY VERY VERY...EXTENSIVE. For more information see JavaView Some examples from over "20" 3D Geometry Calculators include Geodesic Surveyor: Measure Distances on Polyhedral Surfaces Harmonic Maps and Minimal Surfaces Parameterized Surfaces Visualize Scalar Field on a Surface JAVAVIEW - 3D GEOMETRY (JAVAVIEW) - Visualization and Mathematics VERY VERY VERY...EXTENSIVE. Visual Geometry Pages "...are an online geometry book illustrating problems from differential geometry and mathematical visualization using applets, images, animations, and Java software..." Visual Geometry Calculators include: "...Platonic Solids Calculator; Surfaces Calculator; Curves on Surfaces Calculator; Minimal Surfaces Calculator; CMC Surfaces Calculator; Curvature Properties Calculator; Harmonic Maps Calculator; Type a Curve Calculator "...Type the equations of your favorite curve..." Type a Surface Calculator "...Type the equations of your favourite surface..." Study ODEs Calculator "...Type and study ordinary differential equations..." Root Finder Calculator Find Roots of Real-Valued Functions..." For more information see Visualization and Mathematics Some examples of Visual Geometry Applets include Curves on Hypersurfaces Calcuator Curve Calculator Surface Calculator REAL PROJECTIVE STRUCTURES ON HYPERBOLIC SURFACES (JAVA APPLET) - D. Austin, Department of Mathematics, Grand Valley State University, Allendale, Michigan For more information see Mathematical Graphics; David Austin's Home Page or the Department of Mathematics SURFACES CALCULATOR (JAVA APPLET) - I. Nikolov, Department of Mathematics, Northeastern University VERY EXTENSIVE. Surfaces Calculator "...takes a closed polygon in R2, with edges identified in pairs, and returns a closed surface in standard form, specifying its orientability, genus, and Euler characteristic." For more information see Topology I - MTH3105 or Ivo Nikolov's Home Page SURFACES OF CONSTANT CURVATURE: DINI, KUEN & PSEUDOSPHERE PRINCIPALS - CALCULATOR - Wolfram Research Inc. VERY EXTENSIVE. Surfaces of Constant Survature using LiveGraphics3D includes "...Kuen Surface; Pseudoshphere Surface; Dini Surface..." webMathematica; webMathematica: The Way The Web Calculates or Wolfram Research Inc.

VECTOR ANALYSIS MULTIVARIABLE AND VECTOR ANALYSIS - W. Chen, Department of Mathematics, Division of Information and Communication Sciences (ICS), Macquarie University, Sydney, Australia Multimedia Multivariable and Vector Analysis Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Multivariable and Vector Analysis Course Chapters & Subchapters include Function of Serveral Variables; Differentiation "...Partial Derivatives; Total Derivatives; Consequences of Differentiability; Conditions for Differentiability; Properties of the Derivative; etc..." Implicit and Inverse Function Theorems "...Implicit Function Theorem; Inverse Function Theorem; etc..." Higher Order Derivatives "...Taylor's Theorem; Functions of Two Variables; etc..." Double and Triple Integrals "...Conditions for Integrability; Double Integrals over Special Regions; Fubini's Theorem; Mean Value Theorem; etc..." Change of Variables; Paths; etc. For more information see Courses & Lecture Notes of William Chen; William Chen's Home Page or the Department of Mathematics VECTOR CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS VECTOR LAND: AN INTRODUCTION TO 3D VECTOR ANALYSIS - P. Kirby Multimedia Course & Java Applets (Text & Images). VERY VERY EXTENSIVE. Vector Land "...This is the beginning of an online course to get to grips with 3D vectors for anyone who wants to learn..." Some examples from over "8" Vector Calculators include Parametric Curve Plotter Parametric Surfaces Plotter VECTOR ARITHMETIC CALCULATOR (JAVA APPLET) - V. Sorokin, General Physics Laboratory, Department of Physics & Astronomy, University of Kentucky VERY EXTENSIVE. Vector Arithmetic Calculator "...visualizes addition, substraction and scalar multiplication of vectors..." For more information see Java Applets; General Physics Laboratory or the Department of Physics & Astronomy VECTOR CALCULATOR (JAVA APPLET) - J. Gea-Banacloche, Department of Physics, University of Arkansas Vector Calculator is "...intended to give students a "feel" for vectors in two dimensions..." For more information see Julio Gea-Banacloche's Home-Made Page

Lambda LAMBDA LESSONS, MODELING, CALCULATORS, APPLETS, ETC. FINITE LAMBDA MODEL (JAVA APPLET) - P. Selinger, Department of Mathematics & Statistics, Dalhousie University VERY EXTENSIVE. Finite Lambda Model Calculator "...allows you to edit a finite lambda model and several lambda terms. It checks that the model you are entering is well-defined, and automatically calculates the term denotations..." For more information see Software; Research or Peter Selinger's Home Page THE PENN LAMBDA CALCULATOR - L. Champollion, J. Tauberer & M. Romero, Department of Linguistics, University of Pennsylvania VERY VERY EXTENSIVE. The Penn Lambda Calculator "...is an interactive, graphical, pedagogical computer program that helps students of formal semantics practice the typed lambda calculus..." For more information see the Department of Linguistics THE GENERALISED LAMBDA DISTRIBUTION (JAVA APPLET) - R. King, Faculty of Environmental Sciences, Griffith University, Australia Generalised Lambda Distribution Calculator "...is an extension, first suggested by Ramberg & Schmeiser (1974), of Tukey's lambda distribution..." For more information see Robert King's Home Page or the Faculty of Environmental Sciences Lattices LATTICE OVERIEW FOR CRYSTALLOGRAPHY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS SEE CHEMISTRY CALCULATOR CENTER: CRYSTALLOGRAPHY A CATALOGUE OF LATTICES - N.J.A. Sloane, AT&T Shannon Lab, AT&T Labs, AT&T Multimedia Lattice Database (Text & Images). VERY VERY VERY...EXTENSIVE. Catalogue of Lattices Database "...contains about 160,000 lattices..." For more information see Neil J.A. Sloane's Home Page LATTICE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS I(h) CALCULATOR OF A LATTICE - M. Kriechbaum, Institute of Biophysics & X-ray Structure Research, Österreichische Akademie der Wissenschaften (Austrian Academy of Sciences), Austria VERY EXTENSIVE. I(h) Lattice Calculator "...calculates the scattering curve of a 1D (lamellar), 2D (hexagonal), or several 3D (cubic) lattices, respectively..." For more information see Manfred Kriechbaum's Home Page PHASE TRANSITIONS ON LATTICES CALCULATORS & APPLETS PHASE TRANSITIONS ON LATTICES (JAVA APPLETS) - E. Demidov, Department of Semiconductor Physics, Institute for Physics of Microstructures (IPM), Russian Academy of Sciences (RAS), Russia VERY VERY VERY...EXTENSIVE. Available in English & Russian. Examples of Phase Transitions on Lattices Subject Categories include "...The 2D Ising model; Topological Exitations in Ferromagnetics; Percolation; Path Integrals in Quantum Mechanics..." For more information see E-notes Some examples from over "14" Phase Transitions on Lattices Calculators include Antiferromagnetics Calculators Topological Solitons in the Heisenberg Ferromagnetic Calculator Critical Exponents of Characteristic Functions Calculator LATTICE DRAWING CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS LATTICE DRAWING (JAVA APPLET) - R. Freese, Department of Mathematics, University of Hawaii Lattice Drawing Calculator "...demonstrates my program for automatically generating lattice diagrams from abstract representations of lattices (or partially ordered sets)..." For more information see The Lattice Theory Homepage or Ralph Freese's Home Page Lebesgue Integration & Measure Theory LEBESQUE INTEGRATION COURSES & LECTURES INTRODUCTION TO LEBESQUE INTEGRATION - W. Chen, Department of Mathematics, Division of Information and Communication Sciences (ICS), Macquarie University, Sydney, Australia Multimedia Lebesgue Integration Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Lebesgue Integration Course Chapters & Subchapters include The Read Numbers & Countability "...Completeness of the Real Numbers; Consequences of the Completeness Axiom..." The Riemann Integral "...Riemann Sums; Lower and Upper Integrals; Riemann Integrability..." Point Sets "...Open and Closed Sets; Sets of Measure Zero; Compact Sets; etc..." Lebesgue Integral "...Upper Functions on an Interval; Lebesgue Integrable Functions on an Interval; Sets of Measure Zero; etc..." Montone Convergence Theorem; Dominated Convergence Theorem; etc. For more information see Courses & Lecture Notes of William Chen; William Chen's Home Page or the Department of Mathematics MEASURE THEORY AND INTEGRATION COURSES, TEXTBOOKS & LECTURES MEASURE THEORY AND INTEGRATION - D.H. Sattinger, Department of Mathematics and Statistics, Utah State University Multimedia Measure Theory and Integration Course - PDF, 76 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Measure Theory and Integration Course Lectures include "...Measures; Integration; Product Spaces; Differentiation Theory; etc..." For more information see David Sattinger's Home Page or the Department of Mathematics and Statistics MEASURE AND INTEGRATION - J. Viaclovsky, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Measure and Integration Course (Text & Images). VERY VERY VERY...EXTENSIVE. Measure and Integration "...covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform..." Examples of Measure and Integration Course Lectures include "...Measure Theory; Real-valued Measurable Functions; Limits of Measurable Functions; Simple Functions; Positive Measures; Definition of Lebesgue Integral; Comparison of Lebesgue and Riemann Integrals; Properties of Positive Measures; Elementary Properties of the Lebesgue Integral; Measure of Special Rectangles; Measure of Special Polygons; Measure of Open Sets; Dominated Convergence Theorem Holds for Convergence in Measure; etc..." For more information see Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare Level Set Methods LEVEL SET METHODS COURSES, TEXTBOOKS, LESSONS, CALCULATORS & APPLETS FAST MARCHING METHODS AND LEVEL SET METHODS - Author: J.A. Sethian; Contributors to project include: D. Adalsteinsson; D.L. Chopp; J.S. Davis, II; M.L. Hald; R. Kimmel; R. Malladi; J. Rey and J. Zhu, Department of Mathematics, University of California, Berkeley Multimedia Level Set Methods Textbook, Lessons, etc. (Text, Images, Videos/Movies & Applets). VERY VERY VERY...EXTENSIVE. Fast Marching Methods and Level Set Methods "...are numerical techniques which can follow the evolution of interfaces. These interfaces can develop sharp corners, break apart, and merge together..." Level Set Methods and Fast Marching Methods online Textbooks include: "...Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science..." "...Level Set Method: An Act of Violence..." Level Set Methods and Fast Marching Methods Videos include: "...Curvature Collapse; Soap Bubbles; Medical Scans; Rising Bubble; Microchip Manufacturing; etc..." For more information see J.A. Sethian's Home Page or the Department of Mathematics Examples Level Set Methods Applets include Curve Flow Applets Robotic Navigation Limits of Mathematics & Information Theory LIMITS OF MATHEMATICS COURSE, TEXTBOOKS, LESSONS, ETC. LIMITS OF MATHEMATICS - G.J. Chaitin, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y. & Hosted by the Department of Computer Science, University of Maine Multimedia Information Theory and the Limits of Formal Reasoning Course (Text & Images). VERY VERY EXTENSIVE. Available in English & Japanese. Information Theory and the Limits of Formal Reasoning Course "...uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software..." For more information see Gregory J. Chaitin's Home Page LIMITS OF MATHEMATICS CALCULATORS & APPLETS LISP INTERPRETER FOR THE LIMITS OF MATHEMATICS, THE UNKNOWABLE, EXPLORING RANDOMNESS - G.J. Chaitin, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y. & Hosted by the Department of Computer Science, University of Maine VERY VERY EXTENSIVE. LISP interpreter for The Limits of Mathematics, The Unknowable, Exploring Randomness Calculator "...is identical with the "official" C and Mathematica versions, except that it allows several M-exps per line, and in its normal non-echo mode..." For more information see Gregory J. Chaitin's Home Page INFORMATION THEORY CALCULATORS & APPLETS SHANNON'S EXPERIMENT TO CALCULATE THE ENTROPY OF ENGLISH (JAVA APPLET) - D. Little, T. Mastro, M. Zabrocki & A.M. Garsia, Department of Mathematics, Eberly College of Science, Pennsylvania State University VERY EXTENSIVE. Shannon's Experiment to Calculate the Entropy of English "...Claude Shannon, the inventor of information theory, devised an experiment aimed at determining the entropy of an English letter (the amount of information in bits that we obtain on the average when we learn one letter of English)..." For more information see Information Theory; Java Index; David Little's Home Page or the Department of Mathematics

Linear & Nonlinear Programming
including the Simplex Method

Linear Programming Courses, Textbooks, Lectures & Lessons Nonlinear Programming Courses, Textbooks, Lectures & Lessons Linear & Nonlinear Mathematical Programming Affine-Scalling Algorithm ~ Distributed Algorithms Linear Programming Graphers ~ Linear Programming & Pivioting Nonlinear Equations ~ Simplex Method

Linear & Nonlinear Programming including the Simplex Method LINEAR PROGRAMMING COURSES, TEXTBOOKS, LECTURES, LESSONS Introduction to Practical Optimization A GENTLE INTRODUCTION PRACTICAL OPTIMIZATION - J.W. Chinneck, Department of Systems & Computer Engineering, Carleton University, Canada Multimedia Practical Optimization Course (Text, Images & Animations). VERY VERY VERY...EXTENSIVE. Practical Optimization "...is the art and science of allocating scarce resources to the best possible effect. Optimization techniques are called into play every day in questions of industrial planning, resource allocation, scheduling, decision-making, etc..." Examples of Practical Optimization Course Chapters include "...Introduction to Linear Programming; Towards the Simplex Method for Efficient Solution of Linear Programs; The Mechanics of the Simplex Method; Solving General Linear Programs; Sensitivity Analysis; Linear Programming in Practice; PERT for Project Planning and Scheduling; Dynamic Programming; etc..." Examples of Algorithm Animations Subject Categories include "...Linear Programming Animations; Network Animations; Integer Programming Animations; Yeuristics for Discrete Optimization Animations; etc..." For more information see John W. Chinneck Linear Programming - Undergraduate & Graduate LINEAR PROGRAMMING: FOUNDATIONS AND EXTENSIONS - R.J. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton Universtiy Multimedia Linear Programming Textbook, Undergraduate Lectures, Graduate Lectures, Exercises, etc. (Text, Images & Applets). VERY VERY VERY...EXTENSIVE. Examples of Linear Programming Course Lectures include "...The Simplex Method; Degeneracy; Efficiency; Duality; Self-Dual Simplex Method; Parametric Simplex Method; etc..." Linear Programming Graduate Lectures include: Sensitivity and Parametric Analysis; Convex Analysis; Network Flows-Theory; etc..." For more information see Robert J. Vanderbei's Home Page or the Department of Operations Research and Financial Engineering NONLINEAR PROGRAMMING COURSES & TEXTBOOKS NONLINEAR PROGRAMMING (REAL PLAYER) - Robert Freund, Sloan School of Management, & the MIT OpenCourseWare, MIT Multimedia Nonlinear Programming Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Nonlinear Programming Course "...introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming..." Examples of Nonlinear Programming Course Video Lectures include "...Newton's Method Video Lecture; Duality Theory Video Lecture; Semidefinite Optimization Video Lecture..." Examples of Nonlinear Programming Course Lectures include "...Convex Unconstrained Optimization Optimality Condition; Newton's Method; Steepest Descent Method; Constrained Optimization Optimality Conditions; Projection Methods for Equality Constrained Problems; Penalty Methods; Interior-Point Methods for Linear Optimization; Analysis of Convex Sets; etc..." For more information see MIT OpenCourseWare: Sloan School of Management Courses; Sloan School of Management or the MIT OpenCourseWare LINEAR & NONLINEAR MATHEMATICAL PROGRAMMING CALCULATORS & APPLETS AMPL: A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING - AMPL Optimization LLC VERY VERY VERY...EXTENSIVE. Modeling Language for Mathematical Programming (AMPL) "...is a comprehensive and powerful algebraic modeling language for linear and nonlinear optimization problems, in discrete or continuous variables..." "...lets you use common notation and familiar concepts to formulate optimization models and examine solutions, while the computer manages communication with an appropriate solver..." AFFINE-SCALING ALGORITHM CALCULATORS & APPLETS ALGORITHM ANIMATION: AFFINE SCALING (JAVA APPLET) - R. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton University VERY EXTENSIVE. Affine-Scaling Algorithm Applet "...animates the affine-scaling algorithm for solving linear programming problems..." For more information see Linear Programming: Foundations and Extensions; Robert Vanderbei's Home Page or the Department of Operations Research and Financial Engineering DISTRIBUTED ALOGRITHMS CALCULATORS & APPLETS DISTRIBUTED ALOGRITHMS (JAVA APPLETS) - Mordechai (Moti) Ben-Ari, Weizmann Institute of Science, Israel, & hosted by Computer Science Teaching Center (CSTC) VERY EXTENSIVE. Distributed Alogrithms Calculators "...are used for studying distributed algorithms. They presume familiarity with distributed algorithms. The applets are not simple animations where you passively watch the algorithm..." For more information see CSTC Resources or the Computer Science Teaching Center Some examples Distributed Alogrithms Calculators include Ricart-Agrawala Mutual Exclusion Dijkstra-Scholten Termination LINEAR PROGRAMMING GRAPHER CALCULATORS & APPLETS: TWO VARIABLES LINEAR PRIGRAMMING GRAPHER - S. Waner & S.R. Costenoble, Department of Mathematics, Hofstra University VERY VERY EXTENSIVE. Linear Programming Grapher Calculator "...Type in any linear programming problem in two variables and press "Graph." Shows the feasible region, corner points, and optimal solution..." For more information see Online Utilities & Software - Calculators; Finite Mathematics & Applied Calculus Resource Page; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University LINEAR PROGRAMMING AND PIVIOTING CALCULATORS & APPLETS LINEAR PROGRAMMING AND PIVIOTING IN 2D (JAVA APPLET) - G. Aloupis & B. Kaluzny, Computational Geometry Lab, School of Computer Science, McGill University, CA VERY VERY EXTENSIVE. Linear Programming and Pivoting in 2D Calculator: "...The user may either select a hardcoded example, or input their own LP... "...Pivoting: the user may pivot in 2 ways. The first is..." For more information see Bohdan's Computational Geometry Page or Bohdan Kaluzny's Home Page

NONLINEAR EQUATIONS CALCULATORS & APPLETS NONLINEAR APPLET - R.L. Devaney, Dynamical Systems and Technology Project, Department of Mathematics and Statistics, Boston University Nonlinear Calculator "...allows you to see the results of iteration of nonlinear functions such as the quadratic function x2 + c, the logistic function kx(1 - x), and..." For more information see Dynamical Systems and Technology Project Applets; Dynamical Systems and Technology Project; Bob Devaney's Home Page or the Department of Mathematics and Statistics NONLINEAR EQUATIONS CALCULATOR - Engineers' Compendium, Sheba Construction & Management Pty. Limited, Bowral, NSW, Australia VERY VERY EXTENSIVE. Nonlinear Equations Calculator: "...Nonlinear equations occur in all fields of engineering. A given task is reduced to the form f(x)=0. The object is to find values of x that satisfy this condition. This doesn't always have to be ALL values. Most times, we are interested only in values between xmin and xmax..." For more information see Engineers' Compendium SIMPLEX METHOD CALCULATORS & APPLETS THE SIMPLEX PLACE! AN INTRODUCTION TO THE SIMPLEX METHOD - M. Sniedovich, Department of Mathematics & Statistics, The University of Melbourne, Parkville, Australia VERY VERY EXTENSIVE. An Introduction to the Simplex Method "...In this discussion we examine the Simplex Method from the vantage point of the good old Gaussian elimination procedure for the solution of systems of linear equations..." For more information see Moshe's Place or the Department of Mathematics & Statistics LINEAR PROGRAMMING: LP EXPLORER (JAVA APPLET) - J.A. Julain Hall & M. Baird, Department of Mathematics & Statistics, University of Edinburgh, Scotland, U.K. VERY VERY EXTENSIVE. LP Explorer "...enables the simplex method to be applied to a linear programming (LP) problem and allows the sensitivity of the solution to changes in the problem data to be examined...LP Explorer is of particular value for problems with 2 variables when the simplex method and solution sensitivity are interpreted graphically..." For more information see Teaching; J.A. Julian Hall's Home Page or the Department of Mathematics & Statistics NETWORK SIMPLEX METHOD (JAVA APPLET) - R. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton University VERY VERY EXTENSIVE. Network Simplex Method Calculator "...that can be used to solve min-cost network-flow problems..." For more information see Linear Programming: Foundations & Extensions; Robert Vanderbei's Home Page or the Department of Operations Research and Financial Engineering PIVOT AND GAUSS-JORDAN TOOL - S. Waner & S.R. Costenoble, Department of Mathematics, Hofstra University VERY VERY EXTENSIVE. Pivot and Gauss-Jordan Calculator is "...used for Gauss Jordan row reduction and the simplex method; works in fraction, integer, and decimal mode..." For more information see Online Utilities & Software - Calculators; Finite Mathematics & Applied Calculus Resource Page; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University SIMPLEX PIVOT TOOL - ADVANCED (JAVA APPLET) - R. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton University VERY VERY EXTENSIVE. Simplex Pivot Calculator "...solve linear programming problems..." "...features an artificial objective row and an artificial right-hand side column, which can be used to guide pivot choices for either a primal or a dual phase one process..." For more information see Linear Programming: Foundations & Extensions; Robert Vanderbei's Home Page or the Department of Operations Research and Financial Engineering SIMPLEX METHOD TOOL - S. Waner & S.R. Costenoble, Department of Mathematics, Hofstra University VERY EXTENSIVE. Simplex Method Calculator allows you to "...Just type in any linear programming problem..." For more information see Online Utilities & Software - Calculators; Finite Mathematics & Applied Calculus Resource Page; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University

Logarithms LOGARITHM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS DISCRETE LOGARITHM CALCULATOR - D.A. Alpern, Buenos Aires, Argentina VERY VERY EXTENSIVE. Discrete Logarithm Calculator "... finds the exponent in the expression BaseExponent = Power (mod Modulus)... works for both prime and composite moduli..." For more information see Calculators or Darío A. Alpern's Home Page LOGARITHMIC AND TRIGONMETRIC FUNCTIONS CALCULATOR - Maritime Safety Information, National Geospatial Intelligence Agency VERY VERY EXTENSIVE. Logarithmic and Trigonometric Functions Calculator "...will calculate logarithms, trigonometric functions, and the logarithms of trigonometric functions..." For more information see Marine Navigation Calculators or the National Geospatial Intelligence Agency LOGARITHM CALCULATOR (JAVA APPLET) - P. Alfeld, Department of Mathematics, University of Utah VERY EXTENSIVE. Logarithm Calculator explores "...Exponentials, Radicals, and Logarithms..." For more information see Java Page or Peter Alfeld 's Home Page Logic & Abstract Mathematics LOGIC CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS INTRODUCTION & INTERMEDIATE LOGIC CALCULATORS & APPLETS GATEWAY TO LOGIC (JAVA APPLETS) - C. Gottschall, Wien, Austria VERY VERY VERY...EXTENSIVE. Gateway to Logic is "...a collection of web-based logic programs offering a number of logical functions..." For more information see Christian Gottschall's Home Page Examples of Logic Calculators include Server-side Processing Calculator Server-side Processing Calculator operates "...on formulae of classical two-valued propositional logic..." Client-side Processing Calculator Client-side Processing Calculator "...The strengths of the client side functions are the graphical functions (alpha graphs, Frege's notation), the animated visualization of several operations..." Lemmon-style Proof Builder Lemmon-style Proof Builder "...uses the calculus of natural deduction in the version presented in E.J. Lemmon's book Beginning Logic..." Proof Checker Proof Checker "...checks proofs submitted by the user - hence the name. It supports Lemmon's calculus only..." LOGIC TOOLBOX (JAVA APPLETS) - J. Saetti, Department of Philosophy, Lander University, Greenwood, South Carolina Multimedia Logic Lessons (Text, Images, Calculators & Applets). VERY VERY EXTENSIVE. Examples from over "10" Logic Calculators include "...Categorical Proposition Calculator; Syllogism Calculator; Truth Functions Calculator; Truth Tables; Proof Checker; Modus Ponens; Modus Tolens; Disjunctive Syllogism Calculator; Constructive Dilemma Calculator; etc..." For more information see Department of Philosophy INTRODUCTION & INTERMEDIATE ABSTRACT MATHEMATICS APPLETS METAMATH (JAVA APPLETS) - N. Megill VERY VERY VERY...EXTENSIVE. Metamath "...is a tiny language that can express theorems in abstract mathematics, accompanied by proofs that can be verified by a computer program. This site has a collection of web pages generated from those proofs and lets you see mathematics developed in complete detail from first principles, with absolute rigor..." For more information see Metamath Site Selection Examples of Logic Calculators include Metamath Solitaire Calculator Metamath Solitaire Calculator "...lets you build simple proofs in logic and set theory..." Metamath Proof Explorer Metamath Proof Explorer "...has over 5,000 completely worked out proofs in logic and set theory..." Hilbert Space Explorer Hilbert Space Explorer "...The motivation for studying quantum logic (and the related orthomodular lattices) derives from the fact that the set of closed subspaces of Hilbert..." INTERMEDIATE & ADVANCE LOGIC & ABSTRACT ALGEBRA APPLETS LOGIC TOOLS - J. Halleck, Office of Information Technology, University of Utah Multimedia Logic Calculators, Logic Structures, Logic Systems, etc. (Text & Images). VERY VERY VERY...EXTENSIVE. Logic Tools include: "...Expression Evaluator Calculator; Simple World Evaluator Calculator; Frog World Evaluator Calculator; John Halleck's Logic Calculator; etc..." For more information see John Halleck's Home Page or the Office of Information Technology Some examples of Logic Systems include Logic Systems Logic Structures SON OF BIRDBRAIN - W. McCune, Computer Science Department, University of New Mexico VERY VERY VERY...EXTENSIVE. Son of Birdbrain is "...an interactive web page that allows you to easily construct some problems in abstract algebra and logic,..." Select one of the Following & Prove some Theorems: "...Group Theory; Quasigroups and Loops; Ring Theory; Lattice Theory; Boolean Algebras; The Robbings Problem; Combinatory Logic; Equivalential Calculus..." For more information see William McCune's Home Page QUANTUM LOGIC CALCULATORS & APPLETS QUANTUM LOGIC (JAVA APPLET) - N. Megill, Metamath VERY VERY EXTENSIVE. Quantum Logic "...What we mean by quantum logic is the set of all equations that hold in a Hilbert lattice, which is the set of closed subspaces of an infinite dimensional Hilbert space. The subset of these equations that has been studied the most are the equations for orthomodular lattices that we show below. These simple equations can be manipulated with no knowledge of advanced math, and the Quantum Logic Explorer uses them to derive some interesting results worked out in complete detail that anyone with patience can follow..." For more information see Metamath

Math Animations MATH ANIMATIONS & SIMULATIONS A VIRTUAL SPACE-TIME TRAVEL MACHINE: A GATEWAY BETWEEN ART AND SCIENCE - UNE MACHINE VIRTUELLE A EXPLORER L'ESPACE-TEMS: UN PONT ENTRE L'ART ET LA SCIENCE - Jean-Francois Colonna, France Telecom R&D and CMAP/Ecole Polytechnique, France VERY VERY VERY...EXTENSIVE. Includes more than "2820" Images & Animations, including: "...Quantum Mechanics; Deterministic Chaos; Particle Systems; Deterministic Fractal Geometry; Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis; Fluid Mechanics; Celestial Mechanics; Astrophysics; Sensitivity to Rounding-Off Errors; Number Theory; Signal Processing; Texture Synthesis; etc..." For more information see Ecole Polytechnique, France Math Music MATH MUSIC CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FOR MUSIC LESSONS, DATABASES, CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS SEE MUSIC CENTER METAMATH MUSIC - N. Megill VERY VERY EXTENSIVE. Mathematical Proofs Set to Music "...The music generated from these mathematical proofs stands in sharp contrast to certain other experimental music based on such mathematics as the digits of Pi. Unlike a proof's tree structure, which is inherently suggestive of a musical score, the digits of Pi have no obvious pattern..." For more information see Metamath Home Page or Metamath Site Selection VISUALIZING PHYSICS WITH SOUND - Landau Research Group, Department of Physics, Oregon State University VERY EXTENSIVE. Vsualizing Physics with Sound includes "...Inverse Fourier Transformation; Frequency Modulation; Direct Transformation; etc..." For more information see Computational Physics; Rubin H. Landau's Home Page or the Department of Physics Math Video Lectures - NSF Mathematical Sciences Institutes Multidisciplinary Math Workshops MATH VIDEO LECTURES - MULTIDISCIPLINARY WORKSHOPS NSF MATHEMATICAL SCIENCES INSTITUTES IMA MATH VIDEO LECTURES (QUICKTIME, REAL PLAYER, ETC.) - Institute for Mathematics and its Applications, a NSF Mathematical Sciences Institute and located at the University of Minnesota Multimedia Math Video Lectures (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Includes over "500" Math Video Lectures in Various Disciplines including: "...Quantitative Approaches to Cell Motility and Chemotaxis Lecture Videos; Mathematics of Proteins Lecture Videos; Mathematics of DNA Structure, Function, and Interactions Lecture Videos; Mathematics of Nucleic Acids Lecture Videos; Non-Linear Computational Geometry Lecture Videos; Optimization and Control Lecture Videos; Algebraic Algorithms in Optimization Lecture Videos; Algebraic Geometric Methods in Engineering Lecture Videos; The Mathematics and Art of Film Editing and Restoration Lecture Videos; etc..." For more information see the Institute for Mathematics and its Applications MSRI: VMATH, THE NEXT GENERATION FOR MATH LECTURES: MATHEMATICS VIDEO LECTURES (QUICKTIME) - Mathematical Sciences Research Institute (MSRI), a NSF Mathematical Sciences Institute and located at Berkeley, CA Multimedia Math Video Lectures (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Includes over "1,000" Math Video Lectures in Various Disciplines including: "...Combinatorial Representation Theory Lecture Videos; Representation Theory of Finite Groups Lecture Videos; Lie Theory Lecture Videos; Combinatorial Representation Theory Lecture Videos; Homological Methods in Representation Theory Lecture Videos; Exterior Differential Systems and the Method of Equivalence Lecture Videos; Contact structures, dynamics and the Seiberg-Witten equations in dimension 3 Lecture Videos; Continuous Optimization and Applications Lecture Videos; Deformation Theory and Moduli in Algebraic Geometry Lecture Videos; Introduction to Teichmuller Theory and Kleinian Groups Lecture Videos; etc..." For more information see the Mathematical Sciences Research Institute (MSRI) Mathematical Player MATHEMATICA PLAYER - CALCULATORS, ANIMATIONS & SIMULATIONS WOLFRAM DEMONSTRATION PROGRAM - WOLFRAM MATHEMATICA PLAYER - Wolfram Mathematica Player, Wolfram Research, Inc. VERY VERY VERY...EXTENSIVE. Free but Registration Required. Wolfram Demonstrations Project "...Conceived by Mathematica creator and scientist Stephen Wolfram as a way to bring computational exploration to the widest possible audience, The Wolfram Demonstrations Project is an open-code resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a remarkable range of other fields..." Examples of Mathematical Player Subject Categories include "...Mathematics; Computation; Physical Sciences; Systems, Models & Methods; Engineering & Technology; etc..." Wolfram Mathematica Player or Wolfram Research, Inc. Mathematical Constants, Functions, Symbols, Pi, etc. NAMES OF A NUMBER THE ENGLISH NAME OF A NUMBER - L.C. Noll The English Name of a Number includes the "..first 10000 powers of 10 in American system with dashes; American system without dashes; Eurpoean system with dashes; Eurpoean system without dashes..." Example: "...in the 'American system without dashes' the name for 107728 is one domilliaquingenquinseptuagintillion..." For more information see Landon Curt Noll's Home Page or isthe.com MATHEMATICAL CONSTANTS, FUNCTIONS, FORMULAS, SYMBOLS, ETC. LaTeX Equation Editor LATEX EQUATION EDITOR - Sitmo LaTeX Equation Editor "...interactive LaTex equation editor let's you write and download equations in seconds!..." For more information see Sitmo Mathematical Constants PLOUFFE'S INVERTER - S. Plouffe, Laboratoire de combinatoire et d'informatique mathématique, Université du Québec à Montréal VERY VERY VERY...EXTENSIVE. Available in English & French. Plouffe's Inverter " ...is a database of more than 215,000,000 mathematical constants like Pi, E, Catalan or Euler-Mascheroni constant with more than 2 billion digits..." For more information see the Laboratoire de combinatoire et d'informatique mathématique CONSTANTS - TCAEP.co.uk, J. Stott VERY VERY EXTENSIVE. Mathematical Constants includes: "...Over 600 alphabetically listed entries..." For more information see Welcome to TCAEP.co.uk Mathematical Formulas MATHEMATICAL FUNCTIONS: THE WOLFRAM FUNCTIONS SITE - Wolfram Research, Inc Multimedia Mathematical Functions Dictionary (Text & Images). VERY VERY VERY...EXTENSIVE. Mathematical Functions includes over 300,000 Formulas online & over 10,000 Visualizations including: Elementary Functions; Constants; Bessel, Airy, Struve Functions; Integer Functions; Polynomials; Gamma, Beta, Erf; Hypergeometric Functions; Elliptic Integrals; Elliptic Functions, etc..." For more information see Wolfram Research, Inc Mathematical Symbols SYMBOLS - TCAEP.co.uk, J. Stott Multimedia Symbols Glossary (Text & Images). VERY VERY EXTENSIVE. Symbols Glossary includes: "...Electronic Symbols, Greek Alphabet & Mathematical Symbols..." For more information see Welcome to TCAEP.co.uk Pi CALCULATORS & APPLETS Pi COMPUTER - CALCULATOR - R. Simms, Department of Mathematical Sciences, Clemsen University VERY EXTENSIVE. Pi Calculator "...makes use of an elegant representation of Pi, which may be treated like a sum of fractional terms. To generate digits,..." For more information see Neat Math Programs; Robert Simms' Web Corner or the Department of Mathematical Sciences, Clemsen University METHODS OF COMPUTATION Pi - I.K. Rana, Mathematics Resource Center, Department of Mathematics, Indian Institute of Technology, Bombay, India VERY VERY VERY...EXTENSIVE. Methods of Computation of Pi Calculators with Lessons include "...Archimedes Method Applet to Calculate Value of Pi Applet; Area Method Applet to Calculate Value of Pi Applet; Buffon's Needle Applet to Calculate Value of Pi Applet; Measuring Circle Method Applet to Calculate Value of Pi Applet; Monte Carlo Method to Calculate Value of Pi Applet; Ramanujan Circle Method to Calculate Value of Pi Applet; Ramanujan Digit Method to Calculate Value of Pi Applet; Rob's Method to Calculate Value of Pi Applet..." For more information see On the Nmber PI; Resources in the Center; Mathematics Resource Center; Department of Mathematics or the Indian Institute of Technology

Mathematical Cognitive Tools MATHEMATICAL COGNITIVE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS MEMORY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS BAYES FACTOR CALCULATOR - J.N. Rouder, Director of Perception and Cognition Lab, Department of Psychological Sciences, College of Arts & Science, University of Missouri, Columbia, Missouri VERY EXTENSIVE. Bayes Factor Calculator includes Bayes Factor One-Sample Test Calculator "...computes the BIC Odds, Jeffrey-Zellner-Siow Bayes factor, and unit Bayes factor..." Bayes Factor Two-Sample Test Calculator "...computes the BIC Odds and Jeffrey-Zellner-Siow Bayes factor and unit Bayes factor..." For more information see the Perception and Cognition Lab or the Department of Psychological Sciences LNSC CASCADE CORRELATION SIMULATOR APPLET - F. Dandurand, F. Rivest, M. Stolle & T. Shultz, Laboratory for Natural and Simulated Cognition, McGill University, Canada Cascade-correlation Simulator is "...a program that produces an output-activation diagram for a network with two continuous INPUT Values, a single binary output unit, and random connection weights..." For more information see the Laboratory for Natural and Simulated Cognition MATHEMATICAL COGNITIVE TOOLS (JAVA APPLETS) - J. Morey, Cognitive Engineering Lab, Department of Computer Science, University of Western Ontario, London, Ontario, Canada VERY VERY EXTENSIVE. Mathematical Cognitive Simulations include: "...Archimedian Kaleidoscope (AK); Archimedean Confection (AC); Polyvise; 3D Lattice Viewer; TileLand; PolygonRnD..." For more information see Jim Morey's Home Page or the Department of Computer Science Some examples of Mathematical Cognitive Simulations include 3DLattice Viewer 3DLattice Viewer is "...A tool for exploring 3D lattices generated by finite state machines..." Polyvise Polyvise is "...4D polytope explorer that employs a number of interactive visualization techniques to aid in handling the complexity associated with these informationally rich structure..." MODELS OF MEMORY (JAVA APPLETS) - Ian Neath, Department of Psychology, Memorial University of Newfoundland Multimedia Psychology Models, Models of Memory & Psychology Calculators (Text & Images). VERY VERY VERY...EXTENSIVE. Models of Memory "...If you wish to conduct simulations that will be reported in scientific journals or at professional conferences, you should program your own implementation and should test that version against all relevant published simulations..." For more information see Ian Neath's Home Page or the Department of Psychology Some examples from over "17" Memory Models & Psychology Calculators include The Brown & Hulme Model (Brown & Hulme, 1995) Brown & Hulme Model "...The purpose of the Brown and Hulme (1995) model was to show that item length (or word length) effects could be obtained in a model that does not include any rehearsal..." Positional Distinctiveness (Nairne et al., 1997) Positional Distinctiveness Model "...The basic idea was to see whether Estes' (1972) perturbation model could serve as the cause of distinctiveness. An item's position is encoded accurately, but then perturbs (or drifts) in psychological space..." Johnson's Distinctiveness Model (Johnson, 1991) Johnson's Distinctiveness Model "...Johnson (1991) proposed a distinctiveness model of serial learning. This simulation implements his model...." SIMPLE: Absolute Identification (Neath, Brown, McCormack, Chater, & Freeman, 2006) Scale Invariant Memory and Perceptual Learning (SIMPLE) Model "...assumes that the memory representation is a log transform of the physical item. In this version, however, we use a power function such that...." Recognition Memory Simulation Recognition Memory Simulation includes "...Signal Detection Theory; Non-Parametric Analog; Two-High Threshold Model...." THE HEURISTICA APPLET - Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Berlin, Germany VERY EXTENSIVE. Heuristic Calculator "...is an algorithm which will make decisions based on data. In this case, the heuristics are given data which consist of a number of objects, and some information about the objects in terms of binary cues..." For more information see Simple Heuristics That Make Us Smart Mathematical Methods for Engineers RELATED CENTERS FOR ENGINEERING COURSES, LECTURES, TEXTBOOKS, CALCULATORS, VIDEOS, SPREADSHEETS, ETC. SEE THE ENGINEERING CENTER MATHEMATICAL METHODS FOR ENGINEERS COURSES, LECTURES, TEXTBOOKS, ETC. Undergraduate Courses, Lectures, etc. COMPUTATIONAL SCIENCE AND ENGINEERS I (REAL PLAYER) - Gilbert Strang, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Computational Science and Engineers I Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Computational Science and Engineers I Course "...provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems;..." Examples from over "30" Mathematical Methods for Engineers Video Lectures include: "...One-dimensional Applications: A = Difference Matrix Video Lecture; Applications to Linear Estimation Video Lecture; Applications to Dynamics Video Lecture; Applications to Boundary Value Problems: Laplace Equation Video Lecture; Delta Function and Green's Function Video Lecture; Initial Value Problems: Wave Equation and Heat Equation Video Lecture; Finite Difference Methods: Stability and Convergence Video Lecture; Spectral Method: Dynamic Equations Video Lecture; etc..." For more information see Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare INTERACTIVE EDUCATIONAL MODULES IN SCIENTIFIC COMPUTING (JAVA APPLETS) - M.T. Health, E. VanderZee, J. Schoen, J. Naisbitt & N. Exner, Computational Science and Engineering (CSE) Graduate Option Program, College of Engineering, University of Illinois, Urbana-Champaign Multimedia Scientific Computing: An Introductory Survey Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Scientific Computing Subject Categories include "...Floating-Point Arithmetic "...Rounding Rules; Selectable-Precision Calculator; Quadratic Formula; Infinite Series; etc..." Linear Equations "...Condition Number; Gaussian Elimination; Gauss-Jordan Elimination; etc..." Linear Least Squares "...Householder Transformations; Householder QR Factorization; Gram-Schmidt QR Factorization; etc..." Eigenvalue Problems "...QR Iteration with Shifts; Jacobi's Method; etc..." Nonlinear Equations "...Fixed-Point Iteration; Newton's Method; Secant Method; etc..." Optimization "...Optimization in One Dimension; Unconstrained Optimization in Two Dimensions; Constrained Optimization in Two Dimensions; etc..." Interpolation "...Bernstein Polynomials; Taylor Interpolation; Newton Interpolation; Error Bounds; Piecewise Cubic Interpolation; etc..." Integration and Differentiation "...Adaptive Quadrature; Numerical Differentiation; Richardson Extrapolation; Romberg Integration; etc..." Ordinary Differential Equations "...Trapezoid Method; Runge-Kutta; Extrapolation; Predictor-Corrector; Galerkin; etc..." Partial Differential Equations "...Laplace Equation; Advection Equation; Burgers' Equation; etc..." Fast Fourier Transform "...Recursive FFT; Digital Filtering; etc..." Random Numbers and Simulation "...Linear Congruential Generators; Buffon Needle Problem; Quasi-Random Sequences; etc..." For more information see Scientific Computing: An Introductory Survey; Michael T. Health's Home Page or the Computational Science and Engineering (CSE) Graduate Option Program NUMERICAL METHODS IN ENGINEERING - J.J. Westerink, Department of Civil Engineering and Geological Sciences, College of Engineering, University of Notre Dame Multimedia Numerical Methods in Engineering Course - PDF, 250+ Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Numerical Methods in Engineering Course Lectures include "...Lecture 2: Direct Solutions to Linear Systems of Algebraic Equations; Lecture 4: Iterative Solutions to Linear Algebraic Equations; Lecture 6: Lagrange Interpolation; Lecture 9: Hermite Interpolating Polynomicals; Lecture 14: Practical Issues in Applying Finite Difference Approximations; Lecture 17: Numberical Integration; Lecture 22: Multi Step Methods; etc..." For more information see J.J. Westerink's Home Page or the Department of Civil Engineering and Geological Sciences Graduate Courses, Lectures, etc. MATHEMATICAL METHODS FOR ENGINEERS II (REAL PLAYER) - Gilbert Strang, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Mathematical Methods for Engineers II Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Multimedia Mathematical Methods for Engineers II Course "...is a continuation of Mathematical Methods for Engineers I. Topics include numerical methods; initial-value problems; network flows; and optimization..." Examples from over "28" Mathematical Methods for Engineers Video Lectures include: "...Comparison of Methods for the Wave Equation Video Lecture; Second-order Wave Equation Video Lecture; Finite Differences for the Heat Equation Video Lecture; Convection-Diffusion/Conservation Laws Video Lecture; Shocks and Fans from Point Source Video Lecture; Level Set Method Video Lecture; Matrices in Difference Equations (1D, 2D, 3D) Video Lecture; Fast Poisson Solver Video Lecture; Weighted Least Squares Video Lecture; Saddle Points/Inf-sup condition Video Lecture; etc..." For more information see Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare MATHEMATICAL METHODS OF ENGINEERING ANALYSIS - R.J. Vanderbei & E. Cinlar, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton Universtiy Multimedia Mathematical Methods of Engineering Analysis Textbook, PDF, 119 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Mathematical Methods of Engineering Analysis Textbook Chapters include "...Sets and Functions; Metric Spaces; Functions on Metric Spaces; Differential and Integral Equations; Convex Analysis; Measure and Integration; etc..." For more information see Robert J. Vanderbei's Home Page or the Department of Operations Research and Financial Engineering

Mathematical Physics RELATED CENTERS FOR PHYSICS DATABASES, COURSES, TEXTBOOKS, LECTURES, CALCULATORS, SPREADSHEETS, ETC. SEE THE PHYSICS CENTER & ASTROPHYSICS, ASTRONOMY & ASTROBIOLOGY CENTER SOME EXAMPLES MATHEMATICAL PHYSICS COURSES MATHEMATICAL PHYSICS - R.L. Herman, Department of Mathematics and Statistics, University of North Carolina, Wilmington, N.C. Multimedia Mathematical Physics Course (Text & Images). VERY VERY EXTENSIVE. Mathematical Physics Course Topics "...are vector analysis, vector spaces, linear algebra, complex variables, power series, ordinary and partial differential equations, Fourier series, Laplace and Fourier transforms, Sturm-Liouville theory, special functions..." Examples of Mathematical Physics Course Lectures include "...ODEs and SHM; Linear Algebra; Harmonics, Fourier Series; Complex Representations; Transform Techniques; Spherical Symmetry; etc..." For more information see Mathematical Physics (311); Russell L. Herman's Home Page or the Department of Mathematics and Statistics METHODS OF MATHEMATICAL PHYSICS I - M. Trodden, Department of Physics, Syracuse University Multimedia Methods of Mathematical Physics Course (Text & Images). VERY VERY EXTENSIVE. Examples of Methods of Mathematical Physics I Course Lectures include "...Analysis of Complex Functions; Exact and Approximate Evaluation of Sums and Integral; Solution of Ordinary Differential Equations; Transform Calculus; Sturm-Liouville Theory; etc..." For more information see Teaching; Mark Trodden's Home Page or the Department of Physics QUANTUM FIELD THEORY COURSES GEOMETRY AND QUANTUM FIELD THEORY - P. Etingof, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Geometry and Quantum Field Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE. Geometry and Quantum Field Theory Course is "...a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams...." Examples of Geometry and Quantum Field Theory Course Lectures include "...Generalities on Quantum Field Theory; The Steepest Descent and Stationary Phase Formulas; Feynman Calculus; The Euler Characteristic of the Moduli Space of Curves; Matrix Integrals and Counting Planar Diagrams; Quantum Mechanics; Operator Approach to Quantum Mechanics; Quantum Mechanics for Fermions; etc..." For more information see Mathematics Courses; Courses by Departments; MIT OpenCourseWare or the Department of Mathematics QUANTUM FIELD THEORY I - J. Collins, Department of Physics, Pennsylvania State University Multimedia Quantum Field Theory I Course (Text & Images). VERY VERY EXTENSIVE. Examples of Quantum Field Theory I Course Lectures include "...Bosonic and Fermionic Fock Space; Quantization with First-order Lagrangians; Gell-Mann-Low Formula; Wick's Theorem; Perturbation Theory; etc..." For more information see Quantum Field Theory I Home Page; John Collins' Home Page or the Department of Physics STRING THEORY STRING THEORY FOR UNDERGRADUATES - B. Zwiebach & A. Guth, Department of Physics & the MIT OpenCourseWare, MIT Multimedia String Theory for Undergraduates Course (Text & Images). VERY VERY VERY...EXTENSIVE. String Theory for Undergraduates Course "...Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity and basic quantum mechanics. This course develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics..." Examples from over "24" String Theory for Undergraduates Course Lectures include "...Relativistic Electrodynamics, Gauss' Law, Gravitation and Planck's Length; Nonrelativistic Strings and Lagrangian Mechanics; Area Formula for Spatial Surfaces; Relativistic Strings: Nambu-Goto Action, Equations of Motion and Boundary Conditions; Solution of the Open String Motion in the Light-cone Gaug; Closed Strings; etc..." For more information see Department of Physics; Physics Courses or the MIT OpenCourseWare Mathematica, JavaView & LiveGraphics3D LIVE GRAPHICS 3D CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS WEBMATHEMATICA & LIVEGRAPHICS 3D IN OPTICS - J.C. Wyant, College of Optical Sciences, University of Arizona, Tucson, Arizona VERY VERY VERY...EXTENSIVE. WebMathematica & LiveGraphics3D in Optics Subject Categories include: "...Zernike Polynomials; Seidel Aberrations; Fraunhofer Diffraction; Fresnel Diffractions; etc..." For more information see James C. Wyant's Home Page or the College of Optical Sciences Examples from over "25" webMathematica and LiveGraphics3D Calculators include Zernike Polynomials Calculator: PSF & MTF (Zernike Polynomials - 36 Terms) Foucault Knife Edge Patterns for Seidel Aberrations Calculator Rectangular Aperture Fraunhofer Diffraction Pattern Calculator Multiple Beam Interference Fringes Calculator Various Plots and Calculations Calculator JAVAVIEW 3D CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS JAVAVIEW - 3D GEOMETRY (JAVAVIEW) - Visualization and Mathematics VERY VERY VERY...EXTENSIVE. Visual Geometry Pages "...are an online geometry book illustrating problems from differential geometry and mathematical visualization using applets, images, animations, and Java software..." Visual Geometry Calculators include: "...Platonic Solids Calculator; Surfaces Calculator; Curves on Surfaces Calculator; Minimal Surfaces Calculator; CMC Surfaces Calculator; Curvature Properties Calculator; Harmonic Maps Calculator; Type a Curve Calculator "...Type the equations of your favorite curve..." Type a Surface Calculator "...Type the equations of your favourite surface..." Study ODEs Calculator "...Type and study ordinary differential equations..." Root Finder Calculator Find Roots of Real-Valued Functions..." For more information see Visualization and Mathematics Some examples of Visual Geometry Applets include Curves on Hypersurfaces Calcuator Curve Calculator Surface Calculator JAVAVIEW - INTERACTIVE 3D GEOMETRY AND VISUALIZATION (JAVA APPLETS) - The JavaView Project, Germany VERY VERY VERY...EXTENSIVE. For more information see JavaView Some examples from over "20" 3D Geometry Calculators include Geodesic Surveyor: Measure Distances on Polyhedral Surfaces Harmonic Maps and Minimal Surfaces Parameterized Surfaces Visualize Scalar Field on a Surface Mathematics of Plant Patern Formation PLANT PATTERN FORMATION CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS PHYLLOTAXIS APPLETS - P. Atela-Cortés & C. Golé, Department of Mathematics, Smith College VERY VERY EXTENSIVE. Phyllotaxis "...An Interactive site for the Mathematical Study of Plant Pattern Formation..." For more information see Introduction to Phyllotaxis; Pau Atela-Cortés' Home Page; Christophe Golé's Home Page or the Department of Mathematics Some examples Plant Pattern Formation Calculators & Applets include Cylinder Lattices Applet Cylinder Lattices Applet "...shows all the possible (half) cylindrical lattices..." Spiral Lattices Applet Spiral Lattices Applet "...enables the exploration of all possible spiral lattices and their organization according to their divergence angles, expansion rate, and parastichy numbers..." Dynamical Model Applet (Centric Representation) Dynamical Model Applet "...shows a model of primordia growth (represented by dots) at the apical meristem of a plant. The model is a dynamical system which implements Hofmeister's hypotheses: primordia form periodically, once formed..." Matrix FOR MATRIX CALCULATORS & APPLETS SEE LINEAR ALGEBRA: MATRIX CALCULATORS Maximum Entropy MAXIMUM ENTROPY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS MAXIMUM ENTROPY THEORY CALCULATORS & APPLETS MOMENT+ OUTPUT - Centre for Experimental & Constructive Mathematics, Simon Fraser University, British, Columbia, Canada VERY VERY EXTENSIVE. MomEnt+ Output "...a computational engine intended to implement and expand the applicability of much of the maximum entropy theory that has been developed in the past few years..." "...allows one to reconstruct any given number of moments of a user supplied input function. There are a number of types of entropy to chose from. Uniform or Gaussian noise can be added to the recontruction problem and Newton, Conjugate Gradient or Barzilai-Borwein numerical methods can be selected for the computations..." For more information see The MomEnt+ project: A Computational Exercise in Partially Finite Optimization; Research; CECM, Department of Mathematics and Statistics or the Simon Fraser University

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