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

US/Pacific: Tuesday, February 9, 2010 Sydney, Australia: Wednesday, February 10, 2010 File Download Time Calculator Author, E-Mail, Privacy Policy & Disclaimer Currently the Calculators On-Line Center contains over "23,785" Calculators & Spreadsheets, over "3,710" Courses, Lectures, Manuals, Handbooks, & "1,000's" of Movies, Videos, Simulations & Animations

COMPLEX MATH: A-D Algebra I & II Advanced Algebra & Computational Algebra ~ Octonions, Quaternions Geometric Algebra ~ Linear Algebra Abstract Algebra (Fields & Galois Theory, Group Theory, Rubik's Cube, Dihedral Groups, Lie Algebras, Lie Groups, etc., etc.) Applied Mathematics & Applied Analysis Commutative Algebra (Ring Theory, Dimension Theory, Module Theory, etc.) Base Conversion & Hexadecimal/Decimal Conversion ~ Bicycle Central Limit ~ Chaos & Catastrophe ~ Combinatorics Complex Analysis & Complex Numbers ~ Complex Systems (Agent-Based) Computational Science Computer Arithmetic Algorithms, Interval Analysis, Scientific Computing, MATLAB, etc. Continued Fractions ~ Curves ~ Curve Fitting Differential Equations, Partial Differential Equations, etc. Discrete Mathematics Calculus Mathematics Center Calculators On-Line Center

Algebra I & II ALGEBRA I & II: ALGEBRA COURSES & TEXTBOOKS WITH CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ALGEBRA - AlgebraHelp.com Multimedia Algebra Course (Text, Images, Calculators & Applets). VERY VERY EXTENSIVE. Examples of "Algebra" Course Subject Categories include "...Simplifying; Negative Exponents; Substitution and Evaluating; Factoring; Exponents; Graphing; etc..." Examples of "Algebra" Course Calculator Categories include "...Equations Calculators; Expressions Calculators; Functions Calculators; Numbers Calculators; etc..." Examples from over "21" Algebra Calculators include Equation Calculator Equation Calculator "...Solves equations, showing work and detailed explanation..." Equation Factoring Calculator Equation Factoring Calculator "...Solves equations by factoring, resorting to other methods when necessary..." Equation Calculator with Substitution Support Equation Calculator with Substitution Support "...simplifies and solves equations..." PRACTICAL ALGEBRA - Elizabeth Stapel Multimedia Algebra Courses (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Practical Algebra" Courses & Chapters include Examples of "Preliminary Topics Course" Chapters "...Absolute Value; Factoring Numbers; Fractions; Geometric Formulas; LCM and GCF; Metric Conversions; Negative Numbers; etc..." Examples of "Beginning Algebra Topics Course" Chapters include "...Intercepts; Midpoint Formula; Order of Operations; Polynomials; Ratio & Proportion; Scatterplots & Regressions; Scientific Notation; Simple Factoring..." Examples of "Intermediate Algebra Topics Course" Chapters include "...Even and Odd Functions; Factor Theorem; Factoring Polynomials; Function Notation; Function Transformations; Polynomial Graphs; Rational Roots Test; Remainder Theorem; etc..." Examples of "Advanced Algebra Topics Course" Chapters include "...Logarithms; Log Rules; Matrix Addition, Subtraction, Multiplication, Row Operations; Complex Numbers; Composition of Functions; Determinants; Exponentials; etc..." Solving Word Problems; etc. For more information see Purplemath UNDERSTANDING ALGEBRA - ALGEBRA I - J. W. Brennan, Selland College of Applied Technology, Boise State University Multimedia Algebra Course (Text, Images, Calculators & Applets). VERY VERY VERY...EXTENSIVE. Understanding Algebra "...This text is suitable for high-school Algebra I, preparing for the GED, a refresher for college students who need help preparing for college-level mathematics, or for anyone who wants to learn introductory algebra..." Examples of "Understanding Algebra - Algebra I" Course Chapters include "...The Numbers of Arithmetic; Introduction to Algebra; Word Problems; Graphing and Straight Lines; Systems of Linear Equations; Polynomials; Rational Expressions; Exponents and Roots; Quadratic Equations..." For more information see Understanding Algebra or James W. Brennan's Home Page Examples of Algebra Calculators include Line Graphing Applet Quadratic Equation Solver ALGEBRA GRAPHING APPLETS & ALGEBRA GRAPHING CALCULATORS 3D EQUATION GRAPHING CALCULATOR - AlgebraHelp.com Algebra 3D Equation Graphing Calculator "...is a Java calculator which simplifies, solves, and graphs equations in 3D..." For more information see AlgebraHelp EQUATION GRAPHING CALCULATOR - AlgebraHelp.com Albegra Equation Graphing Calculator "...will begin by expanding (simplifying) it. Next, the calculator will plot the function over the range that is given..." For more information see AlgebraHelp LINE GRAPHING APPLET - J. W. Brennan Algebra Line Graphing Calculator "...for exploring slope and intercepts of straight lines..." For more information see Understanding Algebra or James W. Brennan JAVA GRAPHING APPLET WITH EQUATION PARSER - A.S. Pyzdrowski Algebra Graphing Applet with Equation Parser. For more information see ICTCM 2000 or Anthony S. Pyzdrowski's Home Page ALGEBRA LESSONS WITH CALCULATORS, APPLETS & SIMULATIONS ARITHMETIC AND ALGEBRA CALCULATORS - Alexander Bogomolny VERY VERY VERY...EXTENSIVE. For more information see Interactive Mathematics Activities or Interactive Mathematics Miscellany and Puzzles Some examples from over "80" Algebra Calculators & Algebra Applets include Inflection Points of Fourth Degree Polynomials Applet Integer Iterations on a Circle Applet Frieze Patterns Java Applet ALGEBRA CALCULATORS, APPLETS & SIMULATIONS INTERACTIVE ALEGBRA - R. Bunge, Cyber School Services & hosted by Rick Veazey Online Information Center VERY EXTENSIVE. Some examples from over "11" Algebra Calculators include Lesson 1-1: ax + b = c Lesson 2-3: Factoring for ax2 + bx + c ALGEBRA QUIZES ALGEBRA QUIZ GENERATOR - Wolfram Research Inc. Algebra Quiz Generator "...Select the difficulty of the problem: Easy or Hard; & Select how many problems..." For more information see webMathematica or Wolfram Research Inc.

Advanced Algebra

Computational Algebra Querying Albegraic Objects Systems Algebra & Geometry Experimentation ~ Algebraic Computations Commutative Algebra ~ Guassian Integers Quadratic Equations ~ Permutations and Combinations

Advanced Algebra COMPUTATIONAL ALGEBRA CALCULATORS KANT/KASH: COMPUTATIONAL ALGEBRAIC NUMBER THRORY CALCULATOR - The KANT Group, Insitute of Mathematics, Faculty II: Mathematics & Natural Sciences; Technische Universität Berlin, Berlin, Germany VERY VERY VERY...EXTENSIVE. KANT/KASH: Computational Algebraic Number Theory "...is a tool for sophisticated computations in number fields, in global function fields, and in local fields...." KANT/KASH: Computational Algebraic Number Theory includes Calculations for "...Computations in number fields; Ideals in number fields; Relative extensions of number fields; Computations in class field theory; Computations of Galois groups; Lattices; Diophantine equations; Algebraic function fields over finite fields, Q or number fields; etc..." For more information see Algebra & Number Theory MAGMA COMPUTATIONAL ALGEBRA SYSTEM CALCULATOR - Computational Algebra Group, School of Mathematics & Statistics, University of Sydney VERY VERY VERY...EXTENSIVE. MAGMA Computational Algebra System Calculator is a "...High performance software for Algebra, Number Theory, and Geometry..." MAGMA Computational Algebra System includes Calculations for "Sets, Sequences, and Mappings; Basic Rings & Linear Algebra; Lattices & Quadratic Forms; Global Arithmetic Fields; Finite Groups; Lie Groups; Representation Theory; Geometry; Commutative Algebra; Coding Theory; Cryptography; etc..." For more information see the Magma Computational Algebra System Home Page; Computational Algebra Group or the School of Mathematics & Statistics SAGE & SAGE NOTEBOOK - Sage VERY VERY VERY...EXTENSIVE. SAGE "...can be used to study a general and advanced, pure and applied mathematics. This includes a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra..." QUERYING ALGEBRAIC OBJECTS SYSTEMS CALCULATORS & APPLETS QAOS: QUERYING ALGEBRAIC OBJECTS SYSTEM - The KANT Group, Insitute of Mathematics, Faculty II: Mathematics & Natural Sciences; Technische Universität Berlin, Berlin, Germany VERY VERY VERY...EXTENSIVE. Querying Algebraic Objects System (QaoS) Calculator "...is a database interface implemented under the aspect to establish a common gateway via web-browsers and computer algebra systems...." For more information see Algebra & Number Theory ALGEBRA AND GEOMETRY EXPERIMENTATION CALCULATORS & APPLETS ECHIDNA: ALGEBRA AND GEOMETRY EXPERIMENTATION - D.R. Kohel, School of Mathematics and Statistics, University of Sydney VERY VERY VERY...EXTENSIVE. ECHIDNA: Algebra and Geometry Experimentation Calculators include: "...Hilbert class polynomials; Weber class polynomials; Dedekind eta class polynomials; Atkin class polynomials; Absolute Igusa ideal classes; etc..." For more information see David R. Kohel's Home Page; ECHIDNA: Elliptic Curves and Higher Dimensional Analogues or the School of Mathematics and Statistics ALGEBRAIC CALCULATORS & APPLETS 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 JAVASCRIPT SCIENTIFIC CALCULATOR - J.C. Pezzullo, Georgetown University Medical Center VERY VERY EXTENSIVE. Javascript Scientific Calculator "...is a simple but fairly general numeric expression evaluator, with a large number of built-in transcendental functions..." Scientific Calculator Built-in Functions include: "...Algebraic; Transcendental; Trigonometric; Inverse Trig; Hyperbolic; Inverse Hyp; etc..." For more information see Interactive Statistics Calculations Pages or John C. Pezzullo's Home Page COMMUTATIVE ALGEBRA CALCULATORS & APPLETS COCOA SYSTEM: COMPUTATIONS IN COMMUTATIVE ALGEBRAS - Team Leader: L. Robbiano, The The CoCoA Team, Dipartimento di Matematica, Università di Genova, Genova, Italy VERY VERY VERY...EXTENSIVE. Computations in Commutative Algebra Calculator Computes "...Very Big Integers; Rational Numbers; Polynomials; Linear Systems; Non-negative Integer Solutions; Geographical Map Colouring; Heron's Formula; etc..." For more information see Lorenzo Robbiano's Home Page or the Dipartimento di Matematica

GUASSIAN INTEGERS 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 COUNTING GUASSIAN INTEGERS IN A DISK - F. Richman, Department of Mathematics, Florida Atlantic University VERY EXTENSIVE. Counting Guassian Integers in a Disk "...will compute the number of Gaussian integers of norm less than n and the number of norm equal to n..." For more information see JavaScripts or Fred Richman's Home Page Some examples from over "14" related Algebra Calculators include Bézout's Equation Elliptic curves Manipulating poynomials in two variables Bézout's Equation for Gaussian Integers QUADRATIC EQUATION CALCULATORS & APPLETS QUADRATIC EQUATION SOLVER - P. Lutus, Arachnoid VERY EXTENSIVE. Quadratic Equation Calculator "...will provide numerical real and imaginary roots for most cases..." For more information see Arachnoid SOLVING QUADRATIC EQUATIONS (JAVA SCRIPT) - K. Selvakumar, Center for Advanced Manufacturing Studies, Purdue School of Engineering, Purdue University Quadratic Equations Calculator "...solves Quadratic Equations..." For more information see Selvakumar's Home Page PERMUTATIONS AND COMBINATIONS CALCULATORS & APPLETS PERMUTATIONS AND COMBINATIONS - CALCULATOR - Department of Mathematics, Cégep Vanier College, Québec, Canada VERY EXTENSIVE. For more information see What are Permutations and Combinations?; Calculators; Real Life Mathematics or the Department of Mathematics Octonions, Quaternions & Division Algebra OCTONIONS, QUATERNIONS & DIVISION ALGEBRA LESSONS WITH CALCULATORS & APPLETS OCTONION AND OTHER DIVISION ALGEBRA - G. Dixon, Lincoln, MA Multimedia Octonion and other Division Algebras Lessons (Text, Images & Calculators). VERY VERY VERY...EXTENSIVE. Examples of "Octonion and other Division Algebras" Lessons include "...Quaternion Introduction; Division Algebras, Lie Algebras, Lie Groups and Spinors; Octonion Introduction; Octonion Associated Matrices and Adjoint Algebras; Adjoint Octonions, Clifford Algebras and Spinors; Octonion Multiplication Tables; Partial Motivation: Aiming at Leech; etc..." For more information see Mathematical Ideas in Science or 7 Stones Some examples from over "8" Quaternion, Octonion and other Division Algebras Calculators include X-Product Calculator X-Product E8 Lattices Calculator 6th Roots of Unity and G2 Calculator QUATERNION CALCULATOR (JAVA APPLET) - D. Sweetser VERY VERY VERY...EXTENSIVE. Quaternion Calculator is a "...calculator that can take real, complex numbers or quaternions as input, using the scalar, i, j and k buttons for each part..." For more information see Doing Physics with Quaternions or Doug Sweetser's Home Page Algebraic Geometry ALGEBRAIC GEOMETRY COURSES, LECTURES, TEXTBOOKS, ETC. Algebraic Geometry Courses, Textbooks, etc. ALGEBRAIC GEOMETRY - J.S. Milne, Professor Emeritus, Department of Mathematics, College of Literature, Science & Arts, University of Michigan Multimedia Algebraic Geometry Course - PDF, 241 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Algebraic Geometry "...an introduction to the theory of algebraic varieties. In contrast to most such accounts they study abstract algebraic varieties, and not just subvarieties of affine and projective space. This approach leads more naturally into scheme theory..." Examples of "Algebraic Geometry" Course Chapters include "...Algebraic sets; Affine algebraic varieties; Algebaic varieties; Projective varieties; Complete varieties; Finite maps; Dimension theory; Algebraic spaces: geometry over an arbitrary field; Coherent sheaves; invertible sheaves; Descent Theory; etc..." For more information see Course Notes; Mathematics; James Milne's Home Page or the Department of Mathematics Motivic Cohomology Courses, Textbooks, etc. LECTURES IN MOTIVIC COHOMOLOGY - C. Mazza, C.A. Weibel & V. Voevodsky, Hosted by C.A. Weibel, Mathematics Graduate Program, Department of Mathematics, Rutgers University Multimedia Lectures in Motivic Cohomology - PDF, 228 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Lectures in Motivic Cohomology" Chapters include "...Presheaves with Transfers; Nisnevich Sheaves with Transfers; The Triangulated Category of Motives; Higher Chow Groups; Zariski Sheaves with Transfers; etc..." For more information see the Charles A. Weibel's Home Page; Mathematics Graduate Program or the Department of Mathematics GEOMETRIC ALGEBRA CALCULATORS & APPLETS INTERACTIVE AND ANIMATED GEOMETRIC ALGEBRA WITH CINDERELLA (JAVA APPLETS) - E.M.S. Hitzer Department of Mechanical Engineering, Faculty of Engineering, University of Fukui, Japan VERY VERY VERY...EXTENSIVE. Examples of "Geometic Algebra" Calculators Subject Categories include "...Vector Calculators; Bivector Calculators; Outer Product Calculators; Triangle Calculators; Rotation Calculators; Oscillation Calculators; Circular polarized waves Calculators; Clifford's Circle Chain Theorem Calculators; etc..." For more information see Eckhard M. S. Hitzer's Home Page or the Department of Mechanical Engineering Examples from over "40" Geometic Algebra Applets include Vectors Calculators: Commutativity of Vector Addition Calculator Outer Product Calculators: The Outer Product according to Grassmann Calculator Rotations Calculators: Rotations by Rotors Calculator Oscillations Calculators: Symmetrical Transverse Normal Mode Calculator Circular Polarized Waves Calculators: Right-circularly Polarized Wave Form Calculator

Linear Algebra

Linear Algebra Courses Linear Algebra Calculators & Applets ~ Matrix Calculators

Linear Algebra LINEAR ALGEBRA COURSES, LECTURES & TEXTBOOKS WITH CALCULATORS & APPLETS LINEAR ALGEBRA (REAL PLAYER) - G. Strang, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Linear Algebra Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Available in English, Chinese (Simplified), Spanish (Español) & Portuguese/Português. Linear Algebra Course "...This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including s ystems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices..." Examples from over "30" "Linear Algebra" Course Video Lectures include The Geometry of Linear Equations Video Lecture; Multiplication and Inverse Matrices Video Lecture; Column Space and Nullspace Video Lecture; Solving Ax = b: Row Reduced Form R Video Lecture; The Four Fundamental Subspaces Video Lecture; Orthogonal Vectors and Subspaces Video Lecture; Orthogonal Matrices and Gram-Schmidt Video Lecture; Eigenvalues and Eigenvectors Video Lecture; Markov Matrices, Fourier Series Video Lecture; Linear Transformations and Their Matrices Video Lecture; etc. Mini-lectures on Eigenvalues include: "...Eigenvectors and Trace; Powers; Diagonalization; Differential Equations; Symmetry; Positive Definite; etc..." For more information see the Audio/Video Courses; Mathematics Courses; Courses by Departments; MIT OpenCourseWare or the Department of Mathematics Some examples of from over "14" Linear Algebra Calculators & Applets include: Eignevalues Calculator Determinants Calculator Sum of Trigonometric Series Calculator LINEAR ALGEBRA TEXTBOOK - Author: J. Hefferon; Hosted by J. Quigg, Department of Mathematics and Statistics, Arizona State University Multimedia Linear Algebra Textbook (Text & Images). VERY VERY VERY...EXTENSIVE. Linear Algebra Textbook "...The point of view taken here, that linear algebra is about vector spaces and linear maps, is not taken to the complete exclusion of others. Applications and the role of the computer are important and vital aspects of the subject. Consequently, each of this book's chapters closes with a few application or computer-related topics. Some are: network flows, the speed and accuracy of computer linear reductions, Leontief Input/Output analysis, dimensional analysis, Markov chains,..." Examples of "Linear Algebra" Textbook Chapters & Subchapters include Linear Systems "...Solving Linear Systems; Linear Geometry of n-Space; Reduced Echelon Form; etc..." Vector Spaces "...Definition of Vector Space; Linear Independence; Basis and Dimension; etc..." Maps Between Spaces "...Isomorphisms; Homomorphisms; Computing Linear Maps; Matrix Operations; Change of Basis; etc..." Determinants "...Definition; Geometry of Determinant; etc..." Similarity "...Complex Vector Spaces; Similarity; Nilpotence; Jordan Form; etc..." For more information see MAT 342 Linear Algebra or John Quigg's Home Page LINEAR ALGEBRA: MATH 115A - T. Tao, Department of Mathematics, UCLA VERY VERY EXTENSIVE. Multimedia Linear Algebra Course (Text & Images). Examples from over "9" "Linear Algebra" Course Lectures include Vectors, Vector Spaces, Span, Linear Independence, Nases Lecture; Dimension, Lagrange Interpolation, Linear Transformations Lecture; Null Spaces, Range, Co-ordinate Bases, Matrix Representation, Composition Lecture; Matrix Multiplication, Invertibility, Isomorphisms Lecture; Eigenvalues, Eigenvectors, Diagonalization Lecture; etc..." For more information see Terence Tao's Home Page or the Department of Mathematics Some examples from over "5" Linear Algebra Applets include Eigenvalues and Eigenvectors Calculator Gram-Schmidt Orthogonalization Calculator LINEAR ALGEBRA - P. Scott, School of Mathematical Sciences, University of Adelaide, Australia Multimedia Linear Algebra Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Linear Algebra" Course Chapters include "...Vector Spaces; Linear Transformation; Inner Product Space; Eingenvector & Eigevalue..." For more information see Paul Scott's Home Page LINEAR ALGEBRA CALCULATORS & APPLETS LINEAR ALGEBRA - I.K. Rana, Mathematics Resource Center, Department of Mathematics, Indian Institute of Technology, Bombay, India VERY VERY VERY...EXTENSIVE. Examples of Linear Algebra Calculators & Applets Subject Categories include "...Euclidean Space R Calculators; Systems of Linear Equation Calculators; Rank of a Matrix Calculators; Determinants Calculators; Vector Spaces, Bases and Dimensions Calculators; Linear Transformations Calculators; Inner Product Spaces Calculators; Orthogonal Projections and Orthonormal Bases Calculators..." For more information see Resources in the Center; Mathematics Resource Center; Department of Mathematics or the Indian Institute of Technology Some examples from over "40" Linear Algebra Applets include Systems of Linear Equation Calculators: Reducing a Matrix to Row-Echelon Form Calculator Rank of a Matrix Calculators: Linear Span of Vectors Calculator Determinants Calculators: Multiplicative Property Calculator Linear Transformations Calculators: Change in Matrix Representation Calculator LINEAR EQUATIONS: GAUSSIAN ELIMINATOR TOOL (JAVA APPLET) - R.J. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton Universtiy VERY VERY EXTENSIVE. Linear Equations "...For Those Who Hate Doing Arithmetic By Hand...a java applet that can be used to solve linear equations..." For more information see Robert J. Vanderbei's Home Page or the Department of Operations Research and Financial Engineering INTERACTIVE AND ANIMATED LINEAR ALGEBRA (JAVA APPLETS) - E.M.S. Hitzer Department of Mechanical Engineering, Faculty of Engineering, University of Fukui, Japan VERY VERY EXTENSIVE. Linear Algebra Calculators & Applets Subject Categories include "...Reflections and Rotations; Span and Linear Independence; Quadratic Forms; Vector Norms; System of linear equations, etc..." For more information see Linear Algebra Lectures; Eckhard M. S. Hitzer's Home Page or the Department of Mechanical Engineering Some examples from over "15" Linear Algebra Applets include Triple Reflection Applet Span and Linear Independence: Two Dimensional Applet

LINEAR ALGEBRA CALCULATORS & APPLETS - P. Grinfeld, Department of Mathematics, Drexel University VERY VERY EXTENSIVE. Linear Algbra Applets & Calculators include: "...Eigenvalues Calculator; Singular Value Decomposition Calculator (SVD); Gaussian Elimination Calculator; Determinants Calculator; Gram-Schmidt Orthogonalization Calculator..." For more information see Pavel Grinfeld's Home Page or the Department of Mathematics LINEAR ALGEBRA CALCULATOR (JAVA SCRIPT) - M. Kazmierczak For more information see Marcus Kazmierczak's Home Page Other Linear Algebra Calculators include Linear Algebra Calculator I: Trace, Determinant, Adjoint, and Inverse Linear Algebra Calculator II: Addition and Multiplication of Matrices Linear Algebra Calculator III: Solve a Linear System of 3 equations and 3 unknowns LINEAR ALGEBRA TOOLKIT - P. Bogacki, Department of Mathematics and Statistics, Old Dominion University VERY VERY VERY...EXTENSIVE. Linear Algebra Toolkit "...Each module is designed to help a linear algebra student learn and practice a basic linear algebra procedure, such as Gauss-Jordan reduction, calculating the determinant, or checking for linear independence..." Linear Algebra Calculator Subject Categories include: "...Systems of Linear Equations and Matrices Calculators; Determinants Calculators; Vector Spaces Calculators; Linear Transformations Calculators..." For more information see Przemyslaw Bogacki's Home Page or the Department of Mathematics and Statistics Some examples from over "13" Linear Algebra Calculators include Systems of Linear Equations and Matrices Calculators: Calculating the Inverse using Row Operations Calculator Vector Spaces Calculators: Linear Independence and Dependence Calculator Linear Transformation Calculators: Finding the Kernel of the Linear Transformation Calculator LINEAR APPLET - A. Vajiac, Dynamical Systems and Technology Project, Boston University Linear Calculator "...allows you to see the results of iteration of linear functions of the form Ax + B in three different ways..." For more information see Dynamical Systems and Technology Project or Dynamical Systems and Technology Project LINEAR EQUATION SOLVER (JAVA APPLET) - M. Chamness "...Three Equations, Three Unknowns..." For more information see Mark Chamness's Home Page LINEAR TRANSFORMATION APPLET - P. Atela-Cortés, Department of Mathematics, Smith College For more information see Pau Atela-Cortés' Home Page or the Department of Mathematics MATRIX CALCULATORS & APPLETS MATRIX MARKET (CALCULATORS & JAVA APPLETS) - Matrix Market, Mathematical and Computational Science Division, Information Technology Laboratory, National Institute of Standards and Technology (NIST) VERY VERY VERY...EXTENSIVE. Matrix Market "...A visual repository of test data for use in comparative studies of algorithms for numerical linear algebra, featuring nearly 500 sparse matrices from a variety of applications, as well as matrix generation tools and services..." Matrix Calculators include: "...Browse by collection, by matrix name, by generator name, the top ten; Search by matrix properties, by application area, by contributor); Interactive Generation; Matrix Structure Plots; Matrix Cityplots; 3D Interactive Cityplots; Spectral Portraits, etc..." For more information see the Mathematical and Computational Science Division or the National Institute of Standards and Technology (NIST) DISTRIBUTION VECTORS AND POWERS OF THE TRANSITION MATRIX: A UTILITY FOR MARKOV PROCESS COMPUTATION - S. Waner & S.R. Costenoble, Department of Mathematics, Hofstra University VERY VERY EXTENSIVE. Distribution Vectors and Powers of the Transition Matrix Calculator "...Calculates powers of the transition matrix and its action on a distribution vector..." 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 MATRIX CALCULATOR OR CALCULATRICE DE MATIRCE (FRANÇAIS) - Xiao Gang, Laboratoire J.-A. Dieudonné, Université de Nice, Nice, France English & Français. Matrix Calculator "...Give your matrix (enter line by line, separating elements by commas)..." For more information see WIMS MATRIX ALGEBRA TOOL - S. Waner & S.R. Costenoble, Department of Mathematics, Hofstra University VERY VERY EXTENSIVE. Matrix Algebra Calculator "...Does symbolic computations with matrices..." 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 MATRIX CALCULATOR - Bluebit Software, Greece Matrix Calculator "...This online matrix calculator uses Matrix ActiveX Component and will let you perform matrix calculations for up to 12x12 matrices..." For more information see Bluebit Software MATRIX CALCULATOR - SoftIntegration, Inc. For more information see Web Services; Plotting and Scientific Numerical Computing; Numerical Computing or SoftIntegration, Inc. MATRIX CALCULATOR - W. Moshammer, Department of Computer Science, University of Technology in Vienna, Vienna, Austria For more information see Java Script or Werner's Secret Place MATRIX ALGEBRA CALCULATOR AND MARKOV CHAINS - H. Arsham, Division of Economics, Finance and Management Science, Merrick School of Business, University of Baltimore VERY EXTENSIVE. For more information see Matrix Algebra and Markov Chains Home Page; Business Statistics: Revealing Facts from Figures; Hossein Arsham's Home Page or the Merrick School of Business MATRIX CALCULATOR (JAVA APPLET) - R.B. Israel, Department of Mathematics, University of British Columbia. Canada VERY EXTENSIVE. Matrix Calculator "...computes inverses, eigenvalues and eigenvectors of 2 x 2, 3 x 3 and 4 x 4 matrices, multiplies a matrix and a vector..." For more information see Robert B. Israel's Home Page 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

Abstract Algebra

Abstract Algebra Courses, Lectures, etc. Abstract Albegra, Logic, Rubik's Cube, etc. Abelian & Class Field Theory Courses, Lectures, etc. Fields & Galois Theory Courses, Lectures, etc. Atlas of Finite Group Representations Group Theory Courses, Lectures, etc. Algebraic K-Theory Courses, Lectures, etc. Algebraic Theory of D-Modules Courses, Lectures, etc. Cayley, Cyclic & Dihedral Groups ~ Dihedral Groups Homologial Algebra Courses, Textbooks, etc. (Derived Categories, etc.) Lie Algebras, Lie Groups, Algebraic Lie Theory, etc. Courses, Textbooks, etc.

Abstract Algebra ABSTRACT ALGEBRA COURSES, LECTURES, TEXTBOOKS, ETC. ABSTRACT ALGEBRA ONLINE - J.A. Beachy, Department of Mathematical Sciences, Northern Illinois University Multimedia Abstract Algebra Course (Text & Images). VERY VERY VERY...EXTENSIVE. Abstract Algebra Course "...contains many of the definitions and theorems from the area of mathematics generally called abstract algebra. It is intended for undergraduate students taking an abstract algebra class at the junior/senior level, as well as for students taking their first graduate algebra course..." Examples of "Abstract Algebra Online" Course Categories include "...Course Chapters; Index of Abstract Algebra Definitions; Index of Abstract Algebra Theorems; List of Abstract Algebra Theorems..." Examples of "Abstract Algebra Online" Course Chapters include "...Integers; Functions; Groups; Polynomials; Rings; Fields; Structure of Groups; Galois Theory; Unique Factorization; Structure of Noncommutative Rings; Ideal Theory of Commutative Rings; etc..." For more information see John A. Beachy's Home Page or the Department of Mathematical Sciences ABSTRACT ALGEBRA - R.B. Ash, Department of Mathematics, University of Illinois, Urbana, Illinois Multimedia Abstract Algebra Course (Text & Images). VERY VERY VERY...EXTENSIVE. Abstract Algebra "...This is a text for the basic graduate sequence in abstract algebra, offered by most universities. We study fundamental algebraic structures, namely groups, rings, fields and modules, and maps between these structures. The techniques are used in many areas of mathematics, and there are applications to physics, engineering and computer science as well. In addition,..." Examples of "Abstract Algebra" Course Chapters include "...Group Fundamentals; Ring Fundamentals; Field Fundamentals; Module Fundamentals; Some Basic Techniques of Group Theory; Galois Theory; Introducing Algebraic Number Theory; Introducing Algebraic Geometry; Introducing Noncommutative Algebra; Introducing Homological Algebra..." For more information see Robert B. Ash or the Department of Mathematics ABSTRACT ALGEBRA - D.R. Wilkins, School of Mathematics, Faculty of Science, Trinity College, University of Dublin, Ireland Multimedia Abstract Algebra Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Abstract Algebra" Course Lectures include "...Number Theory; Group Theory; Commutative Algebra; Introduction to Galois Theory; Hilbert's Nullstellensatz; Introduction to Affine Schemes; etc..." For more information see Courses & Lecture Notes; David R. Wilkins Home Page or the School of Mathematics ELEMENTS OF ABSTRACT AND LINEAR ALGEBRA - E.H. Connell, Department of Mathematics, University of Miami Multimedia Elements of Abstract and Linear Algebra Course (Text & Images). VERY VERY VERY...EXTENSIVE. Elements of Abstract and Linear Algebra "...This book is a survey of abstract algebra with emphasis on linear algebra. It is intended for students in mathematics, computer science, and the physical sciences. The first three or four chapters can stand alone as a one semester course in abstract algebra..." Examples of "Elements of Abstract and Linear Algebra" Course Chapters include "...Background and Fundamentals of Mathematics; Groups; Rings; Matrices and Matrix Rings; Linear Algebra..." For more information see Edwin H. Connell's Home Page or the Department of Mathematics ABSTRACT ALGEBRA, LOGIC, RUBIK'S CUBE, ETC. CALCULATORS & APPLETS 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 RUBIK'S CUBE (JAVA APPLET) - G.E.M. Helm, Luxembourg VERY EXTENSIVE. Rubik's Cube "...Twist or rotate by pointing and dragging in "natural" directions..." For more information see Georges E.M. Helm's Home Page ABELIAN & CLASS FIELD THEORY Abelian Varieties Courses, Lectures, Textbooks, etc. ABELIAN VARIETIES - J.S. Milne, Professor Emeritus, Department of Mathematics, College of Literature, Science & Arts, University of Michigan Multimedia Abelian Varieties - PDF, 172 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Abelian Varieties "...an introduction to the theory of abelian varieties, including the arithmetic of abelian varieties and Faltings’s proof of certain finiteness theorems...." Examples of "Abelian Varieties" Course Chapters & Subchapters include Chapter I: Abelian Varieties: Geometry "...Rational maps into abelian varieties; The theorem of the cube; Abelian varieties are projective; Isogenies; The dual exact sequence; Endomorphisms; Weil pairings; The Rosati involution; etc..." Chapter II: Abelian Varieties: Arithmetic; Chapter III: Jacobian varieties "...The construction of the Jacobian variety; The Jacobian variety as Albanese variety; autoduality; Generalizations; Obtaining the coverings of curve from its Jacobian; etc..." Chapter IV: Finiteness Theorems. For more information see Course Notes; Mathematics; James Milne's Home Page or the Department of Mathematics Class Field Theory Courses, Lectures, etc. CLASS FIELD THEORY - J.S. Milne, Professor Emeritus, Department of Mathematics, College of Literature, Science & Arts, University of Michigan Multimedia Class Field Theory Course - PDF, 287 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Class Field Theory "...describes the abelian extensions of a local or global field in terms of the arithmetic of the field itself. These notes contain an exposition of abelian class field theory using the algebraic/cohomological approach of Chevalley and Artin and Tate. The explicit approach of Lubin and Tate in the local case and the analytic approach in the global case are also explained..." Examples of "Class Field Theory" Course Chapters include "...Local Class Field Theory: Lubin-Tate Extensions; Cohomology of Groups; Brauer Group; Global Class Field Theory: Statements; L-series and the Density of Primes; Global Class Field Theory: Proofs; etc..." For more information see Course Notes; Mathematics; James Milne's Home Page or the Department of Mathematics FIELDS AND GALOIS THEORY Fields and Galois Theory Courses, Lectures, etc. FIELDS AND GALOIS THEORY - J.S. Milne, Professor Emeritus, Department of Mathematics, College of Literature, Science & Arts, University of Michigan Multimedia Fields and Galois Theory Course - PDF, 111 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Fields and Galois Theory gives "...a concise exposition of the theory of fields, including the Galois theory of finite and infinite extensions and the theory of transcendental extensions..." Examples of "Fields and Galois Theory" Course Chapters include "...Basic Definitions and Results; Splitting fields; multiple roots; The fundamental theorem of Galois theory; Computing Galois groups; Applications of Galois theory; Infinite Galois theory; etc..." For more information see Course Notes; Mathematics; James Milne's Home Page or the Department of Mathematics GALOIS THEORY - D.R. Wilkins, School of Mathematics, Faculty of Science, Trinity College, University of Dublin, Ireland Multimedia Galois Theory Course - PDF, 68 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Galois Theory" Course Chapters include "...Basic Concepts and Results of Group Theory; Rings and Polynomials; Polynomial Rings; Field Extensions; Splitting Fields and the Galois Correspondence; Galois’s Theorem concerning the Solvability of Polynomial Equations; etc..." For more information see Courses & Lecture Notes; David R. Wilkins Home Page or the School of Mathematics ATLAS OF FINITE GROUP REPRESENTATIONS ATLAS OF FINITE GROUP REPRESENTATIONS - Authors: R.A. Wilson, P. Walsh, J. Tripp, I. Suleiman, R. Parker, S. Norton, S. Nickerson, S. Linton, J. Bray & R. Abbott; Hosted by the School of Mathematical Sciences, Queen Mary, University of London VERY VERY VERY...EXTENSIVE. ATLAS of Finite Group Representations "...currently contains information (including 5215 representations) on about 716 groups..." ATLAS of Finite Group Representations includes Sporadic Groups "...Mathieu Groups; Leech Lattice Groups; Monster Sections; Pariahs; etc..." Alternating Groups; Linear Groups; Classical Groups; "...Symplectic Groups; Unitary Groups; Orthogonal Groups; etc..." Exceptional Groups of Lie type; "...Untwisted Groups & Twisted Groups..." Miscellaneous Groups "...Mathieu Group M20; Various Non-split Extension Groups..." For more information see Robert A. Wilson's Home Page or the School of Mathematical Sciences GROUP THEORY, GROUPS, ETC. Group Theory Courses, Lectures, Textbooks, etc. GROUP THEORY - P. Scott, School of Mathematical Sciences, University of Adelaide, Australia Multimedia Group Theory Course (Text & Images). VERY VERY EXTENSIVE. Examples of "Group Theory" Course Chapters include "...Permutations; Abstract Groups; Cyclic Groups; Homomorphisms; Cosets..." For more information see Paul Scott's Home Page or the School of Mathematical Sciences GROUP THEORY - J.S. Milne, Professor Emeritus, Department of Mathematics, College of Literature, Science & Arts, University of Michigan Multimedia Group Theory Course - PDF, 123 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Group Theory" Course Chapters include "...Basic Definitions and Results; Free Groups and Presentations; Coxeter Groups; Automorphisms and Extensions; Groups Acting on Sets; The Sylow Theorems; Applications; Subnormal Series; Solvable and Nilpotent Groups; etc..." For more information see Course Notes; Mathematics; James Milne's Home Page or the Department of Mathematics Group Theory, Groups, Calculators & Applets GALLIAN'S CONTEMPORARY ABSTRACT ALGEBRA - 6TH EDITION (JAVA APPLETS) - J.A. Gallian, University of Minnesota, Duluth VERY VERY VERY...EXTENSIVE. Gallian's Contemporary Abstract Algebra "...Welcome to our home page where you can find software to explore properties of specific groups and rings..." Gallian's Contemporary Abstract Algebra includes over "30" Abstract Algebra Calculators. For more information see Joseph A. Gallian's Home Page; Department of Mathematics and Statistics or the University of Minnesota, Duluth FORM A GROUPOID - EXPLORING ABSTRACT ALGEBRA WITH MATHEMATICA - K.M. Levasseur, Department of Mathematical Sciences, University of Massachusetts Lowell VERY VERY VERY...EXTENSIVE. Form a Groupoid Calculator INPUT Values include: "...Elements; Operation (in the form of a "pure function")..." Form a Groupoid Calculator OUTPUT values include: "...Your Groupoid and its Cayley table; Closure; Commutivity; Identity; Associativity; Inverses; Summary of information..." For more information see UMass Lowell WebMathematicaScripts; Kenneth M. Levasseur's Home Page; Department of Mathematical Sciences or HostSRV Some other examples from over "6" Abstract Albegra Calculators include Polynomial Extensions of Finite Rings Polynomial Extensions of Finite Rings Calculator INPUT Values include: "...Select the ring you want to look at; Enter coefficients of the modulus polynomial..." Polynomial Extensions of Finite Rings Calculator OUTPUT Values include: "...Base Ring; Modulus Polynomial; Quotient ring; Tables of operations..." EAAM Group Tables Calculator EAAM Group Tables Calculator INPUT Values include: "...Enter a positive integer; Select a family of groups..." EAAM Group Tables Calculator OUTPUT Values include: "...Elements of the group; Cayley table for this group..." GROUP THEORY: GROUPS OF ORDER 1-15 (JAVA APPLET) - J.J. Wavrik, Department of Mathematics, University of California, San Diego For more information see John J Wavrik's Home Page or the Department of Mathematics ALGEBRAIC K-THEORY THE K-BOOK: AN INTRODUCTION TO ALGEBRAIC K-THEORY - C.A. Weibel, Mathematics Graduate Program, Department of Mathematics, Rutgers University Multimedia The K-book: An Introduction to Algebraic K-theory (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "The K-book: An Introduction to Algebraic K-theory" Chapters include "...Projective Modules and Vector Bundles; The Grothendieck group K_0; K_1 and K_2 of a ring; Definitions of higher K-theory; The Fundamental Theorems of higher K-theory; etc..." For more information see the Charles A. Weibel's Home Page; Mathematics Graduate Program or the Department of Mathematics ALGEBRAIC THEORY OF D-MODULES ALGEBRAIC THEORY OF D-MODULES - D. Milicic, Department of Mathematics, University of Utah Multimedia Lectures on Algebraic Theory of D-Modules - PDF, 149 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Click on "Notes for the D-modules class" 2007-2008. Examples of "Lectures on Algebraic Theory of D-Modules" Chapters include "...Modules over rings of differential operators with polynomial coefficients; Sheaves of differential operators on smooth algebraic varieties; Direct and inverse images of D-modules; Holonomic D-modules; etc..." For more information see the Dragan Milicic's Home Page or the Department of Mathematics CAYLEY, CYCLIC & DIHEDRAL GROUPS ABSTRACT ALGEBRA HELPER (JAVA APPLET) - J. Beilfuss, L.A. Knatterud & J. Dietz, Department of Mathematics, St. Olaf College VERY EXTENSIVE. Abstract Algebra Calculator INPUT Values include: "...Cyclic Group, Dihedral Group & Cayley Group; Display Cayley Table for Selected Group; Display Subgroups of Your Group; etc..." For more information see Jill Dietz's Home Page or Department of Mathematics DIHEDRAL GROUPS MAGIC SQUARES AND DIHEDRAL GROUP D4 (JAVA APPLET) - L. Burton, Department of Mathematics, Western Oregon University Magic Squares and Dihedral Group D4 Calculator "...The sum of the numbers in each row, column and main diagonal is the same. It is called the magic constant. In the applet, magic squares of order (size) 3, 5, 7 and 9 may be explored. A magic square of odd order n contains the integers from..." For more information see Laurie Burton's Home Page or the Department of Mathematics HOMOLOGICAL ALGEBRA Derived Categories Courses, Lectures, etc. LECTURES ON DERIVED CATEGORIES - D. Milicic, Department of Mathematics, University of Utah Multimedia Lectures on Derived Categories - PDF, 228 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Click on "Notes for the Derived Categories class" Spring 2007. Examples of "Lectures on Derived Categories" Chapters include "...Localization of Categories; Triangulated Categories; Derived Categories; etc..." For more information see the Dragan Milicic's Home Page or the Department of Mathematics LIE ALGEBRAS, LIE GROUPS, ALGEBRAIC LIE THEORY, ETC. Algebraic Lie Theory Course with Text, Images, Videos/Movies & Audio/Sound ALGEBRAIC LIE THEORY - Isaac Newton Institute for Mathematical Sciences, Hosted by: Streaming Media Service, University of Cambridge Multimedia Algebraic Lie Theory (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Includes 143 "Algebraic Lie Theory" Videos. Examples of "Algebraic Lie Theory" Video Seminars include "...Affine Gelfand-Tsetlin bases and affine Laumon spaces Video; Algeraic Lie Theory through the Symmetric Group Video; An algebraic slice in the coadjoint action of the Borel Video; Atypicality, complexity and module varieties for classical Lie superalgebras Video; Braid groups and representations of symmetric groups Video; CFSG and group theory Video; Compactification of Deligne-Lusztig varieties Video; etc..." For more information see Streaming Media Service Collections; Streaming Media Service; Isaac Newton Institute for Mathematical Sciences or the University of Cambridge Lie Groups and Lie Algebras Courses, Textbooks, etc. LIE ALGEBRAS - S. Sternberg, Department of Mathematics, Harvard University Multimedia Lie Algebras Course (Book) - PDF, 194 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Lie Algebras" Course (Book) Chapters include "...The Campbell Baker Hausdorff Formula; The classical simple algebras; Engel-Lie-Cartan-Weyl; Conjugacy of Cartan subalgebras; The simple finite dimensional algebras; Cyclic highest weight modules; Serre’s theorem; Clifford algebras and spin representations; The Kostant Dirac operator; etc..." For more information see Shlomo Sternberg's Home Page or the Department of Mathematics INTRODUCTION TO LIE GROUPS AND LIE ALGEBRAS - A. Kirillov, Jr., Department of Mathematics, State University of New York, Stony Brook (SUNYSB) Multimedia Introduction to Lie groups and Lie algebras - PDF, 177 Pages (Text & Images). Examples of "Introduction to Lie groups and Lie algebras" Course Chapters include "...Lie Groups: Basic Definitions; Lie Groups and Lie algebras; Representations of Lie Groups and Lie Algebras; Structure Theory of Lie Algebras; Complex Semisimple Lie Algebra; Representations of Semisimple Lie Algebras; etc..." For more information see Alexander Kirillov's Home Page or the Department of Mathematics LIE GROUPS - D. Milicic, Department of Mathematics, University of Utah Multimedia Lie Groups Course - PDF, 160 Pages (Text & Images). Examples of "Lie Groups" Course Chapters include "...Basic differential geometry; Lie Groups; Compact Lie Groups; Basic Lie algebra theory; Structure of semisimple Lie algebras; etc..." For more information see Dragan Milicic's Home Page or the Department of Mathematics LIE GROUPS AND REPRESENTATIONS - Peter Woit, Department of Mathematics, Columbia University Multimedia Lie Groups and Representations Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Lie Groups and Representations" Course Lectures include "...Lie Groups, Lie Algebras and the Exponential Map; The Adjoint Representation; More About the Exponential Map; Maximal Tori and the Weyl Group; Roots and Weights; Weyl Reflections and the Classification of Root Systems; Fundamental Representations and Highest Weight Theory; The Weyl Integral and Character Formulas; Homogeneous Vector Bundles and Induced Representations; Borel Subgroups and Flag Manifolds; The Borel-Weil Theorem; Spin Groups; The Heisenberg Algebra; The Metaplectic Representation; etc..." For more information see Peter Woit's Home Page or the Department of Mathematics Lie Group Representation - The Universal Cover of SL(2,R) And Its Representations LIE GROUP REPRESENTATION: THE UNIVERSAL COVER OF SL(2,R) AND ITS REPRESENTATIONS (JAVA APPLET) - R. Shalla, UNIX Systems Automation, Lehman Brothers, New York City VERY EXTENSIVE. The Universal Cover of SL(2,R) And Its Representations "...Representations of the universal cover of SL(2,R) can be realized as global sections of standard weakened Harish-Chandra sheaves on the flag variety of the group PSL(2,C)..." For more information see Robert Shalla's Home Page Applied Mathematics & Applied Analysis APPLIED MATHEMATICS COURSES, TEXTBOOKS, ETC. APPLIED MATHEMATICS (MATH 280) - J.K. Hunger, Applied Mathematics Group, Department of Mathematics, University of California, Davis Multimedia Applied Mathematics Course - PDF, 180 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Applied Mathematics" Course Chapters include "...Dimensional Analysis, Scaling, and Similarity; The Calculus of Variations; Sturm-Liouville Eigenvalue Problems; Stochastic Processes; etc..." For more information see Teaching; John K. Hunter's Home Page or the Department of Mathematics APPLIED MATHEMATICS - P. Olver, School of Mathematics and the Institute of Technology, College of Engineering, Physical Sciences, and Mathematics, University of Minnesota Multimedia Applied Mathematics Course (Text & Images). VERY VERY EXTENSIVE. Examples of "Applied Mathematics" Course Chapters include "...Boundary Value Problems in One Dimension; Vibration and Diffusion in One-Dimensional Media; The Laplace Equation; Dynamics of Planar Media; The Calculus of Variations; etc..." For more information see Peter Olver's Home Page METHODS OF APPLIED MATHEMATICS (MATH 534B) - W.G. Faris, Department of Mathematics, University of Arizona Multimedia "Methods of Applied Mathematics" Course - PDF, 83 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Click on Lecture Notes Examples of "Methods of Applied Mathematics" Course Chapters include "...Distributions; Bounded Operators; Densely Defined Closed Operators; Normal operators; Calculus of Variations; Perturbation Theory; etc..." For more information see William G. Faris's Home Page or the Department of Mathematics APPLIED ANALYSIS COURSES, TEXTBOOKS, ETC. APPLIED ANALYSIS - J.K. Hunger and B. Nachtergaele, Applied Mathematics Group, Department of Mathematics, University of California, Davis Multimedia Applied Analysis Course (Book) - PDF, 429 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Applied Analysis" Course (Book) Chapters include "...Metric and Normed Spaces; The Contraction Mapping Theorem; Banach Spaces; Hilbert Spaces; Bounded Linear Operators on a Hilbert Space; Linear Differential Operators and Green's Functions; Measure Theory and Function Spaces; etc..." For more information see Bruno Nachtergaele's Home Page; John K. Hunter's Home Page or the Department of Mathematics Commutative Algebra COMMUTATIVE ALGEBRA COURSES, TEXTBOOKS, ETC. COMMUTATIVE ALGEBRA - R.B. Ash, Department of Mathematics, University of Illinois, Urbana, Illinois Multimedia Commutative Algebra Course (Text & Images). VERY VERY VERY...EXTENSIVE. Commutative Algebra "...The course should be accessible to those who have studied algebra at the beginning graduate level..." "...The idea is to help the student reach an advanced level as quickly and efficiently as possible. In Chapter 1, the theory of primary decomposition is developed so as to apply to modules as well as ideals. In Chapter 2, integral extensions are treated in detail, including the lying over, going up and going down theorems. The proof..." Examples of "Commutative Algebra" Course Chapters include "...Ring Theory Background; Primary Decomposition and Associated Primes; Integral Extensions; Valuation Rings; Completion; Dimension Theory; Depth; Homological Methods; Regular Local Rings; etc..." For more information see Robert B. Ash or the Department of Mathematics RING THEORY & MODULE THEORY COURSES, TEXTBOOKS, ETC. RING AND MODULE THEORY - Alastair Craw, Department of Mathematics, University of Glasgow, Glasgow, Scotland, UK Multimedia Ring and Module Theory Course (Text & Images). Examples of "Ring and Module Theory" Course Lectures include "...A primer on basic ring theory; Prime elements in a PID; Modules and homomorphisms; Finitely generated modules over a PID; Jordan normal form; etc..." For more information see Alastair Craw's Teaching Page; Alastair Craw's Home Page or the Department of Mathematics

Base Conversion & Hexadecimal/Decimal Conversion BASE CONVERSION LESSONS WITH CALCULATORS & APPLETS ADDITION AND MULTIPLICATION TABLES IN VARIOUS BASES (JAVA APPLET) - Alexander Bogomolny Addition and Multiplication Tables in Various Bases "...combines addition and multiplication tables for bases from 2 through 36..." For more information see Arithmetic & Algebra or Interactive Mathematics Education, Puzzles & Calculators BASE CONVERSION - Department of Mathematics, Cégep Vanier College, Québec, Canada Base Conversion Calculator INPUT Values include: "...Decimal; Binary; Quintal; Hexadecimal; etc..." For more information see Explanation of number base conversion; Calculators; Real Life Mathematics or the Department of Mathematics BASE CONVERSION: BINARY; TERNARY; QUINTAL; OCTAL; DECIMAL & HEXADECIMAL - Alexander Bogomolny Base Conversion Calculator INPUT Values include: "...Binary; Ternary; Quintal; Octal; Decimal; Hexadecimal; Base 36..." For more information see Arithmetic & Algebra or Interactive Mathematics Education, Puzzles & Calculators BASE-N CONVERSIONS CALCULATOR - eFunda, Inc. Base-N Conversions Calculator "...Converts integers expressed in one base to all other bases, up to base 36...and Decimal, Binary & Hexadecimal..." For more information see Unit Conversion Calculator; Calculators or Engineering Fundamentals BINARY, TERNARY, QUINTAL, OCTAL, DECIMAL & HEXADECIMAL CALCULATOR - P. van den Steen, SubnetOnline.Com Base Conversion Calculator INPUT Values include: "...Binary; Ternary; Quintal; Octal; Decimal; Hexadecimal; Base 36..." For more information see SubnetOnline NUMBER BASE ARITHMETIC - Department of Mathematics, Cégep Vanier College, Québec, Canada Number Base Arithmetic Calculator: "...you can do natural number arithmetic (addition, subtraction, multiplication & division) in the binary, octal, decimal, or hexadecimal, number bases..." For more information see What is Number Base Arithmetic?; Calculators; Real Life Mathematics or the Department of Mathematics CONVERT DECIMAL FLOATING-POINT TO 32-BIT AND 64-BIT HEXADECIMAL CONVERT DECIMAL FLOATING-POINT TO 32-BIT AND 64-BIT HEXADECIMAL REPRESENTATIONS ALONG WITH THEIR BINARY EQUIVALENTS: IEEE-754 CONVERSION CALCULATOR - Author: K.J. Brewer, Software Development, Delphi Delco Electronics Systems, and hosted by C. Vickery, Department of Computer Science, Queens College, CUNY VERY EXTENSIVE. Floating-Point Conversion Calculator: From Decimal Floating-Point To 32-bit and 64-bit, Hexadecimal Representations Along with Their Binary Equivalents For more information see IEEE-754 Calculatiors; Delphi Electronics; IEEE-754 References or Christopher Vickery's Web Site CONVERT 32-BIT HEXADECIMAL REPRESENTATION TO DECIMAL FLOATING-POINT CONVERT 32-BIT HEXADECIMAL REPRESENTATION TO DECIMAL FLOATING-POINT ALONG WITH THE EQUIVALENT 64-BIT HEXADECIMAL AND BINARY PATTERNS: IEEE-754 CONVERSION CALCULATOR - Author: K.J. Brewer, Software Development, Delphi Delco Electronics Systems, and hosted by C. Vickery, Department of Computer Science, Queens College, CUNY VERY EXTENSIVE. Floating-Point Conversion Calculator: From 32-bit Hexadecimal Representation To Decimal Floating-Point, Along with the Equivalent 64-bit Hexadecimal and Binary Patterns For more information see IEEE-754 Calculatiors; Delphi Electronics; IEEE-754 References or Christopher Vickery's Web Site CONVERT 64-BIT HEXADECIMAL REPRESENTATION TO DECIMAL FLOATING-POINT CONVERT 64-BIT HEXADECIMAL REPRESENTATION TO DECIMAL FLOATING-POINT ALONG WITH THE EQUIVALENT 32-BIT HEXADECIMAL AND BINARY PATTERNS: IEEE-754 CONVERSION CALCULATOR - Author: K.J. Brewer, Software Development, Delphi Delco Electronics Systems, and hosted by C. Vickery, Department of Computer Science, Queens College, CUNY VERY EXTENSIVE. Floating-Point Conversion Calculator: From 64-bit Hexadecimal Representation To Decimal Floating-Point, Along with the Equivalent 32-bit Hexadecimal and Binary Patterns For more information see IEEE-754 Calculatiors; Delphi Electronics; IEEE-754 References or Christopher Vickery's Web Site

Bicycle BICYCLE COURSES, LESSONS, CALCULATORS, APPLETS, ANIMATIONS, ETC. CYCLING CALCULATORS, APPLETS & ANALYZERS MECHANICS AND THE BICYCLE LESSONS, CALCULATORS & APPLETS LINEAR ALGEBRA AND THE BICYCLE CALCULATORS & APPLETS FOR CYCLING COURSES, LESSONS, CALCULATORS, APPLETS SEE CYCLING Some examples BICYCLE AERODYNAMICS - B.S.H. Royce & A.J. Smits, Gas Dynamics Laboratory, Department of Mechanical and Aerospace Engineering, Princeton University Multimedia Aerodynamics of Bicycles Course (Text, Images & Animations). VERY VERY VERY...EXTENSIVE. For more information see Gas Dynamics Laboratory or the Department of Mechanical and Aerospace Engineering Examples from over "11" "Bicylce Aerodynamics" Course Chapters include Pressure Pressure "...is a stress. It is a scalar given by the magnitude of the force per unit area. In a gas, it is the force per unit area exerted by the change of momentum of the molecules impinging on the surface. We know from Newton's second law that a net resultant force will cause a change of momentum in a body, and that the rate of change of momentum is equal to the applied force..." Streamlines and Streamtubes Streamlines "...is a line that is tangential to the instantaneous velocity direction (velocity is a vector, and it has a magnitude and a direction). To visualize this in a flow, we could imagine the motion of a small marked element of fluid. For example, we could mark..." Drag of Blunt Bodies and Streamlined Bodies Drag of Blunt Bodies and Streamlined Bodies "...A body moving through a fluid experiences a drag force, which is usually divided into two components: frictional drag, and pressure drag. Frictional drag comes from friction between the fluid and the surfaces over which it is flowing. This friction is associated with the development of boundary layers, and..." ANALYTIC CYCLING - T. Compton Multimedia Cycling Lessons with Calculators, etc. (Text, Images, Simulations, etc.) VERY VERY VERY...EXTENSIVE. Analytic Cycling "...provides technical methods for Navigation Bar evaluating and estimating cycling performance and parameters. It makes extensive use of differential equations and advanced numerical methods. Analytic Cycling methods respond in real time, characteristically returning tables and plots as products of the methods..." Some examples from over "30" Analytic Cycling Lessons & Calculators include Wind on Rider Calculator Plot Forces At Pedals Calculator Calculate Optimal Seat Height Calculator Gear Selection Calculator Long Climb Calculator Persuit Calculator Final Sprint Calculator MECHANICS, LINEAR ALGEBRA AND THE BICYCLE - Mathematics and its Applications in Engineering and Science, Department of Mathematical Sciences, The School of Science, Rensselaer Polytechnic Institute (RPI) Multimedia Bicycle Lessons & Calculators (Text & Images). VERY VERY EXTENSIVE. For more information see Linear Systems; Modules Grouped by General Applied Topic; Modules Grouped by General Applied Topic; Project Links; Mathematical Sciences or Rensselaer Polytechnic Institute (RPI) Some examples from over "15" Bicycle Calculators include How Mountain Biking Affects Your Weight Calculator How Mountain Biking Affects Your Weight Calculator "...simulates what would happen if you sat on a bicycle and placed bathroom scales under the tires. As you distributed your weight differently among the seat, the pedals, and the handlebars what would happen to the front tire reaction force?..." Weight Distribution to Bicycle Tires Calculator Weight Distribution to Bicycle Tires Calculator "...imulates what would happen if you sat on a bicycle and placed bathroom scales under the tires. As you distributed your weight differently among the seat, the pedals, and the handlebars what would happen to the front tire reaction force?..." Moments of Bicycle Pedaling Calculator Moments of Bicycle Pedaling Calculator "...simulates pedaling a bicycle. It operates in two modes: user mode which animates the pedal based on forces applied by the user; and experimental mode which animates the pedal based of experimentally determined forces applied by an actual rider..." BIKECAD: THE BICYCLE FOREST'S FRAME DESIGN TOOLS - CALCULATORS - The Bicycle Forest, Waterloo, Ontario, Canada VERY VERY VERY...EXTENSIVE. BikeCAD "...is a parametric CAD tool for bicycle frame design. The Bicycle Forest has created several variations of this program to accommodate specific designs and tasks such as recumbents, full suspension, tandems, and wheel building..." For more information see The Bicycle Forest Some examples of Bicycle Calculators include WheelCAD Calculator WheelCAD "...determine appropriate spoke length for building wheels..." TandemCAD Calculator TandemCAD "...for direct lateral tandem bikes (bicycle built for two)..." FullSuspensionCAD Calculator FullSuspensionCAD "...for four-bar linkage rear suspension..." Central Limit CENTRAL LIMIT THEOREM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS CENTRAL LIMIT THEOREM (JAVA APPLET) - Hong-Jing Lo and G.T. Zhou, School of Electrical and Computer Engineering, Georgia Institute of Technology VERY EXTENSIVE. Central Limit Calculator INPUT Values include: "...Distribution of r.v. (Gaussian, Uniform, Exponential, Double Exponential or Integers); Number of Samples; etc..." For more information see Applets for "Random Signals and Noise" or G. Tong Zhou Home Page CENTRAL LIMIT THEOREM - B. Zielman, Netherlands Central Limit Calculator "...The central limit theorem is one of the most remarkable results of the theory of probability. In its simplest form, the theorem states that the sum of a large number of independent observations from the same distribution has, under certain general conditions, an approximate normal distribution. Moreover,..." For more information see Berrie's Zielman's Statistics Pages CENTRAL LIMIT THEOREM APPLET - R.W. West, Department of Statistics, Texas A&M University Central Limit Calculator "...demonstrates the central limit theorem using simulated dice-rolling experiments..." For more information see Java Applets; R. Webster West's Home Page or the Department of Statistics

Chaos & Catastrophe CATASTROPHE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS CATASTROPHE THEORY CALCULATORS & APPLETS CATASTROPHE THEORY (JAVA APPLETS) - L. Dujardin, Faculty of Pharmacy, Lille Cedex, France Multimedia Catastrophe Theory Lessons with Java Applets (Text & Images). In English & French/Français. VERY VERY EXTENSIVE. For more information see Lucien Dujardin's Home Page Examples from over "14" Catastrophe Theory Calculators include Black Box Calculator: How to Interpret its Behaviour? Gravitational Catastrophe Machine as an Calculator The Seven Elementary Catastrophes: The Hyperbolic Umbilic Calculator CHAOS COURSES & TEXTBOOKS WITH CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS CHAOS ON THE WEB: PHYSICS 161: INTRODUCTION TO CHAOS - M. Cross, Condensed Matter Physics Group, Department of Physics, Division of Physics, Mathematics and Astronomy, California Institute of Technology (Caltech) Multimedia Chaos Course with Chaos Calculators & Applet Demonstrations (Text, Images & Applets). VERY VERY VERY...EXTENSIVE. Introduction To Chaos "...Since chaos is the study of complex dynamics in simple systems, numerical investigations have played a central role in the development of the subject, and remain a vital learning tool..." Examples of "Introduction To Chaos" Subject Categories include "...Introduction; Diagnostics; Application to Experiment; Bifurcations; Period Doubling Route to Chaos; Quasiperiodicity, Chaos and Frequency Locking; etc..." For more information see Chaos on the Web Home Page; Michael Cross's Home Page; Condensed Matter Physics Group; Department of Physics or the Division of Physics, Mathematics and Astronomy Examples from over "50" Chaos Applets & Chaos Calculators include Chapter 1: The Lorenz Model Applets The Lorenz Model Applets include: "...Phase Space Dynamics Applet; Time Series Applet; Power Spectrum Applet; Parameter Dependence Applet; Poincare Section Applet; etc..." Chapter 5: 2-Dimensional Maps Applets 2-Dimensional Maps Applets include: "...Henon Map Applet; Baker's Map Applet; etc..." Chapter 7: Lyapunov Exponents Applets Lyapunov Exponents Applets include: "...Henon Map Applet; Bakers' Map Applet (comparison with known results); 2D Circle Map Applet; etc..." Chapter 14: Bifurcations in the Quadratic Map Applets Bifurcations in the Quadratic Map Applets include: "...Patterns in the Qudratic Map Applet; Patterns in the Sine Map Applet; etc..." Chapter 19: 1D Circle Map Applets 1D Circle Map Applets include "...Basic properties Applet; Onset of Chaos from Quasiperiodic Motion Applet; Onset of Chaos in the Locked Tongues Applet; etc..." CHAOS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS CHAOS (JAVA APPLETS) - Department of Mathematics, College of Liberal Arts and Sciences, Arizona State University For more information see Department of Mathematics Some examples of Chaos Applets & Chaos Calculators include Logistic Map Applet The Henon Map and Box Counting Dimension Applet CHAOS APPLETS - R.L. Devaney, Dynamical Systems and Technology Project, Department of Mathematics and Statistics, Boston University For more information see Dynamical Systems and Technology Project; Bob Devaney's Home Page or the Department of Mathematics and Statistics Some examples of Chaos Applets & Chaos Calculators include Linear Web Applet - A. Vajiac Cycle Practice Applet - A. Vajiac CHAOTIC MAPS (JAVA APPLETS) - E. Demidov, Department of Semiconductor Physics, Institute for Physics of Microstructures (IPM), Russian Academy of Sciences (RAS), Russia VERY VERY VERY...EXTENSIVE. In English & Russian. Examples of Chaotic Maps Subject Categories & Chaotic Maps include: "...1D Maps Calculators & Applets; "...Tent map dynamics; Strange Cantor repeller; Quadratic maps; Bifurcation diagram for quadratic maps; Chaotic quadratic maps; etc..." 2D Maps Calculators & Applets; "...Baker's map; Smale horseshoe and 2D strange repellers; Homoclinic strucrures and horseshoe; etc..." Hamiltonian Chaos Calculators & Applets; "...Nonlinear resonance; The Standard map; Homoclinic structures in the standard map; Resonances; etc..." Two-electron Atom Calculators & Applets..." "...3-body Coulomb dynamics; Symbolic dynamics and Periodic orbits; etc..." For more information see E-notes Some examples from over "16" Chaotic Dynamics Applets & Chaos Calculators include 1D maps: Cantor sets and the Tent map dynamics Applet Hamiltonian chaos Applet Two-electron atom: Poincare maps Applet FEIGENBAUM BIFURCATION APPROACH TO CHAOS - W. Bauer, Department of Physics and Astronomy and the National Superconducting Cyclotron Laboratory, Michigan State University Feigenbaum bifurcation approach to Chaos Calculator allows you to "...zoom in on the bifurcation diagram by specifying the limits of the r- and x-intervals. You can either type these into the text fields or you can drag the mouse inside the plot area to accomplish this..." For more information see Research; Wolfgang Bauer's Home Page or the Department of Physics and Astronomy THE HENON MAP (JAVA APPLET) - B. Casselman, Department of Mathematics, University of British Columbia, Vancouver, Canada Henon Map Applet "...plots the orbits under the Henon map of the points selected by the mouse. It toggles between "Plot" and "Zoom" mode..." For more information see Bill Casselman's Home Page or the Department of Mathematics ITERATIVE MAP DEMO (JAVA APPLET) - E. Woolgar, Department of Mathematical Sciences, University of Alberta Iterative Map "...use this applet to find limit cycles for Feigenbaum's example of a quadratic iterative map..." For more information see Math Java Applets or Eric Woolgar's Home Page PATTERN FORMATION IN NONEQUILIBRIUM SYSTEMS: PHYSICS 161B - M. Cross, Condensed Matter Physics Group, Department of Physics, Division of Physics, Mathematics and Astronomy, California Institute of Technology (Caltech) VERY VERY VERY...EXTENSIVE. Pattern Formation in Nonequilibrium Systems Subject Categories include: "...Nonlinear Saturation; Eckhaus and Zigzag Instabilities; Signal Propagation in Excitable Media..." For more information see Chaos on the Web Home Page; Michael Cross's Home Page; Condensed Matter Physics Group; Department of Physics or the Division of Physics, Mathematics and Astronomy Some examples from over "15" Pattern Formation in Nonequilibrium Systems Applets include Nonlinear saturation: Swift-Hohenberg Equation Applet - Hexagons Signal Propagation in Excitable Media: Spiral - Reaction Diffusion Equations - Barkley Model Applet Eckhaus and zigzag instabilities: Swift-Hohenberg Equation - ZigZag Instability Applet PATTERNS AND SPATIOTEMPORAL CHAOS (JAVA APPLETS) - M. Cross, Condensed Matter Physics Group, Department of Physics, Division of Physics, Mathematics and Astronomy, California Institute of Technology (Caltech) VERY VERY EXTENSIVE. Patterns & Spatiotemporal Choas "...Spatiotemporal chaos is dynamics that is disordered in both space and time in spatially extended systems..." For more information see Michael Cross's Home Page; Condensed Matter Physics Group; Department of Physics or the Division of Physics, Mathematics and Astronomy Some examples of Spatiotemporal Chaos Applets & Spatiotemporal Chaos Calculators include Coupled Quadratic Maps Applet Swift-Hohenberg Equation Applet Reaction Diffusion Equation: Bar-Eiswirth Model Applet Reaction Diffusion Equation: Schnackenberg Model Applet

Combinatorics COMBINATORICS COURSES, TEXTBOOKS, LESSONS, ETC. ADDITIVE COMBINATORICS - B.J. Green, Department of Pure Mathematics & Mathematical Statistics, Faculty of Mathematics, University of Cambridge Multimedia Additive Combinatorics Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Graduate "Additive Combinatorics" Course Lectures include "...Roth's Theorem on progressions of length 3; Sumsets; Small doubling and the Freiman-Ruzsa theorem; The Balog-Szemeredi-Gowers theorem; Longer progressions and higher Gowers norms; The sum-product phenomenon over C; etc..." For more information see Graduate Courses; Ben J. Green's Home Page or the Department of Pure Mathematics & Mathematical Statistics COMBINATORICS CALCULATORS, APPLETS, ETC. SAGE & SAGE NOTEBOOK - Sage VERY VERY VERY...EXTENSIVE. SAGE "...can be used to study a general and advanced, pure and applied mathematics. This includes a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, and exact linear algebra..." Complex Analysis & Complex Numbers COMPLEX ANALYSIS COURSES, TEXTBOOKS, ETC. COMPLEX ANALYSIS - B. Sing, Department of Computer Science, Mathematics & Physics, University of the West Indies, Bridgetown, Barbados Multimedia Complex Analysis Course - PDF, 94 Pages (Text & Images). Click on Lecture Notes. Examples of "Complex Analysis" Course Lectures include "...The Complex Number Plane; Functions of a Complex Variable; Integration in the Complex Plane; Sequences and Series; Residue Calculus; etc..." For more information see Bernd Sing's Home Page or the Department of Computer Science, Mathematics & Physics COMPLEX ANALYSIS - J.H. Mathews, Department of Mathematics, California State University, Fullerton, Fullerton, California Multimedia Complex Analysis Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Complex Analysis" Course Chapters include "...Complex Numbers; Complex Functions; Analytic and Harmonic Functions; Elementary Functions; Complex Integration; Residue Theory; etc..." For more information see Complex Analysis Project; John H. Mathews Home Page or the Department of Mathematics COMPLEX ANALYSIS - Author: B.V. Shabat; Hosted by: L. Ryzhik, Department of Mathematics, University of Chicago Multimedia Complex Analysis Course - PDF, 111 Pages (Text & Images). Click on Lecture Notes on Complex Analysis. Examples of "Complex Analysis" Course Chapters include "...The Holomorphic Functions; Properties of Holomorphic Functions; Properties of Fractional Linear Transformations; Laurent Series and Singular Points; etc..." For more information see Lenya Ryzhik's Home Page COMPLEX ANALYSIS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS COMPLEX ANALYSIS APPLETS: MATH 132 - T. Tao, Department of Mathematics, UCLA VERY VERY EXTENSIVE. Complex Analysis "...is one of the most beautiful areas of pure mathematics, at the same time it is an important and powerful tool in the physical sciences and engineering..." For more information see Terence Tao's Home Page or the Department of Mathematics Examples from over "12" Complex Analysis Applets & Complex Analysis Calculators include Conformal Compactifaction Calculator Conformal Compactifaction Calculator "...demonstrates the Penrose map which conformally maps spacetime (which is of course infinite) to a pre-compact set, which is commonly known as the "Einstein diamond""..." The Honeycomb Calculator The Honeycomb Calculator "...displays a Honeycomb of order n, which is an object which naturally comes up in the study of tensor products of representations of..." Complex Plane Calculator Complex Plane Calculator "...illustrates the complex plane (sometimes called the Argand plane in older books), which can be used to display complex numbers, in the same way the real line is used to display real numbers..." Taylor and Laurent Expansions Calculator Taylor and Laurent Expansions Calculator "...displays the various Taylor and Laurent expansions of the function f(z) = 1/(z-1)(z-2)..." COMPLEX NUMBER CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS BIG NUMBER SCIENTIFIC CALCULATOR - D.A. Alpern, Buenos Aires, Argentina VERY VERY VERY...EXTENSIVE. Big Number Scientific Calculator is a "...high-precision calculator features complex numbers, precision up to 1 million digits and exponents up to 1 billion..." For more information see Number Theory; Calculators or Darío A. Alpern's Home Page COMPLEX NUMBER CALCULATOR - D.A. Alpern, Buenos Aires, Argentina VERY VERY VERY...EXTENSIVE. Complex Number Calculator: "...Reverse polish notation complex number calculator capable of performing all basic operations, powers, roots, logarithms, trigonometric functions, hyperbolic functions, gamma and polygamma functions..." For more information see Number Theory; Calculators or Darío A. Alpern's Home Page COMPLEX NUMBER CALCULATOR - Department of Mathematics, Cégep Vanier College, Québec, Canada VERY VERY EXTENSIVE. Complex Number Calculator "...Enter fractions in the form n/d where n and d are integers, or in the form w n/d where w is an integer and n and d are natural numbers..." For more information see What are Complex Number?; Calculators; Real Life Mathematics or the Department of Mathematics 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 QUATERNION CALCULATOR (JAVA APPLET) - D. Sweetser VERY VERY VERY...EXTENSIVE. Quaternion Calculator is a "...calculator that can take real, complex numbers or quaternions as input, using the scalar, i, j and k buttons for each part..." For more information see Doing Physics with Quaternions or Doug Sweetser's Home Page

Complex Systems - Agent-Based COMPLEX SYSTEMS CALCULATORS & APPLETS - AGENT-BASED COMPUTATIONAL ECONOMICS CALCULATORS & APPLETS LEARNING ALGORITHMS IN THE NELSON & WINTER (1982, PART IV) MODEL - Murat Yildizoglu, Centre de la Vieille Charité, Université Paul Cézanne (Aix-Marseille 3), Marseille, France VERY VERY EXTENSIVE. For more information see Site Index or Murat Yildizoglu's Home Page NELSON & WINTER (1982) MODEL IN JAVA - Murat Yildizoglu, Centre de la Vieille Charité, Université Paul Cézanne (Aix-Marseille 3), Marseille, France VERY VERY EXTENSIVE. For more information see Site Index or Murat Yildizoglu's Home Page NELWIN WITH GRAPHICAL OUTPUT - Murat Yildizoglu, Centre de la Vieille Charité, Université Paul Cézanne (Aix-Marseille 3), Marseille, France VERY VERY EXTENSIVE. Nelwin with Graphical Output "...(1) The initial capital stock of firms is computed in order to have zero net desired investment; (2) Imitative and innovative R&D investment proportions (r_im and r_in) are initialized in order..." For more information see Site Index or Murat Yildizoglu's Home Page COMPLEX SYSTEMS CALCULATORS & APPLETS - AGENT-BASED CONSTRUCTION & DESIGN PLANNING CALCULATORS & APPLETS MANAGEMENT WITH THE PLAN MANAGER (PM) AGENT - C. Petrie, Center for Design Research, Stanford University VERY VERY EXTENSIVE. Plan Manager (PM) Agent Calculator "...will return a schedule of tasks, performing a critical path analysis, when given a set of requirements and tasks, with their expected resource consumption and duration and subtask relationships. It is capable of interacting with the artifact design plans and using artifact features in planning and scheduling, unlike current project management tools that rely on fixed precedence relationships among tasks..." For more information see ProcessLink Project; Design Space Colonization (DSC) or the Center for Design Research COMPLEX SYSTEMS CALCULATORS & APPLETS - AGENT-BASED SCHELLING'S SEGREGATION MODEL CALCULATORS & APPLETS SCHELLING'S SEGREGATION MODEL - R. Singh, MIT For more information see Raf Singh's Home Page

Computational Science COMPUTATIONAL PHYSICS CALCULATORS & APPLETS COMPUTATIONAL PHYSICS - R.H. Landau, Landau Research Group, Department of Physics, Oregon State University and Manuel Páez, Páez Research Group, Instituto de Física, University of Antioquia, Medellin, Colombia VERY VERY EXTENSIVE. Available in English & Spanish/Español. Computational Physics Applets & Computational Physics Calculators Subject Categories include: "...Chaotic Scattering; Solutions of the Wave Equation; Cooling of Bar via Heat Flow; Quantum Wavepackets; Quantum Monte Carlo; Chaotic Pendulum in Phase Space; Interference & Diffraction; KdeV Solitons; Fractals & Statistical Physics; etc..." For more information see Computational Physics for UnderGraduates; Computational Physics; Página de Manuel Páez; Instituto de Física; Rubin H. Landau's Home Page or the Department of Physics Examples from over "40" Computational Physics Applets & Computational Physics Calculators include Chaotic Scattering from 4 Centers Asymetric wavepacket in square well Molecular Dynamics COMPUTATIONAL SCIENCE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS COMPUTATIONAL SCIENCE - SCIENTIFIC COMPUTING - Computational Science and Engineering Graduate Option Program, University of Illinois, Urbana-Champaign VERY VERY VERY...EXTENSIVE. Computational Science Applets & Computational Science Calculators Subject Categories include: "...Floating-Point Arithmetic; Linear Equations; Linear Least Squares; Eigenvalue Problems; Nonlinear Equations; Optimization; Interpolation; Integration and Differentiation; Ordinary Differential Equations; Partial Differential Equations; Fast Fourier Transform; Random Numbers and Simulation; etc..." For more information see the Computational Science and Engineering Graduate Option Program Some examples from over "70" Computational Science Calculators & Applets include Eigenvalues and Eigenvectors Calculators & Applets Eigenvalues and Eigenvectors Calculators & Applets include: Power/Inverse Iteration; Jacobi's Method; QR Iteration with Shifts; Gershgorin's Theorem..." Linear Least Squares Calculators & Applets Linear Least Squares Calculators & Applets include: "...Data Fitting; Gram-Schmidt; Householder Transformations; Lower-Rank Approximation; Householder QR Factorization; Givens QR Factorization; Gram-Schmidt QR Factorization; QR Factorization with Column Pivoting..." Ordinary Differential Equations Calculators & Applets Ordinary Differential Equations Calculators & Applets include: "...Euler's Method; Backward Euler; Trapezoid Method; Picard Iteration; Runge-Kutta; Taylor Series; Extrapolation; Collocation; Predictor-Corrector; etc..." Optimization Calculators & Applets Optimization Calculators & Applets include: "...Golden Section Search; Successive Parabolic Interpolation; Steepest Descent Method; Conjugate Gradient Method; Nelder-Mead Method; Sequential Quadratic Programming Method; Gauss-Newton Method; Levenberg-Marquardt Method; etc..." Computer Arithmetic Algorithms, Interval Analysis, Scientific Computing, MATLAB, etc. ALGORITHMS COURSES INTRODUCTION TO ALGORITHMS (REAL PLAYER, QUICKTIME, MPEG) - E. Demaine & C. Leiserson, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Introduction to Algorithms Course (Text, Images, Videos/Movies & Audio/Sound) VERY VERY VERY...EXTENSIVE. Introduction to Algorithms "...teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms;..." Examples of Introduction to Algorithms Video Lectures include: "...Analysis of Algorithms, Insertion Sort, Mergesort Video Lecture; Divide-and-Conquer: Strassen, Fibonacci, Polynomial Multiplication Video Lecture; Linear-time Sorting: Lower Bounds, Counting Sort, Radix Sort Video Lecture; Hashing, Hash Functions Video Lecture; Red-black Trees, Rotations, Insertions, Deletions Video Lecture; Augmenting Data Structures, Dynamic Order Statistics, Interval Trees Video Lecture; Dynamic Programming, Longest Common Subsequence Video Lecture; Shortest Paths I: Properties, Dijkstra's Algorithm, Breadth-first Search Video Lecture; etc..." For more information see Audio/Video Courses; Mathematics Courses; Courses by Departments; MIT OpenCourseWare or the Department of Mathematics COMPUTER ARITHMETIC ALGORITHMS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS COMPUTER ARITHMETIC ALGORITHMS SIMULATOR - I. Koren, Department of Electrical and Computer Engineering, College of Engineering, University of Massachusetts VERY VERY VERY...EXTENSIVE. Examples of "Computer Arithmetic Algorithms" Calculators Subject Categories include "...Addition Computer Arithmetic Algorithms Calculators; Multiplication Computer Arithmetic Algorithms Calculators; Division Computer Arithmetic Algorithms Calculators; Square Root Computer Arithmetic Algorithms Calculators; Floating-Point Arithmetic Computer Arithmetic Algorithms Calculators; Elementary Functions Computer Arithmetic Algorithms Calculators; Unconventional Number Systems Computer Arithmetic Algorithms Calculators; etc..." For more information see Israel Koren's Home Page or the Department of Electrical and Computer Engineering Examples from over "40" "Computer Arithmetic Algorithms" Calculators include Addition Algorithms: Ripple Carry Adder Calculator Ripple Carry Adder Calculator INPUT Values include: "...A; B; Binary or Decimal; Number of Bits; Signal Delays..." Multiplication Algorithms: 2's Complement Array Multiplier with Timing Calculator 2's Complement Array Multiplier with Timing Calculator INPUT Values include: "...A; X; Binary or Decimal; Number of Bits (>2); Signal Delays..." Division Algorithms: Division using overlapping SRT stages Calculator Division using overlapping SRT stages Calculator INPUT Values include: "...X; D; Binary or Decimal; Number of Bits (odd); Type of divider to use (srt-4 comprised of 2 srt-2; srt-8 comprised of 3 srt-2; srt-16 comprised of 4 srt-2; etc.); Signal Delays (CSA; 3 input Mux; 7 input Mux; etc.)..." Square Root Algorithms: Nonrestoring Square Root Calculator Nonrestoring Square Root Calculator INPUT Values include: "...X (must be between 0 and 1); Binary or Decimal; Number of Bits..." Floating-Point Arithmetic Algorithms: Floating Point Demonstration of FAR and CLOSE cases Calculator Floating Point Demonstration of FAR and CLOSE cases Calculator INPUT Values include: "...A; B; Hexadecimal or Decimal; single or double; Signal Delays (Pred. Exponent; Pred. Leading Zeroes; Simple 2 to 1 Mux; etc.)..." Elementary Functions Algorithms: Trigonometric Functions Calculator Trigonometric Functions Calculator INPUT Values include: "...C; Hexadecimal or Decimal; Number of Bits..." Unconventional Number Systems Algorithms: Residue Addition and Multiplication Calculator Residue Addition and Multiplication Calculator INPUT Values include: "...Moduli; Add, Subtract or Multiply; Input A; Input B..." Miscellaneous Algorithms: Wallace Carry-Save Tree Calculator Wallace Tree Simulations Calculator INPUT Values include: "...Binary or Decimal; Sum Delay; Carry Delay; Input Operand 1, 2, 3, etc..." INTERVAL ANALYSIS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS INTERVAL CALCULATORS - WEBCOMPUTING - Computational Science and Engineering (CSE), Institute of Mathematics and Informatics, Bulgarian Academy of Sciences VERY VERY VERY...EXTENSIVE. webComputing "...is a service which provides automatic interactive computation and visualization. It is intended to deploy technical computing solutions, especially interval computations, through a web interface..." Examples of Interval Computations include "...Interval Calculator; Interval Graphics Calculator; Interval Polynominal Expansion Calculator; Differentiate Interval Functions Calculator; Plot Interval Functions Calculator; Solution Set of Interval Linear System Calculator; AE Solution Sets of Interval Linear Systems Calculator; Solution Set of 3D Interval Linear System Calculator; Parametric Solution Set of Interval Linear System Calculator; etc..." For more information see Computational Science and Engineering (CSE) or the Institute of Mathematics and Informatics Examples of "Interval Calculators" using webMathematic include Interval Calculator Interval Graphics Calculator Differentiate Interval Functions Plot Interval Functions 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 SCIENTIFIC COMPUTING 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" Course Subject Categories & Subcategories 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 MATLAB INTRODUCTION TO MATLAB - Department of Engineering, Cambridge University Multimedia MATLAB Lessons, Technical Reports, Publications, etc. (Text & Images). VERY VERY VERY...EXTENSIVE. MATLAB TUTORIALS - The MathWorks, Inc. Multimedia MATLAB Textbooks, Lessons, etc. (Text & Images). VERY VERY VERY...EXTENSIVE. For more information see MathWorks MATHEMATICAL SOFTWARE INDEXES MATHEMATICAL SOFTWARE INDEX - Department of Mathematics, Penn State University Multimedia Mathematical Software Index (Text & Images). VERY VERY EXTENSIVE. For more information see Department of Mathematics MATHEMATICAL SOFTWARE INDEX - 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 Mathematical Software Index (Text & Images). VERY VERY EXTENSIVE. 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 SOFTWARE FOR MATHEMATICS - American Mathematical Society Multimedia Software for Mathematics Index (Text & Images). VERY VERY EXTENSIVE. For more information see American Mathematical Society

Continued Fractions CONTINUED FRACTIONS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS A CONTINUED FRACTION CALCULATOR - R. Knott, and hosted by the Department of Mathematics, Surrey University, U.K. VERY VERY EXTENSIVE. Continued Fraction Calculator: "...Continued fractions are just another way of writing fractions..." For more information see An Introduction to Continued Fractions; Fibonacci Numbers and the Golden Section or Ron Knott's Home Page CONTINUED FRACTIONS - D.A. Alpern, Buenos Aires, Argentina VERY VERY EXTENSIVE. Continued Fraction Calculator "...can find the continued fraction expansions of rational numbers and quadratic irrationalities..." "...For rational numbers the calculator finds all convergents, but for quadratic irrationalities the calculator stops after the 100000th convergent if the period is larger..." For more information see Calculators or Darío A. Alpern's Home Page CONTINUED FRACTIONS - F. Richman, Department of Mathematics, Florida Atlantic University VERY EXTENSIVE. Continued Fraction Calculator "...Enter a positive real number in decimal form and click on GO..." For more information see JavaScripts or Fred Richman's Home Page CONTINUED FRACTIONS (JAVA APPLETS) - J.J. Holt (University of Virginia) & J.W. Jones (Arizona State University) and hosted by the Department of Mathematical Sciences, Michigan Technological University; a W. H. Freeman and Company Production VERY EXTENSIVE. For more information see Number Theory or the Department of Mathematical Sciences Some examples of Continued Fractions Calculators include Continued Fractions for Square Roots Calculator Approximation with Continued Fractions Calculator "Pell's Equation" Calculator FINITE SIMPLE CONTINUED FRACTIONS - K.M. Levasseur, Department of Mathematical Sciences, University of Massachusetts Lowell VERY EXTENSIVE. Finite Simple Continued Fractions Calculator "...Generates the finite continued fraction representation (or approximation ) of a real number..." For more information see UMass Lowell WebMathematicaScripts; Kenneth M. Levasseur's Home Page; Department of Mathematical Sciences or HostSRV Curves CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS - ALL INCLUSIVE FAMOUS CURVES (JAVA APPLETS) - J.J. O'Connor and E.F. Robertson, School of Mathematics and Statistics, University of St Andrews, St Andrews, Scotland VERY VERY VERY...EXTENSIVE. For more information see MacTutor History of Mathematics archive Examples of over '40' Curve Applets & Curve Calculators Include Astroid Ellipse Hyperbolic Spiral Right Strophoid Watt's Curve CURVES (JAVA APPLETS) - Abteilung Geometrische Datenverarbeitung, Universität Karlsruhe (TH), Germany, (Geometric Design Group, University of Karlsruhe) VERY VERY EXTENSIVE. Curve Applets include: "...B-Splines Applet; Spline Curves Applet; De Boor's Applet; Spline Division Applet; B-Spline Rendering Applet; etc..." For more information see CAGD-Applets: An Interactive Tutorials on Geometric Modeling; CAGD-Applets Home Page or the Abteilung Geometrische Datenverarbeitung (Geometric Design Group) INTEGRAL CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS INTEGRAL CURVES - Wolfram Research Inc. VERY VERY EXTENSIVE. Integral Curves Calculator "...uses webMathematica to plot integral curves of a first-order differential equation..." For more information see webMathematica; webMathematica: The Way The Web Calculates or Wolfram Research Inc. HILBERT CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS, SIERPINSKI CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS PEANO CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS HILBERT, SIERPINSKI AND PEANO SPACE-FILLING CURVES APPLET - V.B. Balayoghan, Department of Computer Science, University of Texas, Austin, Texas VERY EXTENSIVE. Hilbert, Sierpinksi & Peano Space-Filling Curves Calculator "...draws the sequences of curves that define the 2-dimensional Hilbert, Sierpinski and Peano space-filling curves and several of their variations..." Hilbert, Sierpinksi & Peano Space-Filling Curves Calculator INPUT Values include: Select Curve "...Hilbert; Moore; Sierpinski; Sierpinski_C; Sierpinski_R; Peano; Peano_S; Peano_R; or Peano_M..." Select Recursive Level (1 thru 8)..." For more information see A Motley Assemblage of Stuff - Java Applets; V.B. Balayoghan's Home Page or the Department of Computer Science PEANO CURVE APPLET - F.C. Schoute, Information and Communication Theory (ICT), Department of Electrical Engineering, TU Delft, The Netherlands Peano Curve "...This Peano curve is called a plane-filling curve, because a square of given size will be filled ever denser by successive generations of this Peano curve. More mathematically: Given an arbitrairy point in the square and an epsilon > 0, no matter how small, there will be an N such that the Nth generation Peano curve passes by the given point at a distance smaller than epsilon..." For more information see Frits C. Schoute's Home Page or the Information and Communication Theory (ICT) Group SPLINE CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS SPLINES: AN INTERACTIVE INTRODUCTION TO SPLINES (JAVA APPLETS) - E. Demidov, Department of Semiconductor Physics, Institute for Physics of Microstructures (IPM), Russian Academy of Sciences (RAS), Russia VERY VERY VERY...EXTENSIVE. In English & Russian. For more information see E-notes Some examples from over "30" Spline Curves Applets & 3D Spline Surface Applets include Interpolating Cardinal and Catmull-Rom splines B-splines: Building cubic B-spline B-splines: Nonuniform B-splines Bézier spline curves Tensor product spline surfaces SPLINE CURVES AND SURFACES (JAVA APPLETS) - D. Gillies, Department of Computing, Imperial College London, U.K. Multimedia Spline Curves & Spline Surfaces Lessons with Applets (Text & Images). VERY VERY EXTENSIVE. For more information see Duncan Gillies' Home Page or the Department of Computing Examples from over "7" Spline Curves and Surfaces Applets include Explicit Spline Curves Calculators Explicit Spline Curves Calculators include: "...Cubic Curve Calculator; Quadratic Curve Calculator..." B-Spline Curves Calculators B-Spline Curves Calculators include: "...Approximate Gaussian Curve Calculator; Free B-Spline Calculator; B-Spline with Clamped Ends Calculator..." Bézier Surfaces CURVES (JAVA APPLETS) - Abteilung Geometrische Datenverarbeitung, Universität Karlsruhe (TH), Germany, (Geometric Design Group, University of Karlsruhe) VERY VERY EXTENSIVE. Curve Applets include: "...B-Splines Applet; Spline Curves Applet; De Boor's Applet; Spline Division Applet; B-Spline Rendering Applet; etc..." For more information see CAGD-Applets: An Interactive Tutorials on Geometric Modeling; CAGD-Applets Home Page or the Abteilung Geometrische Datenverarbeitung (Geometric Design Group) Curve Fitting NONLINEAR LEAST SQUARES CURVE FITTER CALCULATORS & APPLETS NONLINEAR LEAST SQUARES CURVE FITTER - J.C. Pezzullo, Georgetown University Medical Center VERY VERY EXTENSIVE. Nonlinear Least Squares Regression Curve Fitter Calculator "...lets you fit any function of up to eight parameters to a set of data. Just specify the function, the data points, and initial guesses to the parameters..." Nonlinear Least Squares Regression Curve Fitter Calculator INPUT Values include: "...Number of Data Points; Number of Independent Variables; Number of Parameters; Formula for the Function to be Fitted; Data; Best Guesses for the Parameters..." For more information see Interactive Statistics Calculations Pages or John C. Pezzullo's Home Page

Differential Equations, Partial Differential Equations, etc. DIFFERENTIAL EQUATIONS, PARTIAL DIFFERENTIAL EQUATIONS, ETC. COURSES, TEXTBOOKS, LECTURES, ETC. Undergraduate ELEMENTARY DIFFERENTIAL EQUATIONS WITH LINEAR ALGEBRA (QUICKTIME) - Selwyn Hollis, Department of Mathematics, Armstrong Atlantic State University, Savannah, Georgia Multimedia Elementary Differential Equations with Linear Algebra Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Examples from over "26" "Elementary Differential Equations with Linear Algebra Course" Video Lectures include Introductory Terminology and Concepts Video Lecture; First-order DEs "...Linear First-order Equations Video Lecture; Applications Involving Linear First-order Equations Video Lecture; Direction Fields and Numerical Approximation Video Lecture; etc..." Linear Second- and Higher-order DEs "...Linear Second-order Equations 1 - Fundamentals Video Lecture; Linear Second-order Equations 2 - Homogeneous Equations with Constant Coefficients Video Lecture; Linear Second-order Equations 3 - Nonhomogeneous Equations Video Lecture; etc..." Laplace Transforms "...The Laplace Transform 1 Video Lecture; The Laplace Transform 2 Video Lecture; etc..." Linear Algebra "...Linear Algebraic Equations I & II Video Lectures; Vectors and Matrices Video Lecture; Matrix Algebra Video Lecture; etc..." Linear Differential Systems "...Homogeneous Systems Video Lecture; Homogeneous Systems with Constant Coefficients Video Lecture; The Matrix Exponential Video Lecture; etc..." For more information see Selwyn Hollis' Home Page or the Department of Mathematics DIFFERENTIAL EQUATIONS MOVIES (QUICKTIME) - Selwyn Hollis, Department of Mathematics, Armstrong Atlantic State University, Savannah, Georgia Multimedia Differential Equations Movies (Text, Images & Videos/Movies). VERY VERY VERY...EXTENSIVE. Examples from over "50" "Differential Equations Subject Categories Videos include "...Exponential Growth & Decay; Logistic Growth Videos; Draining Tanks Videos; Spring-Mass Systems Videos; Graphs and Phase Plane Orbits Videos; Mechanical Systems Videos; Three Dimensional Systems Videos; etc..." For more information see Selwyn Hollis' Home Page or the Department of Mathematics DIFFERENTIAL EQUATIONS (REAL PLAYER, QUICKTIME, MPEG) - Arthur Mattuck & Haynes Miller, Department of Mathematics & the MIT OpenCourseWare, MIT VERY VERY VERY...EXTENSIVE. Multimedia Differential Equations Course (Text, Images, Videos/Movies & Audio/Sound). Differential Equations "...are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially..." Examples of "Differential Equations" Course Lectures (PDF) Subject Categories include "...First-order Differential Equations; Second-order Linear Equations; Fourier Series; The Laplace Transform; First Order Systems..." Examples from over "32" "Differential Equations" Course Video Lectures include Differential Equations Video Lecture 4 "...First-order Substitution Methods: Bernouilli and Homogeneous ODE's..." Differential Equations Video Lecture 7 "...First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Method..." Differential Equations Video Lecture 9 "...Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases..." Differential Equations Video Lecture 11 "...Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians..." Differential Equations Video Lecture 20 "...Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's..." Differential Equations Video Lecture 28 "...Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters..." For more information see Audio/Video Courses; Mathematics Courses; Courses by Departments; MIT OpenCourseWare or the Department of Mathematics Examples from over "25" Differential Equations Calculators & Applets include Complex Roots Convolution: Accumulation Isoclines DIFFERENTIAL EQUATIONS - P. Chiou, Department of Mathematics, Lamar University Multimedia Differential Equations Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Differential Equations" Course Chapters & Subchapters include First Order Differential Equations "...Linear Equations; Separable Equations; Intervals of Validity; Modeling with First Order Differential Equations; etc..." Second Order Differential Equations "...Reduction of Order; Fundamental Sets of Solutions; Nonhomogeneous Differential Equations; Undetermined Coefficients; etc..." Laplace Transforms "...Inverse Laplace Transforms; Step Function; Nonconstant Coefficient IVP's; etc..." Systems of Differential Equations "...Systems of Differential Equation; Solutions to Systems; Real Eigenvalues; Complex Eigenvalues; Nonhomogeneous Systems; etc..." For more information see Paul Chiou's Home Page or the Department of Mathematics ORDINARY DIFFERENTIAL EQUATIONS-LECTURE NOTES - E.J. Ionascu, Department of Mathematics, College of Science, Columbus State University, Columbus, Georgia Multimedia Ordinary Differential Equations-Lecture Notes - PDF, 112 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Ordinary Differential Equations-Lecture Notes" Chapters include "...Solving various types of differential equations; Analytical Methods, Second and n-order Linear Differential Equations; Systems of Differential Equations; Nonlinear Systems and Qualitative Methods; Laplace Transform; Power Series Methods; Fourier Series; etc..." For more information see Eugen J. Ionascu's Home Page or the Department of Mathematics PARTIAL DIFFERENTIAL EQUATIONS (231 A, B & C) - B.K. Driver, Department of Mathematics, University of California, San Diego Multimedia Partial Differential Equations Course (Text & Images). VERY VERY VERY...EXTENISVE. Examples of "Partial Differential Equations" Course Lectures include "...PDE Intro and Quasi-linear first order PDE; Non-linear first order PDE; Cauchy - Kovalevskaya Theorem; Elliptic second order ODE; Compact and Fredholm Operators; Surface integrals and the divergence theorem; Fourier Transform; Constant Coefficient PDE; Heat Equation; Abstract wave Equation; Weak and Strong Derivatives; Sobolev Spaces; Holder-spaces; Sobolev Inequalities; etc..." For more information see Math 231 A, B & C: Partial Differential Equations Home Page; Courses; Bruce K. Driver's Home Page or the Department of Mathematics FOURIER ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS - J.N. Kutz, Department of Applied Mathematics, College of Arts & Sciences, University of Washington Multimedia Fourier Analysis and Partial Differential Equations Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples From over "23" "Fourier Analysis and Partial Differential Equations" Course Lectures include "...The Diffusion Equation and Separation of Variables; Fourier Analysis; Nonhomogeneous PDEs and Eigenfunction Expansions; Sturm-Liouville Theory: nonhomogeneous problems; The Dirac Delta Function and Green's Functions; General Theory for Green's Functions; Fourier Transforms; Laplace Tranform; The Wave Equation; Solving the Wave Equation via Transforms; Higher Order Equations; First-order Equations: Method of Characteristics; Nonlinear Waves and Shocks; etc..." For more information see J. Nathan Kutz's Home Page or the Department of Applied Mathematics AN INTRODUCTION TO STOCHASTIC DIFFERENTIAL EQUATIONS - Lawrence C. Evans, Department of Mathematics, University of California, Berkeley Multimedia An Introduction to Stochastic Differential Equations Course - PDF, 139 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "An Introduction to Stochastic Differential Equations" Course Chapters include "...Introduction; A crash course in basic probability theory; Brownian motion and "white noise"; Stochastic integrals, Itô’s formula; Stochastic differential equations; Applications..." For more information see Lawrence C. Evans Home Page or the Department of Mathematics Graduate ENTROPY AND PARTIAL DIFFERENTIAL EQUATIONS - Lawrence C. Evans, Department of Mathematics, University of California, Berkeley Multimedia Entropy and Partial Differential Equations Course - PDF, 213 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Graduate Course. Examples of "Entropy and Partial Differential Equations" Course Chapters include "...Entropy and equilibrium; Entropy and irreversibility; Continuum thermodynamics; Elliptic and parabolic equations; Conservation laws and kinetic equations; Hamilton–Jacobi and related equations; Entropy and uncertainty; etc..." For more information see Lawrence C. Evans Home Page or the Department of Mathematics DIFFERENTIAL EQUATIONS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS BASSEL ZEROS CALCULATOR - Computational Science and Engineering (CSE), Institute of Mathematics and Informatics, Bulgarian Academy of Sciences VERY VERY EXTENSIVE. Bessel Zeros Calculator "...Bessel functions arise in solving differential equations for systems with cylindrical symmetry..." For more information see webComputing; Computational Science and Engineering (CSE) or the Institute of Mathematics and Informatics DFIELD AND PPLANE (JAVA APPPLETS) - J.C. Polking, ODE Software, Department of Mathematics, Rice University VERY VERY VERY...EXTENSIVE. DFIELD & PPLANE Calculators "...contain most of the features of the original MATLAB versions..." DFIELD Calculator "...is an interactive tool for studying single first order differential equations. DFIELD graphs a direction field for a given differential equation...". PPLANE Calculator is "...a tool for 'Phase Plane Analysis' of a System of Differential Equations of the form: x'=dx/dt=f(x,y), y'=dy/dt=g(x,y)..." For more information see ODE Software; John C. Polking's Home Page or the Department of Mathematics INTERACTIVE MATH PROGRAMS:: INTRODUCTION TO DIFFERENTIAL EQUATIONS & MULTIVARIABLE MATHEMATICS - R.E. Williamson & S. Schwarz, Dartmouth University VERY VERY VERY...EXTENSIVE. Multivariable Mathematics & Differential Equations Calculators & Applets Subject Categories include: Multivariable Calculus Calculators & Applets; First Order Equations Calculators & Applets; Second Order Equations Calculators & Applets; Higher Dimensional Systems Calculators & Applets; Partial Differential Equations Calculators & Applets. For more information see the Department of Mathematics Examples from over "35" Multivariable Mathematics & Differential Equations Calculators & Applets include First Order Equations: Direction Field Calculator Direction Field Calculator "...draws a direction field corresponding to a differential equation, and then, when the user clicks in the direction field, draws a solution graph starting at that point..." First Order Equations: First-Order DE Calculator First-Order DE Calculator "...uses the improved Euler method to plot graphs of solutions to initial-value problems of the form y'=f(x,y), y(x0)=y0..." Second Order Equations: Timesect Calculator Timesect Calculator "...allows the user to see the points plotted when the phase vectors (y,y') of a solution to an equation y''= f(t,y,y') is sampled at times tau units apart..." JDOE WITH SOME MODIFICATIONS & ADDITIONS: APPLETS FOR STUDING ORDINARY DIFFERENTIAL EQUATIONS - Author: M. Rychlik, Department of Mathematics, University of Arizona and and Additions & Modifications by the Department of Mathematics, Johns Hopkins University VERY VERY VERY...EXTENSIVE. Examples of Differential Equations Calculators & Applets include "...An example of a circuit; An Application to Population Dynamics; Slope Field Calculator; ODE 2D Calculator; ODE 3D Calculator; A Lotke-Volterra System; 2D Map Calculator; A model of sunam; The two body problem; Van der Pol Equation; Browser test; etc..." For more information see Mathematics 302: Differential Equations with Applications or the Department of Mathematics Some examples of Differential Equations Applets include Circuit Model Calculator ODE 3D Calculator: Lorenz System Slope Field Calculator Lotke-Volterra System Calculator JDOE WITH SOME MODIFICATIONS & ADDITIONS: APPLETS FOR STUDING ORDINARY DIFFERENTIAL EQUATIONS - Author: M. Rychlik, Department of Mathematics, University of Arizona and and Additions & Modifications by Eduardo D. Sontag, Department of Mathematics, Rutgers University VERY VERY VERY...EXTENSIVE. Examples of Differential Equations Calculators & Applets include "...Slope fields; Direction fields; 2D,3D,4D,5D,6D,7D,8D systems; Population Dynamics: Elks, Coyotes and Wolves in Yellowstone Park; Circuit; Limit cycle for the Van der Pol equation; Hodgin-Huxley equations; Chemostat; Gardner/Cantor/Collins Synthetic E.Coli Toggle Switch equations; etc..." For more information see Eduardo D. Sontag's Home Page or the Department of Mathematics JDOE: APPLETS FOR STUDING ORDINARY DIFFERENTIAL EQUATIONS - M. Rychlik, Department of Mathematics, University of Arizona VERY VERY VERY...EXTENSIVE. For more information see Marek Rychlik's Home Page or the Department of Mathematics Some examples from over "10" Differential Equations Applets include ODE 2D Calculator ODE 2D Calculator "...Direction fields and solutions of equations of systems of equations of form x'=f(x,y), y'=g(x,y)..." The Two Body Problem Calculator The Two Body Problem Calculator "...creates trajectories of a particle of unit mass in a gravitational field of an attracting center..." Solution Verifier Calculator Solution Verifier Calculator "...can be used to compare numerical solutions to exact and approximate formulas. In particular, can be used to test series solutions..."

DIFFERENTIAL EQUATIONS CALCULATOR: ODE SOLVER: TYPE AND SOLVE AN ODE (JAVAVIEW) - The JavaView Project, Germany VERY VERY EXTENSIVE. ODE Calculator: "...The integrator is a fourth-order Runge-Kutta method with constant step size..." For more information see JavaView INTERACTIVE DIFFERENTIAL EQUATIONS (JAVA APPLETS) - Authors: B. West, S. Strogatz, J.M. McDill & J. Cantwell, Addison Wesley Interactive, Addison-Wesley and Benjamin Cummings, Pearson Education, Inc. VERY VERY VERY...EXTENSIVE. Interactive Differential Equations (IDE) "...website is specifically designed for students taking a differential equations course. It is remarkably easy to use and focuses on helping students visualize the mathematics..." Includes Over "90" Differential Equations Calculators including: First Order Differential Equations Calculators include: "...Newton's Law of Cooling; Graphing Differential Equations; Single Species Population Models; Falling Bodies and Golf; Numerical Methods; Isoclines and Fences; Existence and Uniqueness; Orthogonal Trajectories; etc...." Second Order Differential Equations Calculators include: "...Linear Oscillators; Free Vibrations; Forced Vibrations; Forced Vibrations; Electrical Circuits; Laplace Transforms; etc..." Systems of Differential Equations Calculators include: "...Graphing Two-Dimensional Equations; Nonlinear Oscillators; Predator-Prey Population Models; Competing Species Population Models; etc..." Chaos & Bifurcation Calculators include: "...Bifurcations; Bifurcations in Planar Systems; Chaos in Forced Nonlinear Oscillators; The Lorenz Equations, etc..." For more information see Interactive Differential Equations BIFURCATION DIAGRAM PLOTTER (JAVA APPLET) - Jun-Ping Shi, Department of Mathematics, College of William and Mary VERY VERY EXTENSIVE. Bifurcation Diagram Plotter "...computes bifurcation diagram of a semilinear elliptic equation..." For more information see Jun-Ping Shi's Home Page or the Department of Mathematics DIFFERENTIAL EQUATIONS (JAVA APPLETS) - J. Feldman, Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada VERY EXTENSIVE. For more information see Joel Feldman's Home Page or the Department of Mathematics Some examples from over "10" Differential Equations Calculators & Applets include Simple ODE Solvers Simple ODE Solver "...illustrates some simple ODE solvers, namely Euler's method, the Improved Euler method and Runge-Kutta..." Euler's Method Applet Euler's Method Applet "...contains an annotated implementation of Euler's method..." Phase Plane Plots Calculator Phase Plane Plots Calculator "...exhibits a phase plane plotter that can be used to determine the qualitative behaviour of solutions of systems of first order ordinary differential equations..." The Heat Equation Calculator The Heat Equation Calculator "...illustrates the behaviour of solutions of the heat equation. The demonstration plots the solution given by separation of variables..." DIFFERENTIAL EQUATIONS (JAVA APPLETS) - Mathematics and its Applications in Engineering and Science, Department of Mathematical Sciences, The School of Science, Rensselaer Polytechnic Institute (RPI) Multimedia Differential Equations Lessons & Java Applets (Text & Images). VERY VERY EXTENSIVE. For more information see Modules Grouped by General Mathematics Topic; Project Links; Mathematical Sciences or Rensselaer Polytechnic Institute (RPI) NUMERICAL ADVECTION (JAVA APPLET) - S.A. Sarra, Department of Mathematics, Marshall University VERY VERY EXTENSIVE. Numberical Advection Calculator "...allows the user to experiment with various classical and modern schemes used to obtain numerical solutions of Partial Differential Equations..." For more information see the A Survey of Numerical Advection; Scott A. Sarra's Home Page or the Department of Mathematics THE SHOCK APPLET - S.A. Sarra, Department of Mathematics, Marshall University Shock Calculator "...introduces the method of characteristics for solving first order partial differential equations (PDEs)..." For more information see the The Method of Characteristics with applications to Conservation Laws; Scott A.Sarra's Home Page or the Department of Mathematics VISUAL DIFERENTIAL EQUATION SOLVER (JAVA APPLET) - P. Falstad VERY EXTENSIVE. Visual Differential Equation Solver "...displays solutions to some common differential equations..." Visual Differential Equation Solver includes: "...First-order Linear Differential Equation with Constant Coefficients; Second-order Linear Differential Equation with Constant Coefficient; Harmonic Oscillator; Bessel's Equation; Legendre's Equation; Hermite's Equation; Jacobi's Equation; Duffing's Equation; Van der Pol's Equation; etc..." For more information see Math, Physics & Engineering Applets or Paul Falstad's Home Page DIFFERENTIAL EQUATION SOFTWARE PROGRAMS FOR DOWNLOADING OVERTURE - Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laborabory (LLNL) VERY VERY VERY...EXTENSIVE. Overture "...is an object-oriented code framework for solving partial differential equations. It provides a portable, flexible software development environment or applications that involve the simulation of physical processes in complex moving geometry..." For more information see CASC Software; Center for Applied Scientific Computing (CASC) or the LLNL SUITE OF NONLINEAR AND DIFFERENTIAL/ALGEBRATIC EQUATION SOLVERS (SUNDIALS) - Center for Applied Scientific Computing (CASC), Lawrence Livermore National Laborabory (LLNL) VERY VERY VERY...EXTENSIVE. SUNDIAL Software Includes: CVODE: "...solves initial value problems for ordinary differential equation (ODE) systems..." CVODES: "...solves ODE systems and includes sensitivity analysis capabilities (forward and adjoint)..." IDA: "...solves initial value problems for differential-algebraic equation (DAE) systems..." KINSOL: "...solves nonlinear algebraic systems..." For more information see CASC Software; Center for Applied Scientific Computing (CASC) or the LLNL Discrete Mathematics DISCRETE MATHEMATICS COURSES DISCRETE MATHEMATICS FOR COMPUTER SCIENCE (CS70) - D. Wagner, Computer Science Division, University of California, Berkeley Multimedia Discrete Mathematics for Computer Science Course (Text & Images). VERY VERY EXTENSIVE. Examples of "Discrete Mathematics for Computer Science" Course Lectures include "...Strong Induction; Structural Induction; Proofs about Algorithms; Algebraic Algorithms; Number Theory; RSA, Fingerprints; Number Theory Applications; Random Variables, Expected Values; Linearity of Expectation, Variance; etc..." For more information see the Teaching; David Wagner or the Computer Science Division DISCRETE MATHEMATICS AND ALGORITHMS (CME305) - A. Saberi, Department of Management Science & Engineering, Stanford University Multimedia Discrete Mathematics and Algorithms Course (Text & Images). VERY VERY EXTENSIVE. Examples of "Discrete Mathematics and Algorithms" Course Lectures include "...Eulerian, Hamiltonian Paths; DNA Sequencing; Matchings, Alternating Paths; Hungarian Algorithm for Bipartite Matching; Network Flow; Ford-Fulkerson; Max-flow/Min-cut; etc..." For more information see the Discrete Mathematics and Algorithms Home Page; Amin Saberi's Home Page or the Department of Management Science & Engineering DISCRETE MATHEMATICS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS DISCRETE MATHEMATICS LESSONS USING CALCULATORS & APPLETS DISCRETE MATHEMATICS ALGORITHMS (JAVA APPLETS) - P. Athanasios, D. Nikolaos, & P. Panagiiotis, Univercity Of Patras, Greece Multimedia Discrete Mathematics Lessons (Text & Images). VERY VERY EXTENSIVE. For more information see Papagelis Athanasios' Home Page Some examples from over "8" Discrete Mathematics Applets include Kruskal Algorithm Applet Heuristic Algorithms Applet: Traveling Salesman Problem (T.S.P) Minimum Routes: Dijkstra Algorithm Applet Order Projects by Deadlines Precedence Applet DISCRETE MATHEMATICS (JAVA APPLETS) - Mathematics and its Applications in Engineering and Science, Department of Mathematical Sciences, The School of Science, Rensselaer Polytechnic Institute (RPI) Multimedia Discrete Mathematics Lessons & Applets (Text & Images). VERY VERY EXTENSIVE. For more information see Modules Grouped by General Mathematics Topic; Project Links; Mathematical Sciences or Rensselaer Polytechnic Institute (RPI) Some examples from over "8" Discrete Mathematics Applets include Graph Theory: Industrial Drilling Game Theory: Networking CASINO CALCULATORS & APPLETS SLOT MACHINE (JAVA APPLET) - D. Clark & C. Smith, Department of Mathematics, University of Rhode Island Slot Machine "...What makes this slot machine different and interesting is that you get to position the dice yourself before playing..." For more information see A Casino Game or the Department of Mathematics CATALAN NUMBERS CALCULATORS & APPLETS CATALAN STRUCTURES (JAVA APPLET) - D. E Taylor, School of Mathematics and Statistics, University of Sydney, Australia Catalan Structures "...Catalan numbers count many other types of finite structures, such as binary trees, planar trees, polygon dissections, and so on..." For more information see Activities or Don Taylors's Home Page FAIR DIVISION ALGORITHMS CALCULATORS & APPLETS THE FAIR DIVISION CALCULATOR (JAVA APPLET) - F.E. Su, Department of Mathematics, Harvey Mudd College, Claremont, CA For more information see Francis Edward Su's Home Page or the Department of Mathematics MARKOV CHAINS CALCULATORS & APPLETS MARKOV CHAIN MONTE CARLO CALCULATORS (JAVA APPLETS) - L.A. Breyer VERY VERY EXTENSIVE. Multimedia Markov Chain Monte Carlo Lessons & Calculators (Text & Images). Markov Chain Monte Carlo Calculators "...Try out various interactive Metropolis Hastings algorithms, such as the Independence Sampler, Random Walk methods, Langevin algorithms etc. You can draw your own target densities, too..." For more information see Laird A. Breyer's Home Page or Jeffrey S. Rosenthal's Home Page Some examples of Markov Chain Monte Carlo Calculators include Metropolis-Hastings Calculator Metropolis-Hastings Algorithms "...are a class of Markov chains which are commonly used to perform large scale calculations and simulations in Physics and Statistics..." Simulated Annealing Calculator Simulated Annealing "...is a mutation of the Metropolis-Hastings applet which shows how to use MCMC algorithms to find the global maxima of a given function..." Catalytic Coupling Calculator Coupling Constructions for Markov Chains "...are closely related to the study of convergence to the stationary distribution and so called mixing times..." PumpSimulator Calculator PumpSimulator Calculator "...shows how to use catalytic coupling to simulate perfectly from an autogamma model, also known as the Bayesian posterior for the pump dataset..." MARKOV CHAIN SIMULATIONS, CALCULATORS (JAVA APPLETS) - J.S. Rosenthal, Department of Statistics, University of Toronto VERY VERY EXTENSIVE. For more information see Applets or Jeffrey S. Rosenthal's Home Page Some examples from "6" Markov Chain Simulations include One-Dimensional "Independence Sampler" Metropolis Algorithm Markov Chain Calculator One-Dimensional "Independence Sampler" Metropolis Algorithm Markov Chain Calculator "...is a simulation of a one-dimensional "independence sampler" Metropolis algorithm Markov chain, started in stationarity...Try restarting the chain several times to see different simulation runs. Note that the mean sample value "should" be 1.0. However, with the default value of k=5, it is in fact often somewhat less and occasionally much more..." One-dimensional "slice sampler" Markov Chain One-dimensional "slice sampler" Markov Chain "...Slice samplers are an interesting way to simulate from a distribution, by sampling uniformly from the region underneath the graph of the density function. In general the samplers are multi-dimensional,..." "Coupling from the past" Algorithm "Coupling from the past" Algorithm "...Coupling from the past is an interesting new way to simulate exactly from a distribution, using only a Markov chain for which that distribution is stationary..." ROBINSON-SCHENSTED CALCULATORS & APPLETS ROBINSON-SCHENSTED: SCHENSTED ALGORITHM (JAVA APPLET) - T. Roby, Department of Mathematics, University of Connecticut For more information see The two-dimensional pictorial Schensted webpage; Tom Roby's Home Page or the Department of Mathematics Examples of other Two-dimensional Pictorial Schensted Applets include Schützenberger's Jeu de Taquin algorithm Fomin Table-based tableau workbench

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