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, January 6, 2009 Sydney, Australia: Wednesday, January 7, 2009 File Download Time Calculator Author, E-Mail, Privacy Policy & Disclaimer Currently the Calculators On-Line Center contains over "23,635" Calculators & Spreadsheets, over "3,475" 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 (Groups, Rings, etc.) ~ Commutative Algebra Base Conversion & Hexadecimal/Decimal Conversion ~ Bicycle Central Limit ~ Chaos & Catastrophe ~ Combinatorial Complex Analysis & Complex Numbers ~ Complex Systems (Agent-Based) Computational Science Computer Arithmetic Algorithms, Scientific Computing, MATLAB, etc. Continued Fractions ~ Curves ~ Curve Fitting Differential Equations ~ Discrete Mathematics Calculus Mathematics Center Calculators On-Line Center

Algebra I & II ALGEBRA I & II: ALGEBRA CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ALGEBRA I & II: COURSES WITH CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ALGEBRA - AlgebraHelp.com Multimedia Algebra Course (Text, Images, Calculators & Applets). VERY VERY EXTENSIVE. Algebra Subject Categories include: "...Simplifying; Negative Exponents; Substitution and Evaluating; Factoring; Exponents; Graphing; etc..." Algebra Calculator Categories include: "...Equations; Expressions; Functions; Numbers; 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 Algebra Subject Categories & Subcategoreis include Preliminary Topics "...Absolute Value; Factoring Numbers; Fractions; Geometric Formulas; LCM and GCF; Metric Conversions; Negative Numbers; etc..." Beginning Algebra Topics "...Intercepts; Midpoint Formula; Order of Operations; Polynomials; Ratio & Proportion; Scatterplots & Regressions; Scientific Notation; Simple Factoring..." Intermediate Algebra Topics "...Even and Odd Functions; Factor Theorem; Factoring Polynomials; Function Notation; Function Transformations; Polynomial Graphs; Rational Roots Test; Remainder Theorem; etc..." Advanced Algebra Topics "...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 Algebra I 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 ALGEBRA 1: GRAPHING LINEAR EQUATIONS - T. O'Brien Algebra Graphing Linear Equations Plotter "...can plot functions, differentials and integrals, including trigonometric functions. Use this to help with your algebra, trigonometry or calculus homework..." 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 GRAPHING TOOL (JAVA APPLETS) - C.J. Kentler, Department of Mathematics, Washington State University Algebra Graphing Tool "...Interactively graph curves. Learn the shapes of graphs. Learn about domain and range..." For more information see Math Lessons or the Department of Pure & Applied Mathematics 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 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 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 PRECALCULUS ALGEBRA LEANING ASSISTANCE (JAVA APPLETS) - C.J. Kentler, Department of Mathematics, Washington State University For more information see Department of Pure & Applied Mathematics Some examples from over "6" Algebra Calculators include Parabolas and Quadratic Equations Secant and Tangent Lines 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 ONLINE SAGE CALCULATOR & SAGE NOTEBOOK CALCULATOR - William Stein, Department of Mathematics, University of Mathematics VERY VERY VERY...EXTENSIVE. SAGE Calculator (Software for Algebra and Geometry Exploration) & SAGE Notebook Calculator are a "...studying 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..." For more information see William Stein's Home Page or the Department of Mathematics 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 CALCULATORS & APPLETS OCTONION AND OTHER DIVISION ALGEBRA - G. Dixon, Lincoln, MA Multimedia Octonion and other Division Algebras Teaching Modules (Text, Images & Calculators). VERY VERY VERY...EXTENSIVE. Examples of Octonion and other Division Algebras Teaching Modules 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 Geometric Algebra GEOMETRIC ALGEBRA COURSES, LECTURES, 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 Mathematics; James Milne's Home Page 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. 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 Some 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 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,..." 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; Projection; 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 of Linear Algebra 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. Linear Algebra Chapters include: "...Vector Spaces; Linear Transformation; Inner Product Space; Eingenvector & Eigevalue..." For more information see Paul Scott's Home Page or the School of Mathematical Sciences 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. Linear Algebra Calculators & Applets Subject Categores 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 CALCUATOR 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. ~ Cayley, Cyclic & Dihedral Groups Dihedral Groups ~ Lie Groups

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..." Abstract Algebra Course includes "...Course Chapters; Index of Abstract Algebra Definitions; Index of Abstract Algebra Theorems; List of Abstract Algebra Theorems..." Examples of Abstract Algebra 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,..." Abstract Algebra 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. Abstract Algebra 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..." Elements of Abstract and Linear Algebra 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, 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 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 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 Mathematics; James Milne's Home Page or the Department 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 GROUP THEORY - P. Scott, School of Mathematical Sciences, University of Adelaide, Australia Multimedia Group Theory Course (Text & Images). VERY VERY EXTENSIVE. Group Theory 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 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 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 LIE GROUPS 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 Commutative Algebra COMMUTATIVE ALGEBRA COURSES 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

Base Conversion & Hexadecimal/Decimal Conversion BASE CONVERSION 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 NUMBER SYSTEM CONVERSION TOOL - WITH CONVERSION PROCESS EXPLAINED - C. Gurwitz, Department of Computer and Information Science, Brooklyn College, & hosted by Computer Science Teaching Center (CSTC) VERY EXTENSIVE. Number System Calculator is "...a tool to practice converting between different number systems, using bases 2-16..." For more information see CSTC Resources or the Computer Science Teaching Center 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 CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS: CYCLING CALCULATORS, APPLETS & ANALYZERS MECHANICS AND THE BICYCLE CALCULATORS & APPLETS LINEAR ALGEBRA AND THE BICYCLE CALCULATORS & APPLETS FOR CYCLING CALCULATORS & APPLET SEE 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 Teaching Modules, 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 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 Teaching Modules & 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 Teaching Modules with Java Applets (Text & Images). In English & French/Français. VERY VERY EXTENSIVE. For more information see Lucien Dujardin's Home Page Some 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 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..." 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 Some 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; Evgeny Demidov's Home Page or the Institute for Physics of Microstructures 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 HENON MAP WITH DAMPING AND EXCITATION (JAVA APPLET) - C-AD Accelerator Physics, Brookhaven National Laboratory (BNL) Henon Map with Damping and Exciation Calculator "...You may also simulate the effects of adding synchrotron damping and excitation, by inserting non-zero values for the "damping decrement" Delta and..." For more information see C-AD Accelerator Physics 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

Combinatorial COMBINATORIAL COURSES WITH CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS COMBINATORIAL OBJECTS CALCULATORS & APPLETS COMBINATORIAL COURSE WITH CALCULATORS & APPLETS - Computer Science Department, University of Victoria, Victoria, British Columbia, Canada Multimedia Combinatorial Course with Combinatorial Applets & Combinatorial Calculators (Text & Images). VERY VERY EXTENSIVE. Combinatorial Objects "...can generate permutations, combinations, various types of trees, unlabelled graphs, linear extensions of posets, pentomino puzzle solutions, numerical partitions, and a host of other combinatorial objects..." Examples of Combinatorial Course Chapters include Permutations "...A permutation of objects is an arrangement of those objects in some order; that is, some object is placed in the first position, another in the second position, and so on, until all objects have been placed. For our purposes, a permutation is a string a(1), a(2), ..., a(n), where each a(i) is an element of the.." Subsets or Combinations "...A set is a collection of objects, and a subset is a sub-collection of those objects. The number of subsets of an n element set is 2n. In the Object Server, the set from which subsets are made is always the set [n] of the first n positive integers (i.e., [n] = {1,2,...,n})..." Necklaces, Unlabelled necklaces, Lyndon words, DeBruijn Sequences "...A k-ary necklace is an equivalence class of k-ary strings under rotation. We take the lexicographically smallest such string as the representative of each equivalence class and use this in the output of the program. A Lyndon word is an aperiodic necklace representative..." For more information see Index of Information Pages or the Combinatorial Object Server Examples of Combinatorial Applets & Combinatorial Calculators include Generate Necklaces Permutations and their restrictions Numerical Partitions and relatives Necklaces, Lyndon words, DeBruijn Sequence Complex Analysis & Complex Numbers 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 CALCULATOR - A. Bunkenburg, Department of Computing Science, University of Glasgow, Glasgow, Scotland, U.K. VERY VERY VERY...EXTENSIVE. Complex Calculator "...implements the functions of a usual desk calculator, but accepts input and displays output both symbolically and geometrically. In