CALCULATORS ON-LINE CENTER MATHEMATICS CENTER: A-D

U.S.: Saturday, December 28, 2019

Sydney, Australia: Sunday, December 29, 2019

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Currently the Calculators On-Line Center contains
over “22,125” Calculators & Spreadsheets,

over “4,420” 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 Algorithms, Interval Analysis, Scientific Computing, MATLAB, etc.

Continued Fractions ~
Curves

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 I & II – Kan Academy,
Mountain View,
California
Multimedia Algebra I & II Courses (Text, Images, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Browse down to Algebra and/or Algebra: Worked Examples

Examples from over “90” Algebra I & II Video Lectures include

• • “…Algebra: Equation of a line Video Lecture;

• • Complex Numbers Video Lecture;

• • Quadratic Equation Video Lecture;

• • Conic Sections: Circles, Ellipses & Hyperbolas Video Lectures;

• • Proof: Hyperbola Foci Video Lecture;

• • Partial Fraction Expansion Video Lecture;

• • Rational Inequalities Video Lecture; etc…”

Examples from over “100” Algebra I & II Worked Examples Video Lectures include

• • “…Absolute Value Equations Video Lecture;

• • Basic Linear Function Video Lecture;

• • Graphing systems of inequalities Video Lecture;

• • Solving Radical Equations Video Lecture;

• • Quadratic Functions Video Lecture;

• • Non-Linear Systems of Equations Video Lecture; etc…”

For more information see the

Kan Academy Team

ALGEBRA HELP – Wyzant, Inc.
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…”

For more information see the

Wyzant Math Lessons & Help;

Lessons;

Resources or

Wyzant

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

EQUATION GRAPHING CALCULATOR – Wyzant, Inc.

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

Calculator List;

Algebra Help;

Wyzant Math Lessons & Help;

Lessons;

Resources or

Wyzant

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 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.

Computational Algebra

Querying Albegraic Objects Systems

Algebraic Computations

Commutative Algebra ~
Guassian Integers

Permutations and Combinations

Advanced Algebra

COMPUTATIONAL ALGEBRA CALCULATORS

KANT/KASH: COMPUTATIONAL ALGEBRAIC NUMBER THRORY CALCULATOR – The KANT Group (Algebra and Number Theory),
Institute 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;

• • Galois groups;

• • Lattices;

• • Diophantine equations;

• • Algebraic function fields over finite fields, Q or number fields; etc…”

For more information see the

KANT Group (Algebra and 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,
Institute 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 the

KANT Group (Algebra and Number Theory)

ALGEBRAIC CALCULATORS & APPLETS

ALGEBRAIC SURFACE SOLVER (JAVAVIEW) – The JavaView Project, Germany
VERY VERY EXTENSIVE.

Algebraic Surface Solver (Algebraic Level 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

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

PERMUTATIONS AND COMBINATIONS CALCULATORS & APPLETS

PERMUTATIONS AND COMBINATIONS – CALCULATOR – WolframAlpha,
Wolfram
VERY EXTENSIVE.
For more information see

Mathematics;

Gallery;

Widgets or

WolframAlpha

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

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 Physics,
College of Liberal Arts,
International Christian University, Japan
VERY VERY VERY…EXTENSIVE.

Examples of “Geometic Algebra” Calculators Subject Categories which include over “40” Geometic Algebra Applets 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

Geometric Calculus in Fukui;

Eckhard M. S. Hitzer’s Home Page;

College of Liberal Arts or the

International Christian University

Linear Algebra Courses

Linear Algebra Calculators & Applets ~
Matrix Calculators

Linear Algebra

LINEAR ALGEBRA COURSES, LECTURES & TEXTBOOKS WITH CALCULATORS & APPLETS

LINEAR ALGEBRA – G. Strang,
Department of Mathematics & the
MIT OpenCourseWare, MIT
Multimedia Linear Algebra Course (Text, Images, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Linear Algebra Course

• • “…This course covers matrix theory and linear algebra, emphasizing topics

• • useful in other disciplines such as physics, economics and social sciences,

• • natural sciences, and engineering…”

Examples of “Linear Algebra” Course Sections (Units) & PDF & Video Lectures include

• • Ax = b and the Four Subspaces
    • “…Multiplication and Inverse Matrices PDF & Video Lectures;

• • • Factorization into A = LU PDF & Video Lectures;

• • • Column Space and Nullspace PDF & Video Lectures;

• • • Solving Ax = b: Row Reduced Form R PDF & Video Lectures;

• • • The Four Fundamental Subspaces PDF & Video Lectures;

• • • Graphs, Networks, Incidence Matrices PDF & Video Lectures; etc…”

Least Squares, Determinants and Eigenvalues

• • • “…Orthogonal Vectors and Subspaces PDF & Video Lectures;

• • • Projection Matrices and Least Squares PDF & Video Lectures;

• • • Orthogonal Matrices and Gram-Schmidt PDF & Video Lectures;

• • • Cramer’s Rule, Inverse Matrix and Volume PDF & Video Lectures;

• • • Eigenvalues and Eigenvectors PDF & Video Lectures;

• • • Diagonalization and Powers of A PDF & Video Lectures;

• • • Markov Matrices; Fourier Series PDF & Video Lectures; etc…”

Positive Definite Matrices and Applications

• • • “…Symmetric Matrices and Positive Definiteness PDF & Video Lectures;

• • • Positive Definite Matrices and Minima PDF & Video Lectures;

• • • Similar Matrices and Jordan Form PDF & Video Lectures;

• • • Linear Transformations and their Matrices PDF & Video Lectures;

• • • Left and Right Inverses; Pseudoinverse PDF & Video Lectures; etc…”

For more information see

Gilbert Strang’s Home Page;

Department of Mathematics;

Audio/Video Courses;

Mathematics Courses or the

MIT OpenCourseWare

LINEAR ALGEBRA TEXTBOOK – Jim Hefferon;
Department of Mathematics,
Saint Michael’s College,
Colchester, Vermont
Multimedia Linear Algebra Textbook – PDF, 443 Pages (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

Linear Algebra;

Jim Hefferon’s Home Page or the

Department of Mathematics

LINEAR ALGEBRA: MATH 115A – T. Tao,
Analysis Group,
Department of Mathematics,
Division of Physical Sciences,
College of Letters and Science,
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;

Analysis Group or the

Department of Mathematics

• • Some examples from over “5” Linear Algebra Applets include

Eigenvalues and Eigenvectors Calculator

Gram-Schmidt Orthogonalization Calculator

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

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 TRANSFORMATION APPLET – P. Atela-Cortés,
Department of Mathematics & Statistics,
Smith College
For more information see

Pau Atela-Cortés’ Home Page or the

Department of Mathematics & Statistics

MATRIX CALCULATORS & APPLETS

MATRIX MARKET (CALCULATORS & JAVA APPLETS) – Matrix Market,
Math, Statistics, and Computational Science,
Applied and Computational Mathematics 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

Math, Statistics, and Computational Science;

Applied and Computational Mathematics Division;

Information Technology Laboratory 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 (Emeritus),
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;

Stefan Waner’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 (Emeritus),
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;

Stefan Waner’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 12×12 matrices…”

For more information see

Bluebit Software

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 (Emeritus),
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;

Stefan Waner’s Home Page;

Department of Mathematics or

Hofstra University

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.

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 (Emeritus),
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,
Department of Computer Science,
School of Engineering,
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 or the

Department of Computer Science

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

• • • • “…This is a course on Class Field Theory, roughly along the lines of the

• • • • articles of Serre and Tate in Cassels-Fröhlich, except that the notes are

• • • • more detailed and cover more…”

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

Galois 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

Polynomials over Galois Fields

POLYNOMIALS OVER GALOIS FIELDS – Florent Chabaud,
Paris,
France
VERY VERY VERY…EXTENSIVE.

Examples of “Polynomials over Galois Fields” Calculators with Tables include

• • • • “…irreducible and primitive polynomials over binary field GF(2);

• • • • irreducible polynomials over ternary field GF(3);

• • • • primitive polynomials over field GF(7);

• • • • a server that computes irreducible and primitive polynomials on demand…”

For more information see

Florent Chabaud’s Home Page

ATLAS OF FINITE GROUP REPRESENTATIONS

ATLAS OF FINITE GROUP REPRESENTATIONS – Authors: R.A. Wilson (Emeritus),
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 – 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

HILBERTS FIFTH PROBLEM (254A) – T. Tao,
Analysis Group,
Department of Mathematics,
Division of Physical Sciences,
College of Letters and Science,
UCLA
Multimedia Hilberts Fifth Problem Graduate Topics Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Hilberts Fifth Problem Graduate Topics Course

• • • • “…The structural theory of locally compact groups. Haar measure.

• • • • Lie groups and Lie algebras. The Peter-Weyl theorem. Local groups.

• • • • The Gleason-Yamabe theorem, and the solution to Hilbert’s fifth problem.

• • • • The structural theory of approximate groups…”

Examples of Hilberts Fifth Problem” Graduate Topics Course Chapters include

• • • • “…Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula

• • • • Building Lie structure from representations and metrics;

• • • • Haar measure and the Peter-Weyl theorem;

• • • • The structure of locally compact groups, and Hilbert’s fifth problem;

• • • • The microstructure of approximate groups;

• • • • Applications of the structural theory of approximate groups; etc…”

For more information see

254A;

Terence Tao’s Home Page;

Analysis Group or the

Department of Mathematics

Group Theory, Groups, Calculators & Applets

GALLIAN’S CONTEMPORARY ABSTRACT ALGEBRA – 7TH EDITION (JAVA APPLETS) – J.A. Gallian,
Department of Mathematics and Statistics,
Swenson College of Science & Engineering,
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;

Swenson College of Science & Engineering or the

University of Minnesota, Duluth

GROUP THEORY: GROUPS OF ORDER 1-15 (JAVA APPLET) – J.J. Wavrik,
Department of Mathematics,
Division of Physical Sciences,
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,
College of Science,
University of Utah
Multimedia Lectures on Algebraic Theory of D-Modules – PDF, 143 Pages (Text & Images).
VERY VERY VERY…EXTENSIVE.

Under Lecture Notes: Click on “Lectures on Algebraic Theory of D-modules”.

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

HOMOLOGICAL ALGEBRA

Derived Categories Courses, Lectures, etc.

LECTURES ON DERIVED CATEGORIES – D. Milicic,
Department of Mathematics,
College of Science,
University of Utah
Multimedia Lectures on Derived Categories – PDF, 228 Pages (Text & Images).
VERY VERY VERY…EXTENSIVE.

Under Lectures: Click on “Lectures on Derived Categories”.

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,
Faculty of Arts and Sciences,
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,
College of Science,
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

Applied Mathematics & Applied Analysis

APPLIED MATHEMATICS COURSES, TEXTBOOKS, ETC.

APPLIED MATHEMATICS (MATH 280) – J.K. Hunger,
Applied Mathematics Group,
Department of Mathematics,
Division of Mathematical and Physical Sciences,
College of Letters and Science,
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,
College of Science & Engineering,
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 or the

School of Mathematics

METHODS OF APPLIED MATHEMATICS (MATH 534B) – W.G. Faris,
Department of Mathematics,
College of Science,
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: Lecture Notes;

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,
Division of Mathematical and Physical Sciences,
College of Letters and Science,
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

LINEAR OPERATORS IN HILBERT SPACE COURSES, TEXTBOOKS, ETC.

LECTURE NOTES AND BACKGROUND MATERIALS ON LINEAR OPERATORS IN HILBERT SPACE – Willard Miller,
Program in Applied, Computational & Industrial Mathematics and the
Institute for Mathematics and its Applications,
School of Mathematics,
University of Minnesota
Multimedia Lecture Notes and Background Materials on Linear Operators in Hilbert Space – PDF, 175 Pages (Text & Images).

Examples of “Lecture Notes and Background Materials on Linear Operators in Hilbert Space” Chapters include

• • • • “…Strum-Liouville Operators;

• • • • Completely Continuous Operators;

• • • • Spectral Theory for Self-Adjoint Operators;

• • • • Spectral Theory for Second-order Ordinay Differential Optereators; etc…”

For more information see

Willard Miller’s Home Page;

Program in Applied, Computational & Industrial Mathematics;

Institute for Mathematics and its Applications or the

School of Mathematics

Commutative Algebra

COMMUTATIVE ALGEBRA COURSES, TEXTBOOKS, ETC.

COMMUTATIVE ALGEBRA – R.B. Ash (Emeritus),
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 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: 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

CONVERT DECIMAL FLOATING-POINT TO 32-BIT, 64-BIT & 128 BIT HEXADECIMAL

CONVERT DECIMAL FLOATING-POINT TO 32-BIT, 64-BIT & 128-BIT HEXADECIMAL REPRESENTATIONS
ALONG WITH THEIR BINARY EQUIVALENTS: IEEE-754 CONVERSION CALCULATOR – C. Vickery,
Department of Computer Science,
Queens College, CUNY
VERY EXTENSIVE.

Floating-Point Conversion Calculator:

• • From Decimal Floating-Point To 32-bit, 64-bit & 128 bit,

• • Hexadecimal Representations Along with Their Binary Equivalents

For more information see

Christopher Vickery’s Web Site

CONVERT 32-BIT HEXADECIMAL REPRESENTATION TO DECIMAL FLOATING-POINT

CONVERT DECIMAL FLOATING-POINT TO 32-BIT, 64-BIT & 128-BIT HEXADECIMAL REPRESENTATIONS
ALONG WITH THEIR BINARY EQUIVALENTS: IEEE-754 CONVERSION CALCULATOR – C. Vickery,
Department of Computer Science,
Queens College, CUNY
VERY EXTENSIVE.

Floating-Point Conversion Calculator:

• • From Decimal Floating-Point To 32-bit, 64-bit & 128 bit,

• • Hexadecimal Representations Along with Their Binary Equivalents

For more information see

Christopher Vickery’s Web Site

CONVERT 64-BIT HEXADECIMAL REPRESENTATION TO DECIMAL FLOATING-POINT

CONVERT DECIMAL FLOATING-POINT TO 32-BIT, 64-BIT & 128-BIT HEXADECIMAL REPRESENTATIONS
ALONG WITH THEIR BINARY EQUIVALENTS: IEEE-754 CONVERSION CALCULATOR – C. Vickery,
Department of Computer Science,
Queens College, CUNY
VERY EXTENSIVE.

Floating-Point Conversion Calculator:

• • From Decimal Floating-Point To 32-bit, 64-bit & 128 bit,

• • Hexadecimal Representations Along with Their Binary Equivalents

For more information see

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

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

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;

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) – School of Mathematical & Statistical Sciences,
College of Liberal Arts and Sciences,
Arizona State University
For more information see the

School of Mathematical & Statistical Sciences

• • • • 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: Nonlinear Resonance 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,
Faculty of Science,
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,
Edmonton, Alberta, Canada

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;

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;

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

ADDITIVE COMBINATORICS (21-801) – Alan Frieze,
Department of Mathematical Sciences,
Carnegie Mellon University
Multimedia Additive Combinatorics Course (Text & Images).
VERY VERY VERY…EXTENSIVE.
For more information see

Combinatorics Home Page;

Teaching;

Alan Frieze’s Home Page or the

Department of Mathematical Sciences

• • • • Examples of “Additive Combinatorics” Course Lecture Notes include

Additive Combinatorics: Arithmetic Combinatorics Lecture Notes by Terence Tao, Analysis Group, Department of Mathematics, UCLA

• • • • • Multimedia Additive Combinatorics Lecture Notes PDF, 118 Pages (Text & Images

Additive Combinatorics: Sumsets and Structure Lecture Notes by Imre Z. Ruzsa, Alfred Renyi Institute of Mathematics, Budapest, Hungary
Multimedia Additive Combinatorics: Sumsets and Structure Lecture Notes PDF, 102 Pages (Text & Images

Combinatorics

COMBINATORICS (MATH 636) – C. Hanusa,
Department of Mathematics,
Queens College,
The City University of New York,
New York
Multimedia Combinatorics Course (Text & Images).
VERY VERY EXTENSIVE.

Examples of “Combinatorics” Course Lectures include

• • • • “…Principle of Inclusion-Exclusion;

• • • • Generating Functions;

• • • • Multiplying two generating functions;

• • • • Solving recurrence relations;

• • • • Pattern avoidance; etc…”

For more information see

Combinatorics Home Page (Math 636);

Christopher Hanusa’s Courses;

Christopher Hanusa’s Home page or the

Department of Mathematics

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 – Author: B.V. Shabat;
Hosted by: L. Ryzhik,
Department of Mathematics,
Stanford University
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,
Analysis Group,
Department of Mathematics,
Division of Physical Sciences,
College of Letters and Science,
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;

Analysis Group 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

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

Complex Systems – Agent-Based

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 or the

Design Space Colonization (DSC)

COMPLEX SYSTEMS CALCULATORS & APPLETS – AGENT-BASED

• • • SCHELLING’S SEGREGATION MODEL CALCULATORS & APPLETS

SCHELLING’S MODEL OF SEGREGATION – F. McCown,
Department of Computer Science,
Harding University;
Hosted by Nifty Assignments Session at the annual SIGCSE,
Department of Computer Science,
Stanford University
For more information see

Frank McCown’s Home Page

Computational Science

COMPUTATIONAL PHYSICS COURSES, LECTURES, CALCULATORS, APPLETS, ETC.

COMPUTATIONAL PHYSICS (PHYSICS 115/242) – A. Peter Young,
Department of Physics,
Division of Physical and Biological Sciences,
University of California, Santa Cruz
Multimedia Computational Physics Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples from over “30” “Computational Physics” Course Lectures include

• • • • “…Romberg Integration;

• • • • Runge-Kutta code for integrating the simple harmonic oscillator;

• • • • The Kepler problem;

• • • • Monte Carlo simulations in Statistical Physics;

• • • • The zeroes of the Riemann zeta function;

• • • • The Duffing equation (transition to chaos in a differential equation) ;

• • • • The Sierpinski gaske;

• • • • Quantum wells – Eigenvalues of the Schrödinger equation for a rectangular well;

• • • • Quantum wells – Eigenvalues of the Schrödinger equation for a sech2 well; etc…”

For more information see

Classes;

A. Peter Young’s Home Page or the

Department of Physics

COMPUTATIONAL SCIENCE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

COMPUTATIONAL SCIENCE – SCIENTIFIC COMPUTING – Developers: M.T. Heath,
E. VanderZee, J. Schoen, J. Naisbitt, S. Sakshuwong, J. Zou, and N. Exner;
Sponsored by: Computational Science and Engineering;
M.T. Heath (Fulton Watson Copp Chair Emeritus),
Department of Computer Science,
College of Engineering
University of Illinois,
Urbana-Champaign,
Illinois
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;