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MATHEMATICS CENTER: I-M

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Handbooks, Simulations, Animations, Videos, etc.)

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Currently the Calculators On-Line Center contains
over "24,310" Calculators & Spreadsheets,
over "4,110" Courses, Lectures, Manuals, Handbooks,
& "1,000's" of Movies, Videos, Simulations & Animations

COMPLEX MATH: I-M

Image Processing ~ Integers & Integer Sequences ~ Integrals

Interval Arithmetic

Knots, Knot Theory, Vectors, Vector Analysis,
Topology, Algebraic Topology, Computational Topology, etc.

Lambda ~ Lattices

Lebesgue Integration, Measure Theory & Measure and Integration Theory

Level Set Methods ~ Limits of Mathematics & Information Theory

Linear & Nonlinear Programming & Simplex

Logarithms

Logic - Mathematical Logic, Universal Algebra
Foundations of Mathematics, Set Theory, Model Theory,
Descriptive Set Theory, Axiomatic Set Theory, etc.

Math Animations ~ Math Music

Math Video Lectures & Seminars
in Various Disciplines
(includes over 5,000 Videos)

Mathematical Player

Mathematical Constants, Functions & Symbols (Pi, Stieltjes, etc.)

Mathematical Cognitive Tools

Mathematical Methods for Engineers ~ Mathematical Physics

Mathematica, JavaView,
LiveGraphics3D, 3D-XplorMath

Mathematics of Plant Patern Formation

Mathematics Center

Calculators On-Line Center

Image Processing

IMAGE PROCESSING COURSES, CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

IMAGE PROCESSING: ALL OPERATOR EXPERIMENTATION (JAVA APPLETS) - R. Fisher, S. Perkins, A. Walker and E. Wolfart, School of Informatics, University of Edinburgh, Edinburgh, Scotland, U.K. Multimedia Image Processing Course, Lessons, Calculators, Applets (Text & Images). VERY VERY VERY...EXTENSIVE.

"...provides on-line reference and tutorial information on a wide range of image processing operations, extensively illustrated with actual digitized images, and bound together in a hypermedia format for easy browsing, searching and cross-referencing. Amongst the features offered by HIPR are:
Reference information on around 50 of the most common classes of image processing operations in use today;
Detailed descriptions of how each operation works;
A JAVA demonstration of each operator, with online JAVA code for the core of the algorithm;
An interactive tableau where multiple operators can be linked together to demonstrate sequences of operations; etc..."

Examples of "Image Processing" Subject Categories include
"...Image Arithmetic;
Point Operations;
Geometric Operations;
Image Analysis;
Morphology;
Digital Filters;
Feature Detectors;
Image Transforms;
Image Synthesis;
Convolution..."
For more information see Robert Fisher's Home Page or the School of Informatics

Some examples from over "50" Image Processing Applets include

Image Arithmetic: Image AND Experimentation

Point Operations: Contrast Stretching Experimentation

Geometric Operations: Rotation Experimentation

Morphology: Thinning Experimentation

Image Transforms: Interactive Fourier Transform Experimentation

Image Processing Concepts

Integers & Integer Sequences

INTEGERS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

INTEGER SEQUENCES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

ENCYCLOPEDIA OF INTEGER SEQUENCES

SLOANE'S ON-LINE ENCYCLOPEDIA OF INTEGER SEQUENCES - N.J.A. Sloane, The OEIS Foundation Inc. VERY VERY VERY...EXTENSIVE.
What comes next after 1, 2, 4, 9, 20, 48, 115, 286, 719, ...?
"...This is the place to find out!..."
Sloane's On-Line Encyclopedia of Integer Sequences is available in
Arabic, Chinese, Czech, Danish, Dutch, English, Esperanto, Finnish,
French, German, Hebrew, Hindi, Hungarian, Italian, Japanese, Korean, Polish,
Portuguese, Romanian, Russian, Serbian, Spanish, Swedish, Turkish, etc.
For more information see Neil J.A. Sloane's Home Page

INTEGER CALCULATORS & APPLETS

ARBITARY-PRECISION INTEGER CALCULATORS - R.R. Howell, Department of Computing and Information Sciences, Kansas State University VERY VERY EXTENSIVE.
Arbitrary-Precision Integer Calculators
"...Both calculators use RPN (Reverse Polish Notation) data entry. The computational model is stack-based, with operations taking their arguments from the top of the stack and replacing them with their results. The value in the display is always the value at the top of the stack. The size of the stack is bounded only by the available memory..."
For more information see Java; Rodney R. Howell's Home Page or the Department of Computing and Information Sciences

INTEGER FACTORIZATION CALCULATORS & APPLETS

GAUSSIAN INTEGER FACTORIZATION CALCULATORS & APPLETS

GAUSSIAN INTEGER FACTORIZATION APPLET - D.A. Alpern, Buenos Aires, Argentina VERY VERY VERY...EXTENSIVE.
Gaussian Integer Factorization Calculator
"...finds the factors of complex numbers of the form a+bi where a and b are integers. It also includes a complete calculator with operators and functions using gaussian integers...You can enter numbers of up to 500 digits,..."
For more information see Number Theory; Calculators or Darío A. Alpern's Home Page

Integrals

INTEGRALS CALCULATORS & APPLETS

INTEGRALS: THE INTEGRATOR - Wolfram Research, Inc VERY VERY VERY...EXTENSIVE.
Wolfram Mathematica Online Integrator
"...The Power To Do Integrals As The World Has Never Seen Before..."
Wolfram Mathematica Online Integrator
"...is powered by webMathematica, so it expects input to be in Mathematica syntax. It can also parse many expressions when they are not in exactly the right form, so people who are unfamiliar with Mathematica syntax details will not usually encounter problems..."
For more information see Wolfram Research, Inc

Interval Arithmetic

INTERVAL CALCULATORS & APPLETS

INTERVAL ARITHMETIC CALCULATORS & APPLETS

INTERVAL ARITHMETIC CALCULATORS - T.J. Hickey, Department of Computer Science, Brandeis University VERY VERY EXTENSIVE.
Examples of "Interval Arithmetic" Calculators include
IA-Solver "...a solver for non-linear constraints...."
IA-Eval "...a simple Interval Arithmetic Evaluator..."
GIA-Eval "...A General Interval Arithmetic Evaluator..."
For more information see JScheme Applications; JScheme or Timothy J. Hickey's Home Page

JAVA-INTERVAL CALCULATOR - M.G. Arnold, Computer Architecture & Arithmetic Research (CAAR), Department of Computer Science and Engineering, P.C. Rossin College of Engineering & Applied Science, Lehigh University VERY VERY EXTENSIVE.
Java-Interval Calculator
"...The calculator performs interval arithmetic operations and computers interval version of mathematical functions..."
For more information see Mark G. Arnold's Home Page; Computer Architecture & Arithmetic Research (CAAR) or the Department of Computer Science and Engineering

Knots, Knot Theory, Vectors, Vector Analysis,
Topology, Algebraic Topology, Computational Topology, etc.

KNOT CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

KNOT THEORY S COURSES, TEXTBOOKS, LECTURES, LESSONS, CALCULATORS, ETC.

KNOTS COURSES, TEXTBOOKS, LECTURES, LESSONS, ETC.

MATHEMATICS AND KNOTS - Designed by: R. Brown , N. Gilbert, & T. Porter; W.W.W. Production by: C. Quinton, Schools of Electronics and Computer Science, Department of Mathematics, University of Wales, Bangor Multimedia Mathematics and Knots Lessons (Text & Images).
Mathematics and Knots
"...For mathematicians, the first object of study is the form of a knot..."
For more information see Sculpture Mathematics or the Centre for the Popularisation of Mathematics

THE KNOTPLOT SITE - R.G. Scharein, Hypnagogic Software VERY VERY VERY...EXTENSIVE.
The KnotPlot Site
"...Here you will find a collection of knots and links, viewed from a (partly) mathematical perspective. The images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions..."
For more information see Robert G. Scharein's Home Page or Hypnagogic Software

KNOT CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

HYPERBOLIC KNOT CENSUS: 3D INTERACTIVE VIEWER (JAVA APPLETS) - R.G. Scharein, Hypnagogic Software VERY VERY VERY...EXTENSIVE.
Hyperbolic Knot Census
"...Click on an image to bring up a 3D interactive viewer... change the model parameters..."
For more information see The Knotplot Site; Robert G. Scharein's Home Page or Hypnagogic Software

KNOT SIMPLIFIER (JAVAVIEW) - M. Andreeva, I. Dynnikov, S. Koval, K. Polthier & I. Taimanov, The JavaView Project, Germany VERY VERY EXTENSIVE. For more information see JavaView

TORUS KNOTS 2D & 3D: CREATE 2D & 3D TORUS KNOTS - CALCULATOR - Wolfram Research Inc. VERY EXTENSIVE.
Torus Knots
"...The torus is the mathematical figure that looks like the surface of a doughnut..."
For more information see webMathematica; webMathematica: The Way The Web Calculates or Wolfram Research Inc.

TOPOLOGY COURSES & TEXTBOOKS

ALGEBRAIC TOPOLOGY - A. Hatcher, Department of Mathematics, Cornell University, and Published by: Cambridge University Press Multimedia Algebraic Topology Textbook, PDF (Text & Images). VERY VERY VERY...EXTENSIVE.
Algebraic Topology
"...This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in spirit, and stays well within the confines of pure algebraic topology..."
Examples of "Algebraic Topology" Textbook Chapters include
"...The Fundamental Group;
Homology;
Cohomology;
Homotopy Theory; etc..."
For more information see Algebraic Topology Book Home Page; Allen Hatcher's Home Page or the Department of Mathematics

ALGEBRAIC TOPOLOGY II - D.R. Wilkins, School of Mathematics, Faculty of Science, Trinity College, University of Dublin, Ireland Multimedia Algebraic Topology II Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples from Algebraic Topology II Course Parts & Sections include
Part I
"...Rings and Modules;
Free Modules..."
Part II
"...Simplicial Complexes;
Homology Calculations; etc..."
Part III
"...Exact Sequences of Homology Groups;
The Topological Invariance of Simplicial Homology Groups; etc..."

For more information see Algebraic Topology I Course Home Page; Courses & Lecture Notes; David R. Wilkins Home Page or the School of Mathematics

ALGEBRAIC TOPOLOGY II - M. Behrens, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Algebraic Topology Course (Text & Images). VERY VERY EXTENSIVE.
Algebraic Topology
"...topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and..."
Examples of "Algebraic Topology" Course Lectures include
"...Compactly Generated Spaces;
Pointed Spaces and Homotopy Groups;
Cofibers;
Puppe Sequences;
Fibrations;
The Hurewicz Homomorphism;
The Spectral Sequence of a Filtered Complex;
Line Bundles; etc..."
For more information see the Mathematics Courses; MIT OpenCourseWare; Mark Behrens' Home Page or the Department of Mathematics

GENERAL TOPOLOGY AND REAL ANALYSIS - D.R. Wilkins, School of Mathematics, Faculty of Science, Trinity College, University of Dublin, Ireland Multimedia General Topology and Real Analysis Course, PDF (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "General Topology and Real Analysis" Course Lectures include
"...Sets, functions and countability;
Complete metric spaces, normed vector spaces, and Banach spaces;
Topological spaces;
Compact spaces;
The Lebesgue integral;
Signed measures and the Radon-Nikodym Theorem; etc..."
For more information see Courses & Lecture Notes; David R. Wilkins Home Page or the School of Mathematics

POINT-SET TOPOLOGY - B. Ikenaga, Department of Mathematics, School of Science and Mathematics, Millersiville University, Millersville, PA Multimedia Point-set Topology Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Point-set Topology" Course Lectures include
"...Topological Spaces, Bases;
Hausdorff Spaces;
Homeomorphisms;
Quotient Spaces;
Connected Subsets of the Reals;
Limit Point Compactness and Sequential Compactness;
Urysohn's Lemma;
The Tietze Extension Theorem; etc..."
For more information see Math Resources; Bruce Ikenaga's Home Page; Bruce Ikenaga's Faculty Home Page or the Department of Mathematics

SPECTRAL SEQUENCES IN ALGEBRAIC TOPOLOGY - A. Hatcher, Department of Mathematics, Cornell University Multimedia Spectral Sequences in Algebraic Topology Textbook, PDF (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Spectral Sequences in Algebraic Topology" Textbook Chapters include
"...Introduction to the Serre Spectral Sequence;
Adams Spectral Sequence;
Eilenberg-Moore Spectral Sequences..."
For more information see Allen Hatcher's Home Page or the Department of Mathematics

VECTOR BUNDLES & K-THEORY - A. Hatcher, Department of Mathematics, Cornell University Multimedia Bundles & K-Theory Textbook - PDF, 115 Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
Vector Bundles & K-Theory
"...The primary goal of the course is to present basic concepts from topology to enable a non-specialist to grasp and participate in current research in computational topology. As such, this course will not be a readings course in computational topology. Rather, it will present mathematics from a computer scientist's point of view..."
Examples of "Vector Bundles & K-Theory Textbook" Chapters & Subchapters include
Vector Bundles
"...Basic Definitions and Constructions;
Classifying Vector Bundles..."
K-Theory
"...The Functor K(X), Bott Periodicity;
Division Algebras and Parallelizable Spheres; etc..."
Characteristic Classes
"...Stiefel-Whitney and Chern Classes;
Euler and Pontryagin Classes; etc..."
The J-Homomorphism
"...Lower Bounds on Im J;
Upper Bounds on Im J..."

For more information see Vector Bundles & K-Theory Home Page; Allen Hatcher's Home Page or the Department of Mathematics

Computational Topology

INTRODUCTION TO COMPUTATIONAL TOPOLOGY - A. Zomorodian, Computer Graphics, Stanford University Multimedia Introduction to Computational Topology Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Introduction to Computational Topology
"...primary goal of the course is to present basic concepts from topology to enable a non-specialist to grasp and participate in current research in computational topology..."
Examples of "Computational Topology Course" Lectures include
"...Point Set Topology;
Surface Topology;
Simplicial Complexes;
Group Theory;
Homotopy;
Isosurface Topology Simplification;
Topology Matching for fully Automatic Similarity Estimation of 3D Shapes; etc..."
For more information see Computer Graphics

TOPOLOGY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

SURFACE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

ALGEBRAIC SURFACE SOLVER (JAVAVIEW) - The JavaView Project, Germany VERY VERY EXTENSIVE.
Algebraic Surface Solver
"...Algebraic surfaces are level sets of a scalar valued function F(x,y,z) from R3 to R where..."
For more information see JavaView

GALLERY OF SURFACES (JAVA APPLETS) - I. McIntosh, Department of Mathematics, University of York, U.K. VERY EXTENSIVE.
Surface Applets include:
"...Round Sphere;
Delaunay Unduloid;
Delaunay Nodoid;
Smyth Surface;
Smyth-Delaunay;
Generalized Smyth Surface;
Triunduloid, etc..."
For more information see Ian McIntosh's Home Page or the Department of Mathematics

JAVAVIEW - INTERACTIVE 3D GEOMETRY AND VISUALIZATION (JAVA APPLETS) - The JavaView Project, Germany VERY VERY VERY...EXTENSIVE. For more information see JavaView

Some examples from over "20" 3D Geometry Calculators include

Geodesic Surveyor: Measure Distances on Polyhedral Surfaces

Harmonic Maps and Minimal Surfaces

Parameterized Surfaces

Visualize Scalar Field on a Surface

REAL PROJECTIVE STRUCTURES ON HYPERBOLIC SURFACES (JAVA APPLET) - D. Austin, Department of Mathematics, Grand Valley State University, Allendale, Michigan For more information see Mathematical Graphics; David Austin's Home Page or the Department of Mathematics

SURFACES OF CONSTANT CURVATURE: DINI, KUEN & PSEUDOSPHERE PRINCIPALS - CALCULATOR - Wolfram Research Inc. VERY EXTENSIVE.
Surfaces of Constant Survature using LiveGraphics3D includes
"...Kuen Surface;
Pseudoshphere Surface;
Dini Surface..."
For more information see webMathematica; webMathematica: The Way The Web Calculates or Wolfram Research Inc.

VECTOR ANALYSIS

MULTIVARIABLE AND VECTOR ANALYSIS - W. Chen (Emeritus), Department of Mathematics, Division of Information and Communication Sciences (ICS), Faculty of Science, Macquarie University, Sydney, Australia Multimedia Multivariable and Vector Analysis Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Multivariable and Vector Analysis" Course Chapters & Subchapters include
Function of Serveral Variables;
Differentiation
"...Partial Derivatives;
Total Derivatives;
Consequences of Differentiability;
Conditions for Differentiability;
Properties of the Derivative; etc..."
Implicit and Inverse Function Theorems
"...Implicit Function Theorem;
Inverse Function Theorem; etc..."
Higher Order Derivatives
"...Taylor's Theorem;
Functions of Two Variables; etc..."
Double and Triple Integrals
"...Conditions for Integrability;
Double Integrals over Special Regions;
Fubini's Theorem;
Mean Value Theorem; etc..."
Change of Variables; Paths; etc.
For more information see Courses & Lecture Notes of William Chen; William Chen's Home Page or the Department of Mathematics

VECTOR CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

VECTOR LAND: AN INTRODUCTION TO 3D VECTOR ANALYSIS - P. Kirby Multimedia Course & Java Applets (Text & Images). VERY VERY EXTENSIVE.
Vector Land
"...This is the beginning of an online course to get to grips with 3D vectors for anyone who wants to learn..."

Some examples from over "8" Vector Calculators include

Parametric Curve Plotter

Parametric Surfaces Plotter

VECTOR ARITHMETIC CALCULATOR (JAVA APPLET) - V. Sorokin, General Physics Laboratory, Department of Physics & Astronomy, College of Arts and Sciences, University of Kentucky VERY EXTENSIVE.
Vector Arithmetic Calculator
"...visualizes addition, substraction and scalar multiplication of vectors..."
For more information see Java Applets; General Physics Laboratory or the Department of Physics & Astronomy

VECTOR CALCULATOR (JAVA APPLET) - J. Gea-Banacloche, Department of Physics, Natural Sciences, Fulbright College of Arts & Sciences, University of Arkansas
Vector Calculator is
"...intended to give students a "feel" for vectors in two dimensions..."
For more information see Julio Gea-Banacloche's Home-Made Page; Julio Gea-Banacloche's Faculty Home Page or the Department of Physics

Lambda

LAMBDA LESSONS, MODELING, CALCULATORS, APPLETS, ETC.

FINITE LAMBDA MODEL (JAVA APPLET) - P. Selinger, Department of Mathematics & Statistics, Dalhousie University, Halifax, Nova Scotia, Canada VERY EXTENSIVE.
Finite Lambda Model Calculator
"...allows you to edit a finite lambda model and several lambda terms. It checks that the model you are entering is well-defined, and automatically calculates the term denotations..."
For more information see Software; Research; Peter Selinger's Home Page or the Department of Mathematics & Statistics

THE PENN LAMBDA CALCULATOR - L. Champollion, J. Tauberer & M. Romero, Department of Linguistics, University of Pennsylvania VERY VERY EXTENSIVE.
The Penn Lambda Calculator
"...is an interactive, graphical, pedagogical computer program that helps students of formal semantics practice the typed lambda calculus..."
For more information see the Department of Linguistics

Lattices

LATTICE OVERIEW

FOR CRYSTALLOGRAPHY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS SEE CHEMISTRY CALCULATOR CENTER: CRYSTALLOGRAPHY

A CATALOGUE OF LATTICES - N.J.A. Sloane, AT&T Shannon Lab, AT&T Labs, AT&T Multimedia Lattice Database (Text & Images). VERY VERY VERY...EXTENSIVE.
Catalogue of Lattices Database
"...contains about 160,000 lattices..."
For more information see Neil J.A. Sloane's Home Page

LATTICE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

I(h) CALCULATOR OF A LATTICE - M. Kriechbaum, Institute of Biophysics and Nanosystems Research, Österreichische Akademie der Wissenschaften (Austrian Academy of Sciences), Austria VERY EXTENSIVE.
I(h) Lattice Calculator
"...calculates the scattering curve of a 1D (lamellar), 2D (hexagonal), or several 3D (cubic) lattices, respectively..."
For more information see Manfred Kriechbaum's Home Page (Small Angle Scattering); Institute of Biophysics and Nanosystems Research or the Austrian Academy of Sciences

PHASE TRANSITIONS ON LATTICES CALCULATORS & APPLETS

PHASE TRANSITIONS ON LATTICES (JAVA APPLETS) - E. Demidov, Department of Semiconductor Physics, Institute for Physics of Microstructures (IPM), Russian Academy of Sciences (RAS), Russia VERY VERY VERY...EXTENSIVE.
Available in English & Russian.
Examples of Phase Transitions on Lattices Subject Categories include
"...The 2D Ising model;
Topological Exitations in Ferromagnetics;
Percolation;
Path Integrals in Quantum Mechanics..."
For more information see E-notes

Some examples from over "14" Phase Transitions on Lattices Calculators include

Antiferromagnetics Calculators

Topological Solitons in the Heisenberg Ferromagnetic Calculator

Critical Exponents of Characteristic Functions Calculator

LATTICE DRAWING CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

LATTICE DRAWING (JAVA APPLET) - R. Freese, Department of Mathematics, College of Natural Sciences, University of Hawaii, Manoa, Hawaii
Lattice Drawing Calculator
"...demonstrates my program for automatically generating lattice diagrams from abstract representations of lattices (or partially ordered sets)..."
For more information see The Lattice Theory Homepage; Ralph Freese's Home Page or the Department of Mathematics

Lebesgue Integration, Measure Theory & Measure and Integration Theory

LEBESQUE INTEGRATION COURSES & LECTURES

INTRODUCTION TO LEBESQUE INTEGRATION - W. Chen (Emeritus), Department of Mathematics, Division of Information and Communication Sciences (ICS), Faculty of Science, Macquarie University, Sydney, Australia Multimedia Lebesgue Integration Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Introduction to Lebesgue Integration" Course Chapters & Subchapters include
The Read Numbers & Countability
"...Completeness of the Real Numbers;
Consequences of the Completeness Axiom..."
The Riemann Integral
"...Riemann Sums;
Lower and Upper Integrals;
Riemann Integrability..."
Point Sets
"...Open and Closed Sets;
Sets of Measure Zero;
Compact Sets; etc..."
Lebesgue Integral
"...Upper Functions on an Interval;
Lebesgue Integrable Functions on an Interval;
Sets of Measure Zero; etc..."
Montone Convergence Theorem;
Dominated Convergence Theorem; etc.
For more information see Courses & Lecture Notes of William Chen; William Chen's Home Page or the Department of Mathematics

MEASURE THEORY COURSES, TEXTBOOKS & LECTURES

MEASURE THEORY - L.E. Miller, Department of Mathematics, College of Liberal Arts and Sciences, University of Connecticut VERY VERY EXTENSIVE. Multimedia Measure Theory Course Notes - PDF, 80 Pages (Text & Images).
Examples of "Measure Theory" Course Lectures include
"...Measure;
Measureable Functions;
Littlewood Principles;
Lebesgue Integral and Convergence Theorems;
General Mesaure;
Fundamental Theorem;
Convex Functions;
Modes of convergence; etc..."
For more information see Lance E. Miller's Home Page or the Department of Mathematics

MEASURE THEORY (MATH 206) - 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 Measure Theory Course - PDF (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Measure Theory" Course Chapters include
"...Lebesgue Measure;
Integration and Convergence Theorems;
Product Measures and Fubini's Theorem;
Differentiation and Lebesgue's Theorem;
Radon Measures and Integrals as Linear Functionals; etc..."
For more information see Teaching; John K. Hunter's Home Page or the Department of Mathematics

MEASURE THEORY AND INTEGRATION THEORY COURSES, TEXTBOOKS & LECTURES

Undergraduate Measure and Integration Courses

MEASURE AND INTEGRATION - J. Viaclovsky, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Measure and Integration Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Measure and Integration
"...covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform..."
Examples of "Measure and Integration" Course Lectures include
"...Measure Theory;
Real-valued Measurable Functions;
Limits of Measurable Functions;
Simple Functions;
Positive Measures;
Definition of Lebesgue Integral;
Comparison of Lebesgue and Riemann Integrals;
Properties of Positive Measures;
Elementary Properties of the Lebesgue Integral;
Measure of Special Rectangles;
Measure of Special Polygons;
Measure of Open Sets;
Dominated Convergence Theorem Holds for Convergence in Measure; etc..."
For more information see Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare

Graduate Measure and Integration Courses, Textbooks, etc.

REAL ANALYSIS FOR GRADUATE STUDENTS: MEASURE AND INTEGRATION THEORY (2011) - Richard F. Bass, Department of Mathematics, College of Liberal Arts and Sciences, University of Connecticut Multimedia Real Analysis for Graduate Students: Measure and Integration Theory - PDF, 194 Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Real Analysis for Graduate Students: Measure and Integration Theory" Textbook Chapters include
"...Families of Sets;
Measures;
Measurable Functions;
The Lebesgue Integral;
Properties of Lebesgue Integrals;
Product Measures;
The Radon-Nikodym Theorem;
Diffenentiation;
Riesz Representations;
Banach Spaces;
Hilbert Spaces; etc..."
For more information see Lecture Notes; Richard Bass Home Page or the Department of Mathematics

Level Set Methods

LEVEL SET METHODS COURSES, TEXTBOOKS, LESSONS, CALCULATORS & APPLETS

FAST MARCHING METHODS AND LEVEL SET METHODS - Author: J.A. Sethian; Contributors to project include: D. Adalsteinsson; D.L. Chopp; J.S. Davis, II; M.L. Hald; R. Kimmel; R. Malladi; J. Rey and J. Zhu, Department of Mathematics, College of Letters & Science, University of California, Berkeley Multimedia Level Set Methods Textbook, Lessons, etc. (Text, Images, Videos/Movies & Applets). VERY VERY VERY...EXTENSIVE.
Fast Marching Methods and Level Set Methods
"...are numerical techniques which can follow the evolution of interfaces. These interfaces can develop sharp corners, break apart, and merge together..."
Examples of "Level Set Methods and Fast Marching Methods" Textbooks include
"...Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science..."
"...Level Set Method: An Act of Violence..."
Examples of "Level Set Methods and Fast Marching Methods" Videos include
"...Curvature Collapse Video;
Soap Bubbles Video;
Medical Scans Video;
Rising Bubble Video;
Microchip Manufacturing Video; etc..."
For more information see J.A. Sethian's Home Page or the Department of Mathematics

Examples Level Set Methods Applets include

Curve Flow Applets

Robotic Navigation

Limits of Mathematics & Information Theory

LIMITS OF MATHEMATICS COURSE, TEXTBOOKS, LESSONS, ETC.

THE LIMITS OF MATHEMATICS---THE BOOK (JUNE, 1994) - G.J. Chaitin, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y. & Hosted by the Department of Computer Science, University of Maine Multimedia The Limits of Mathematics---The Book - PDF, 270 Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
The Limits of Mathematics---The Book
"...This is a revised version of the course notes handed to each participant at the limits of mathematics short course, Orono, Maine, June 1994..."
For more information see Gregory J. Chaitin's Home Page

THE LIMITS OF MATHEMATICS---ALTERNATIVE VERSION (JULY, 1994) - G.J. Chaitin, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y. & Hosted by the Department of Computer Science, University of Maine Multimedia The Limits of Mathematics---Alternative Version - PDF, 255 Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
The Limits of Mathematics---Alternative Version
"...This version is based on measuring the size of what I call lisp m-expressions, which are lisp s-expressions with most parentheses omitted..."
For more information see Gregory J. Chaitin's Home Page

LIMITS OF MATHEMATICS CALCULATORS & APPLETS

LISP INTERPRETER FOR THE LIMITS OF MATHEMATICS, THE UNKNOWABLE, EXPLORING RANDOMNESS - G.J. Chaitin, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y. & Hosted by the Department of Computer Science, University of Maine VERY VERY EXTENSIVE.
LISP interpreter for The Limits of Mathematics, The Unknowable, Exploring Randomness Calculator
"...is identical with the "official" C and Mathematica versions, except that it allows several M-exps per line, and in its normal non-echo mode..."
For more information see Gregory J. Chaitin's Home Page

INFORMATION THEORY COURSES, TEXTBOOKS, ETC.

INFORMATION THEORY CALCULATORS & APPLETS

INFORMATION THEORY IN COMPUTER SCIENCE (2010) - A. Rao, Theory and Algorithms Research, University of Washington Computer Science & Engineering, University of Washington Multimedia Information Theory in Computer Science Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples from over "20" "Information Theory in Computer Science" Course Lectures include
"...Relative entropy and mutual information.;
Monotone formula lower bounds via graph entropy;
Shearer’s lemma, with applications to counting graph embeddings and the size of intersecting families;
The parallel repetition theorem;
On data structures and asymmetric communication complexity;
The space complexity of approximating the frequency moments;
Unbalanced expanders and randomness extractors from parvaresh-vardy codes; etc..."
For more information see Information Theory in Computer Science Home Page; Anup Rao's Home Page; Theory and Algorithms Research or University of Washington Computer Science & Engineering

SHANNON'S EXPERIMENT TO CALCULATE THE ENTROPY OF ENGLISH (JAVA APPLET) - D. Little, T. Mastro, M. Zabrocki & A.M. Garsia, Department of Mathematics, Eberly College of Science, Pennsylvania State University VERY EXTENSIVE.
Shannon's Experiment to Calculate the Entropy of English
"...Claude Shannon, the inventor of information theory, devised an experiment aimed at determining the entropy of an English letter (the amount of information in bits that we obtain on the average when we learn one letter of English)..."
For more information see Information Theory; Java Index; David Little's Home Page or the Department of Mathematics

Linear & Nonlinear Programming
including the Simplex Method

Linear Programming
Courses, Textbooks, Lectures & Lessons

Nonlinear Programming
Courses, Textbooks, Lectures & Lessons

Linear & Nonlinear Mathematical Programming

Affine-Scalling Algorithm

Linear Programming Graphers ~ Linear Programming & Pivioting

Nonlinear Equations ~ Simplex Method

Linear & Nonlinear Programming including the Simplex Method

LINEAR PROGRAMMING COURSES, TEXTBOOKS, LECTURES, LESSONS

Introduction to Practical Optimization

PRACTICAL OPTIMIZATION: A GENTLE INTRODUCTION - J.W. Chinneck, Department of Systems & Computer Engineering, Carleton University, Canada Multimedia Practical Optimization Course (Text, Images & Animations). VERY VERY VERY...EXTENSIVE.
Practical Optimization: A Gentle Introduction
"...is the art and science of allocating scarce resources to the best possible effect. Optimization techniques are called into play every day in questions of industrial planning, resource allocation, scheduling, decision-making, etc..."
Examples of "Practical Optimization: A Gentle Introduction" Course Chapters include
"...Introduction to Linear Programming;
Towards the Simplex Method for Efficient Solution of Linear Programs;
The Mechanics of the Simplex Method;
Solving General Linear Programs;
Sensitivity Analysis;
Linear Programming in Practice;
PERT for Project Planning and Scheduling;
Dynamic Programming; etc..."
Examples of "Algorithm Animations" Subject Categories include
"...Linear Programming Animations;
Network Animations;
Integer Programming Animations;
Yeuristics for Discrete Optimization Animations; etc..."
For more information see John W. Chinneck's Home Page or the Department of Systems & Computer Engineering

Linear Programming - Undergraduate & Graduate

LINEAR PROGRAMMING: FOUNDATIONS AND EXTENSIONS - R.J. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton Universtiy Multimedia Linear Programming Textbook, Introductory Graduate Lectures, Exercises, etc. (Text, Images & Applets). VERY VERY VERY...EXTENSIVE.
Examples of "Linear Programming: Foundations and Extension" Course Lectures include
"...The Simplex Method;
Degeneracy;
Efficiency;
Duality;
Self-Dual Simplex Method;
Parametric Simplex Method; etc..."
For more information see Robert J. Vanderbei's Home Page or the Department of Operations Research and Financial Engineering

NONLINEAR PROGRAMMING COURSES & TEXTBOOKS

NONLINEAR PROGRAMMING (REAL PLAYER) - Robert Freund, Sloan School of Management, & the MIT OpenCourseWare, MIT Multimedia Nonlinear Programming Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE.
Nonlinear Programming Course
"...introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming..."
Examples of "Nonlinear Programming" Course Video Lectures include
"...Newton's Method Video Lecture;
Duality Theory Video Lecture;
Semidefinite Optimization Video Lecture..."
Examples of "Nonlinear Programming" Course Lectures include
"...Convex Unconstrained Optimization Optimality Condition;
Newton's Method;
Steepest Descent Method;
Constrained Optimization Optimality Conditions;
Projection Methods for Equality Constrained Problems;
Penalty Methods;
Interior-Point Methods for Linear Optimization;
Analysis of Convex Sets; etc..."
For more information see MIT OpenCourseWare: Sloan School of Management Courses; Sloan School of Management or the MIT OpenCourseWare

LINEAR & NONLINEAR MATHEMATICAL PROGRAMMING CALCULATORS & APPLETS

AMPL: A MODELING LANGUAGE FOR MATHEMATICAL PROGRAMMING - AMPL Optimization LLC VERY VERY VERY...EXTENSIVE.
Modeling Language for Mathematical Programming (AMPL)
"...is a comprehensive and powerful algebraic modeling language for linear and nonlinear optimization problems, in discrete or continuous variables..."
"...lets you use common notation and familiar concepts to formulate optimization models and examine solutions, while the computer manages communication with an appropriate solver..."

AFFINE-SCALING ALGORITHM CALCULATORS & APPLETS

ALGORITHM ANIMATION: AFFINE SCALING (JAVA APPLET) - R. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton University VERY EXTENSIVE.
Affine-Scaling Algorithm Applet
"...animates the affine-scaling algorithm for solving linear programming problems..."
For more information see Linear Programming: Foundations and Extensions; Robert Vanderbei's Home Page or the Department of Operations Research and Financial Engineering

LINEAR PROGRAMMING GRAPHER CALCULATORS & APPLETS: TWO VARIABLES

LINEAR PRIGRAMMING GRAPHER - S. Waner, Department of Mathematics, Hofstra University VERY VERY EXTENSIVE.
Linear Programming Grapher Calculator
"...Type in any linear programming problem in two variables and press "Graph." Shows the feasible region, corner points, and optimal solution..."
For more information see Online Utilities & Software - Calculators; Finite Mathematics & Applied Calculus; Stefan Waner's Home Page; Department of Mathematics or Hofstra University

LINEAR PROGRAMMING AND PIVIOTING CALCULATORS & APPLETS

LINEAR PROGRAMMING AND PIVIOTING IN 2D (JAVA APPLET) - G. Aloupis & B. Kaluzny, Computational Geometry Lab, School of Computer Science, McGill University, CA VERY VERY EXTENSIVE.
Linear Programming and Pivoting in 2D Calculator:
"...The user may either select a hardcoded example, or input their own LP...
"...Pivoting: the user may pivot in 2 ways. The first is..."
For more information see Bohdan's Computational Geometry Page or Bohdan Kaluzny's Home Page

NONLINEAR EQUATIONS CALCULATORS & APPLETS

NONLINEAR APPLET - R.L. Devaney, Dynamical Systems and Technology Project, Department of Mathematics and Statistics, Boston University
Nonlinear Calculator
"...allows you to see the results of iteration of nonlinear functions such as the quadratic function x2 + c, the logistic function kx(1 - x), and..."
For more information see Dynamical Systems and Technology Project Applets; Dynamical Systems and Technology Project; Bob Devaney's Home Page or the Department of Mathematics and Statistics

SOLVE NONLINEAR EQUATIONS ONLINE - Engineers' Compendium, Sheba Construction & Management Pty. Limited, Bowral, NSW, Australia VERY VERY EXTENSIVE.
Nonlinear Equations Calculator:
"...Nonlinear equations occur in all fields of engineering. A given task is reduced to the form f(x)=0. The object is to find values of x that satisfy this condition. This doesn't always have to be ALL values. Most times, we are interested only in values between xmin and xmax..."
For more information see Engineers' Compendium

SIMPLEX METHOD CALCULATORS & APPLETS

THE SIMPLEX PLACE! AN INTRODUCTION TO THE SIMPLEX METHOD - M. Sniedovich, Operations Group, Department of Mathematics & Statistics, The University of Melbourne, Parkville, Australia VERY VERY EXTENSIVE.
An Introduction to the Simplex Method
"...In this discussion we examine the Simplex Method from the vantage point of the good old Gaussian elimination procedure for the solution of systems of linear equations..."
For more information see Welcome to Tutor; Moshe's Place (Old Home Page); Moshe Sniedovich Place (New Home Page); Operations Research Group or the Department of Mathematics & Statistics

LINEAR PROGRAMMING: LP EXPLORER (JAVA APPLET) - J.A. Julain Hall & M. Baird, Department of Mathematics & Statistics, University of Edinburgh, Scotland, U.K. VERY VERY EXTENSIVE.
LP Explorer
"...enables the simplex method to be applied to a linear programming (LP) problem and allows the sensitivity of the solution to changes in the problem data to be examined...LP Explorer is of particular value for problems with 2 variables when the simplex method and solution sensitivity are interpreted graphically..."
For more information see Teaching; J.A. Julian Hall's Home Page or the Department of Mathematics & Statistics

NETWORK SIMPLEX METHOD (JAVA APPLET) - R. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton University VERY VERY EXTENSIVE.
Network Simplex Method Calculator
"...that can be used to solve min-cost network-flow problems..."
For more information see Linear Programming: Foundations & Extensions; Robert Vanderbei's Home Page or the Department of Operations Research and Financial Engineering

PIVOT AND GAUSS-JORDAN TOOL - S. Waner, 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

SIMPLEX PIVOT TOOL - ADVANCED (JAVA APPLET) - R. Vanderbei, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton University VERY VERY EXTENSIVE.
Simplex Pivot Calculator
"...solve linear programming problems..."
"...features an artificial objective row and an artificial right-hand side column, which can be used to guide pivot choices for either a primal or a dual phase one process..."
For more information see Linear Programming: Foundations & Extensions; Robert Vanderbei's Home Page or the Department of Operations Research and Financial Engineering

SIMPLEX METHOD TOOL - S. Waner, Department of Mathematics, Hofstra University VERY EXTENSIVE.
Simplex Method Calculator allows you to
"...Just type in any linear programming problem..."
For more information see Online Utilities & Software - Calculators; Finite Mathematics & Applied Calculus; Stefan Waner's Home Page; Department of Mathematics or Hofstra University

Logarithms

LOGARITHM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

DISCRETE LOGARITHM CALCULATOR - D.A. Alpern, Buenos Aires, Argentina VERY VERY EXTENSIVE.
Discrete Logarithm Calculator
"... finds the exponent in the expression Base^Exponent = Power (mod Modulus)... works for both prime and composite moduli..."
For more information see Calculators or Darío A. Alpern's Home Page

LOGARITHMIC AND TRIGONOMETRIC FUNCTIONS CALCULATOR - Maritime Safety Information, National Geospatial Intelligence Agency VERY VERY EXTENSIVE.
Logarithmic and Trigonometric Functions Calculator
"...will calculate logarithms, trigonometric functions, and the logarithms of trigonometric functions..."
For more information see Marine Navigation Calculators; Maritime Safety Information or the National Geospatial Intelligence Agency

LOGARITHM CALCULATOR (JAVA APPLET) - P. Alfeld, Department of Mathematics, University of Utah VERY EXTENSIVE.
Logarithm Calculator explores
"...Exponentials, Radicals, and Logarithms..."
For more information see Java Page or Peter Alfeld 's Home Page

Logic - Mathematical Logic, Universal Algebra,

Foundations of Mathematics, Set Theory, Model Theory,
Descriptive Set Theory, Axiomatic Set Theory, etc.

MATHEMATICAL LOGIC COURSES, TEXTBOOKS, ETC.

Foundations of Mathematics - Set Theory, Model Theory

FOUNDATIONS OF MATHEMATICS (MATH 770) - K. Kunen, Department of Mathematics, University of Wisconsin Multimedia Foundations of Mathematics Course - PS & PDF, 148 Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Foundations of Mathematics" Course Sections include
"...Introduction;
Set Theory;
Model Theory; etc..."
For more information see Math 770; Kenneth Kunen's Home Page or the Department of Mathematics

Descriptive Set Theory

DESCRIPTIVE SET THEORY, SECOND EDITION, 2009 - Y.N. Moschovakis, Department of Mathematics, University of California, Los Angeles (UCLA) & the Department of Mathematics, University of Athens, Panepistimioupolis, Athens, Greece Multimedia Descriptive Set Theory, 2nd Edition Online Book - PDF, 516 Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Descriptive Set Theory" Chapters include
"...The Basic Classical Notions;
Basci Notions of the Effective Theory;
Structure theory for pointclasses;
The Constructible Universe;
The Recursion Theorem;
Metamathematics; etc..."
For more information see Yiannis N. Moschovakis' Home Page or the Department of Mathematics (UCLA)

DESCRIPTIVE SET THEORY (MATH 512) - D. Marker, Department of Mathematics, Statistics, and Computer Science, College of Liberal Arts & Sciences, University of Illinois, Chicago, Illinois Multimedia Descriptive Set Theory Course - PDF, 105 Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Descriptive Set Theory" Course Sections & Chapters include
Classical Descriptive Set Theory;
"...Polish Spaces;
Borel Sets;
Eﬀective Descriptive Set Theory: The Arithmetic Hierarchy;
Coanalytic Sets;
Hyperarithmetic Sets; etc..."
Borel Equivalence Relations
"...Tame Borel Equivalence Relations;
Countable Borel Equivalence Relations;
Hyperﬁnite Equivalence Relations; etc..."

For more information see David Marker's Home Page or the Department of Mathematics, Statistics, and Computer Science

Axiomatic Set Theory

INTRODUCTION TO AXIOMATIC SET THEORY - Scott Weinstein, Department of Philosophy, Department of Computer and Information Science; Department of Mathematics and the Logic and Computation Group; Typed by Brent Yorgey & Vilhelm Sjoberg, School of Arts and Sciences, University of Pennsylvania Multimedia Introduction to Axiomatic Set Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Introduction to Axiomatic Set Theory" Course Lectures include
"...Well orderings;
Ordinals, transfinite induction;
Transfinite recursion, cardinals;
Cardinals (Axiom of Choice, cardinality, normal functions, cofinality, cardinal arithmetic);
Proof of the Lowenheim-Skolem Theorem and related results;
Strongly inaccessible cardinals and ZF;
Independence of CH from ZFC (partial orders, filters, P-genericity); etc..."
For more information see Brent Yorgey's Home Page or Scott Weinstein's Home Page

UNIVERSAL ALGEBRA COURSES, TEXTBOOKS, CALCULATORS, ETC.

Universal Algebra Courses & Textbooks

UNIVERSAL ALGEBRA - J. Jezek, Department of Algebra, School of Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic Multimedia Universal Algebra Course (Book) - PDF, 331 Pages (Text & Images).
Examples of "Universal Algebra" Course (Book) Chapters include
"...Set Theory;
Structures and Algebras;
Lattices and Boolean Algebras;
Model Theory;
Varieties;
Mal'cev Type Theorems;
Commutator Theory and Abelian Algebras;
Algorithms in Universal Algebra;
Minimal Sets;
The Lattice of Equational Theories; etc..."
For more information see Jaroslav Jezek's Home Page or the School of Mathematics

UNIVERSAL ALGEBRA - S.N. Burris (Emeritus), (Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo); & H.P. Sankappanavar, (Department of Mathematics and Computer Science, SUNY, New Paltz, New York) Multimedia A Course in Universal Algebra - The Millennium Edition - PDF, 331 Pages (Text & Images).
Examples of "A Course in Universal Algebra" Sections and Chapters include
Lattices;
The Elements of Universal Algebra
"...Isomorphic Algebras, and Subalgebras;
The Irredundant Basis Theorem;
Homomorphisms and the Homomorphism and Isomorphism Theorems;
Subdirect Products, Subdirectly Irreducible Algebras, and Simple Algebras;
Class Operators and Varieties;
Terms, Term Algebras, and Free Algebras;
Identities, Free Algebras, and Birkhoﬀ ’s Theorem; etc..."
Selected Topics
"...Quasigroups, Loops, and Latin Squares;
Orthogonal Latin Squares; etc..."
Starting from Boolean Algebras
"...Boolean Algebras;
Boolean Rings;
Stone Duality;
Primal Algebras;
Discriminator Varieties;
Quasiprimal Algebras; etc..."
Connections with Model Theory etc.
For more information see Stanley N. Burris Home Page or the Department of Pure Mathematics

Universal Algebra Calculators & Applets

UACALC - A UNIVERSAL ALGEBRA CALCULATOR - R. Freese, Department of Mathematics, College of Natural Sciences, University of Hawaii, Manoa, Hawaii VERY VERY VERY...EXTENSIVE.
UACalc - A Universal Algebra Calculator - Download - Java
For more information see An algebra calculator program; The Lattice Theory Homepage; Ralph Freese's Home Page or the Department of Mathematics

Math Animations & Math Museums

MATH ANIMATIONS & SIMULATIONS

A VIRTUAL SPACE-TIME TRAVEL MACHINE: A GATEWAY BETWEEN ART AND SCIENCE - UNE MACHINE VIRTUELLE A EXPLORER L'ESPACE-TEMS: UN PONT ENTRE L'ART ET LA SCIENCE - Jean-Francois Colonna, France Telecom R&D and CMAP/Ecole Polytechnique, France VERY VERY VERY...EXTENSIVE.
Includes more than "2820" Images & Animations, including:
"...Quantum Mechanics;
Deterministic Chaos;
Particle Systems;
Deterministic Fractal Geometry;
Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis;
Fluid Mechanics;
Celestial Mechanics;
Astrophysics;
Sensitivity to Rounding-Off Errors;
Number Theory;
Signal Processing;
Texture Synthesis; etc..."
For more information see Ecole Polytechnique, France

Math Music

MATH MUSIC CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

FOR MUSIC & COMPUTER MUSIC COURSES, LESSONS, DATABASES, CALCULATORS, SIMULATIONS, ETC. SEE MUSIC CENTER

METAMATH MUSIC - N. Megill VERY VERY EXTENSIVE.
Mathematical Proofs Set to Music
"...The music generated from these mathematical proofs stands in sharp contrast to certain other experimental music based on such mathematics as the digits of Pi. Unlike a proof's tree structure, which is inherently suggestive of a musical score, the digits of Pi have no obvious pattern..."
For more information see Metamath Home Page or Metamath Site Selection

VISUALIZING PHYSICS WITH SOUND - Landau Research Group, Department of Physics, Oregon State University VERY EXTENSIVE.
Vsualizing Physics with Sound includes
"...Inverse Fourier Transformation;
Frequency Modulation;
Direct Transformation; etc..."
For more information see Computational Physics; Rubin H. Landau's Home Page or the Department of Physics

Math Video Lectures & Seminars in Various Disciplines

MATH VIDEO LECTURES & SEMINARS IN VARIOIUS DISCIPLINES

VIDEO FORMATS INCLUDE FLASH, MPEG, WINDOWS MEDIA, REALPLAYER, QUICKTIME, ETC.

NSF MATHEMATICAL SCIENCES INSTITUTES

MSRI: VMATH, THE NEXT GENERATION FOR MATH LECTURES: MATHEMATICS VIDEO LECTURES (QUICKTIME) - Mathematical Sciences Research Institute (MSRI), Berkeley, CA Multimedia Mathematical Sciences Research Institute (MSRI) Math Lectures (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE.
Includes over "2,000" Mathematical Sciences Research Institute (MSRI) Math Video Lectures in Various Disciplines including
"...Algebraic, Geometric, and Combinatorial Methods for Optimization Video Lectures;
Random Matrix Theory and Its Applications Video Lectures;
Kervaire invariant Video Lectures;
Inverse Problems: Theory and Applications Video Lectures;
Symplectic and Contact Topology and Dynamics: Puzzles and Horizons Video Lectures;
Symplectic and Poisson Geometry in interaction with Algebra, Analysis and Topology Video Lectures;
Symplectic Geometry, Noncommutative Geometry and Physics Video Lectures;
Elliptic Curves and Applications Video Lectures;
Computing with Elliptic Curves Video Lectures; etc..."
For more information see the Mathematical Sciences Research Institute (MSRI)

ISAAC NEWTON INSTITUTE MATH SEMINARS - Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. Multimedia Isaac Newton Institute for Mathematical Sciences Math Seminars (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE.
Example from over "1,500" Isaac Newton Institute for Mathematical Sciences Math Video Seminars Subject Categories include
"...Inverse Problems in Analysis and Geometry Video Lectures;
Analytic and Geometric Methods in Medical Imaging Video Lectures;
Experiments for Processes with Time or Space Dynamics Video Lectures;
Optimum Design for Mixed Effects Non-linear and Generalised Linear Models Video Lectures;
Inverse Problems in Science and Engineering Video Lectures; etc..."
For more information see Isaac Newton Institute for Mathematical Sciences

Also see

Isaac Newton Institute for Mathematical Sciences Collections
Example of Collections Subject Categories include
"...Cardiac Physiome Project: 56 Video Lectures;
Combinatorics and Statistical Mechanics: 143 Video Lectures;
Design and Analysis of Experiments: 244 Video Lectures;
Inverse Problems: 136 Video Lectures; etc..."

FIELDS INSTITUTE MATH SEMINARS - Fields Institute for Research in Mathematical Sciences, Fields Institute, Toronto, Ontario, Canada Multimedia Fields Institute for Research in Mathematical Sciences Math Seminars (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE.
Includes over 1,500 Videos.
Example of Fields Institute for Research in Mathematical Sciences Math Video Seminars Subject Categories include
"...Quantitative Finance Video Lectures;
Computational Topology Video Lectures;
Sphere Arrangments Video Lectures;
Rigidity Video Lectures;
Rigidity and Symmetry Video Lectures;
Graphs, Maps and Polytopes Video Lectures;
Optimization in Finance and Risk Management Video Lectures; etc..."
For more information see Fields Institute

IMA MATH VIDEO LECTURES (QUICKTIME, REAL PLAYER, ETC.) - Institute for Mathematics and its Applications, a NSF Mathematical Sciences Institute and located at the University of Minnesota Multimedia Institute for Mathematics and its Applications Math Video Lectures (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE.
Includes over "500" Institute for Mathematics and its Applications Math Video Lectures in Various Disciplines including
IMA Annual Program Workshops and Tutorials
"...Mathematics of Information Video Lectures;
Simulating Our Complex World: Modeling, Computation and Analysis Video Lectures;
Complex Fluids and Complex Flows Video Lectures; etc..."
IMA Hot Topics Workshops and Special Events
"...Instantaneous Frequencies and Trends for Nonstationary Nonlinear Data Video Lectures;
Uncertainty Quantification in Industrial and Energy Applications: Experiences and Challenges Video Lectures;
Integral Equation Methods, Fast Algorithms and Applications Video Lectures; etc..."
IMA Seminars on Industrial Problems; etc.
For more information see the Institute for Mathematics and its Applications

DUKE UNIVERSITY MATH SEMINARS - Department of Mathematics, Trinity College of Arts & Sciences, Duke University Multimedia Duke University Department of Mathematics Math Seminars (Text, Images, Videos/Movies & Audio/Sound). VERY EXTENSIVE.
Examples of "Duke University Department of Mathematics Math Seminars Math Video Seminars & Math Videos" include
"...F-Theory Video Lectures;
Geometry Topology Video Lectures;
Introduction to F-Theory Video Lectures;
Applied Mathematics Video Lectures; etc..."
For more information see Department of Mathematics

Mathematical Player

MATHEMATICA PLAYER - CALCULATORS, ANIMATIONS & SIMULATIONS

WOLFRAM DEMONSTRATION PROGRAM - WOLFRAM MATHEMATICA PLAYER - Wolfram Mathematica Player, Wolfram Research, Inc. VERY VERY VERY...EXTENSIVE.
Wolfram Demonstrations Project
"...Conceived by Mathematica creator and scientist Stephen Wolfram as a way to bring computational exploration to the widest possible audience, The Wolfram Demonstrations Project is an open-code resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a remarkable range of other fields..."
Examples of Mathematical Player Subject Categories include
"...Mathematics;
Computation;
Physical Sciences;
Systems, Models & Methods;
Engineering & Technology; etc..."
For more information see Wolfram Research, Inc.

Mathematical Constants, Functions, Symbols, Pi, etc.

NAMES OF A NUMBER

THE ENGLISH NAME OF A NUMBER - L.C. Noll, Cryptologist/Security Architect, Cisco Systems, Inc.
The English Name of a Number includes the
"..first 10000 powers of 10 in American system with dashes; American system without dashes; Eurpoean system with dashes; Eurpoean system without dashes..."
Example: "...in the 'American system without dashes' the name for 10⁷⁷²⁸
is one domilliaquingenquinseptuagintillion..."
For more information see Landon Curt Noll's Home Page or isthe.com

MATHEMATICAL CONSTANTS, FUNCTIONS, FORMULAS, SYMBOLS, ETC.

LaTeX Equation Editor

ONLINE LATEX EQUATION EDITOR - A. Rundquist, Department of Physics, College of Liberal Arts, Hamline University, Saint Paul, Minnesota VERY VERY VERY...EXTENSIVE.
Online LaTeX Equation Editor
"...interactive LaTeX equation editor let's you write and download equations in seconds!..."
For more information see Andy Rundquist's Home Page or the Department of Physics

INTERACTIVE TEX EDITOR (ITE) - AZ: Jim Hefferon's Web Views of the Comprehensive TeX Archive Network, J. Hefferon Multimedia Interactive TeX Editor (Text & Images). VERY VERY EXTENSIVE.
Interactive TeX Editor
"...easy to use, interactive authoring tool for LaTeX documents..."
For more information see CTAN directory: /support; tex-archive or AZ: Jim Hefferon's Web Views of the Comprehensive TeX Archive Network

Mathematical Constants

PLOUFFE'S INVERTER - S. Plouffe, Laboratoire de combinatoire et d'informatique mathématique, Université du Québec à Montréal VERY VERY VERY...EXTENSIVE.
Available in English & French.
Plouffe's Inverter
"...is a database of more than 215,000,000 mathematical constants like Pi, E, Catalan or Euler-Mascheroni constant with more than 2 billion digits..."
For more information see the Laboratoire de combinatoire et d'informatique mathématique

Mathematical Functions, Formulas, etc.

BP-TYPE FORMULA DATABASE - Written by M. Tam with assistance from D. Allingham, D.H. Bailey, J. Borwein and A. Mattingly; Computer Assisted Research Mathematics and its Applications (CARMA), School of Mathematical and Physical Sciences, Faculty of Science and Information Technology, University of Newcastle, Callaghan NSW, Australia VERY VERY VERY...EXTENSIVE.
BBP-type Formula Database
"...Mathematical constants who can be represented by BBP-type formula have the property that their n-th digit can be directly calculated without needing to compute any of the first (n-1) digits. This online database presents a comprehensive compilation of both formal and experimental BBP-type formulae..."
For more information see Johathan (Jon) Borwein's Home Page; David H. Bailey's Home Page (Department of Computational Research, Lawrence Berkeley National Laboratory); Computer Assisted Research Mathematics and its Applications (CARMA) or the School of Mathematical and Physical Sciences

MATHEMATICAL FUNCTIONS - THE WOLFRAM FUNCTIONS SITE - Wolfram Research, Inc Multimedia "The Wolfram Functions Site" - Mathematical Functions Dictionary (Text & Images).
"The Wolfram Functions Site" includes over 300,000 Formulas online & over 10,000 Visualizations including:
Elementary Functions;
Constants;
Bessel, Airy, Struve Functions;
Integer Functions;
Polynomials;
Gamma, Beta, Erf;
Hypergeometric Functions;
Elliptic Integrals;
Elliptic Functions, etc..."
For more information see Wolfram Research, Inc

NIST DIGITAL LIBRARY OF MATHEMATICAL FUNCTIONS - Editors: F.W.J. Olver, D.W. Lozier, R.F. Boisvert & C.W. Clark, Applied and Comutational Mathematics Division, Information Technology Laboratory, National Institute of Standards and Technology (NIST) Multimedia "NIST Digital Library of Mathematical Functions" (Text, Images, etc.). VERY VERY VERY...EXTENSIVE.
Examples from over "35" "NIST Digital Library of Mathematical Functions" Chapters include
"...Gamma Function;
Error Functions, Dawson’s and Fresnel Integrals;
Bessel Functions;
Parabolic Cylinder Functions;
Legendre and Related Functions;
Hypergeometric Function;
Jacobian Elliptic Functions;
Bernoulli and Euler Polynomials;
Functions of Number Theory;
Mathieu Functions and Hill’s Equation;
Spheroidal Wave Functions;
Coulomb Functions; etc..."
For more information see the Applied and Computational Mathematics Division; Information Technology Laboratory or the National Institute of Standards and Technology (NIST)

DYNAMIC DICTIONARY OF MATHEMATICAL FUNCTIONS (DDMF) - Authors: A. Benoit, F. Chyzak, A. Darrasse, S. Gerhold, M. Mezzarobba & B. Salvy; DDMF project hosted and supported by the Microsoft Research – INRIA Joint Centre; Centre de Recherche Commun INRIA-Microsoft Research Parc Orsay Université, France Multimedia "Dynamic Dictionary of Mathematcial Functions (DDMF)" (Text, Images, Calculators, etc.). VERY VERY VERY...EXTENSIVE.
"Dynamic Dictionary of Mathematcial Functions (DDMF)"
"...interactive site on Mathematical Functions, with properties, truncated expansions, numerical evaluations, plots, and more. The functions currently presented are elementary functions and special functions of a single variable..."
Examples of Mathematical Functions Calculators include
"...The inverse cotangent Calculator;
The Airy function of the first kind Calculator;
The inverse secant Calculator;
The inverse tangent Calculator;
The cosine integral Calculator;
The error function Calculator;
The imaginary error function Calculator;
The inverse hyperbolic cotangentv;
The inverse hyperbolic tangent Calculator;
The hyperbolic sine Calculator;
The dilogarithm Calculator;
The hyperbolic sine integral Calculator; etc..."
For more information see the Microsoft Research-INRIA Joint Centre or INRIA

EXPERIMENTAL MATHEMATICAN'S TOOLKIT - D.H. Bailey (CRD, LBL) & J. Borwein (CARMA, University of Newcastle); Hosted by the Computational Research Division (CRD), Berkeley Lab Computing Sciences, LBL Multimedia Experimental Mathematicans's Toolkit (Text & Images).
Free but Registration Required.
Experimental Mathematicans's Toolkit
"...an online facility to numerically evaluate mathematical expressions to high precision. Many mathematical functions are supported, including..."
For more information see the Experimental Mathematics Website; David H. Bailey's Home Page; Computational Research Division (CRD); Johathan Borwein's Home Page or the Computer Assisted Research Mathematics and its Applications (CARMA)

Pi CALCULATORS & APPLETS

THE Pi-SEARCH PAGE - D. Anderson, School of Computer Science, Carnegie Mellon University VERY VERY VERY...EXTEINSIVE.
Pi Searcher
"...lets you search for any string of digits (up to 120 of them) in the first 200 million digits of Pi..."
For more information see the Dave Anderson's Home Page; Dave Anderson's Faculty Home Page or the School of Computer Science

Pi COMPUTER - CALCULATOR - R. Simms, Department of Mathematical Sciences, College of Engineering and Science, Clemsen University VERY EXTENSIVE.
Pi Calculator
"...makes use of an elegant representation of Pi, which may be treated like a sum of fractional terms. To generate digits,..."
For more information see Neat Math Programs; Robert Simms' Web Corner or the Department of Mathematical Sciences

METHODS OF COMPUTATION Pi - I.K. Rana, Mathematics Resource Center, Department of Mathematics, Indian Institute of Technology, Bombay, India VERY VERY VERY...EXTENSIVE.
Methods of Computation of Pi Calculators with Lessons include
"...Archimedes Method Applet to Calculate Value of Pi Applet;
Area Method Applet to Calculate Value of Pi Applet;
Buffon's Needle Applet to Calculate Value of Pi Applet;
Measuring Circle Method Applet to Calculate Value of Pi Applet;
Monte Carlo Method to Calculate Value of Pi Applet;
Ramanujan Circle Method to Calculate Value of Pi Applet;
Ramanujan Digit Method to Calculate Value of Pi Applet;
Rob's Method to Calculate Value of Pi Applet..."
For more information see On the Nmber PI; Resources in the Center; Mathematics Resource Center; Department of Mathematics or the Indian Institute of Technology

Mathematical Cognitive Tools

MATHEMATICAL COGNITIVE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

MEMORY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

BAYES FACTOR CALCULATOR - J.N. Rouder, Director of Perception and Cognition Lab, Department of Psychological Sciences, College of Arts & Science, University of Missouri, Columbia, Missouri VERY EXTENSIVE.
Bayes Factor Calculator includes
Bayes Factor One-Sample Test Calculator
"...computes the BIC Odds, Jeffrey-Zellner-Siow Bayes factor, and unit Bayes factor..."
Bayes Factor Two-Sample Test Calculator
"...computes the BIC Odds and Jeffrey-Zellner-Siow Bayes factor and unit Bayes factor..."

For more information see the Perception and Cognition Lab or the Department of Psychological Sciences

MODELS OF MEMORY (JAVA APPLETS) - Ian Neath, Department of Psychology, Memorial University of Newfoundland Multimedia Psychology Models, Models of Memory & Psychology Calculators (Text & Images). VERY VERY VERY...EXTENSIVE.
Models of Memory
"...If you wish to conduct simulations that will be reported in scientific journals or at professional conferences, you should program your own implementation and should test that version against all relevant published simulations..."
For more information see Ian Neath's Home Page or the Department of Psychology

Some examples from over "17" Memory Models & Psychology Calculators include

The Brown & Hulme Model (Brown & Hulme, 1995)
Brown & Hulme Model
"...The purpose of the Brown and Hulme (1995) model was to show that item length (or word length) effects could be obtained in a model that does not include any rehearsal..."

Positional Distinctiveness (Nairne et al., 1997)
Positional Distinctiveness Model
"...The basic idea was to see whether Estes' (1972) perturbation model could serve as the cause of distinctiveness. An item's position is encoded accurately, but then perturbs (or drifts) in psychological space..."

Johnson's Distinctiveness Model (Johnson, 1991)
Johnson's Distinctiveness Model
"...Johnson (1991) proposed a distinctiveness model of serial learning. This simulation implements his model...."

SIMPLE: Absolute Identification (Neath, Brown, McCormack, Chater, & Freeman, 2006)
Scale Invariant Memory and Perceptual Learning (SIMPLE) Model
"...assumes that the memory representation is a log transform of the physical item. In this version, however, we use a power function such that...."

Recognition Memory Simulation
Recognition Memory Simulation includes
"...Signal Detection Theory; Non-Parametric Analog; Two-High Threshold Model...."

THE HEURISTICA APPLET - Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Berlin, Germany VERY EXTENSIVE.
Heuristic Calculator
"...is an algorithm which will make decisions based on data. In this case, the heuristics are given data which consist of a number of objects, and some information about the objects in terms of binary cues..."
For more information see Simple Heuristics That Make Us Smart

Mathematical Methods for Engineers

RELATED CENTERS

FOR ENGINEERING COURSES, LECTURES, TEXTBOOKS, CALCULATORS, VIDEOS, SPREADSHEETS, ETC. SEE THE ENGINEERING CENTER

MATHEMATICAL METHODS FOR ENGINEERS COURSES, LECTURES, TEXTBOOKS, ETC.

Undergraduate Courses, Lectures, etc.

COMPUTATIONAL SCIENCE AND ENGINEERING I (REAL PLAYER) - Gilbert Strang, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Computational Science and Engineering I Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE.
Computational Science and Engineering I Course
"...provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems;..."
Examples from over "30" "Mathematical Methods for Engineers" Video Lectures include:
"...One-dimensional Applications: A = Difference Matrix Video Lecture;
Applications to Linear Estimation Video Lecture;
Applications to Dynamics Video Lecture;
Applications to Boundary Value Problems: Laplace Equation Video Lecture;
Delta Function and Green's Function Video Lecture;
Initial Value Problems: Wave Equation and Heat Equation Video Lecture;
Finite Difference Methods: Stability and Convergence Video Lecture;
Spectral Method: Dynamic Equations Video Lecture; etc..."
For more information see Gilbert Strang's Home Page; Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare

INTERACTIVE EDUCATIONAL MODULES IN SCIENTIFIC COMPUTING (JAVA APPLETS) - M.T. Health, E. VanderZee, J. Schoen, J. Naisbitt & N. Exner, Computational Science and Engineering (CSE) Graduate Option Program, College of Engineering, University of Illinois, Urbana-Champaign Multimedia Scientific Computing: An Introductory Survey Course (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Scientific Computing" Course Subject Categories & Subcategories include
"...Floating-Point Arithmetic
"...Rounding Rules; Selectable-Precision Calculator;
Quadratic Formula;
Infinite Series; etc..."
Linear Equations
"...Condition Number;
Gaussian Elimination;
Gauss-Jordan Elimination; etc..."
Linear Least Squares
"...Householder Transformations;
Householder QR Factorization;
Gram-Schmidt QR Factorization; etc..."
Eigenvalue Problems
"...QR Iteration with Shifts;
Jacobi's Method; etc..."
Nonlinear Equations
"...Fixed-Point Iteration;
Newton's Method;
Secant Method; etc..."
Optimization
"...Optimization in One Dimension;
Unconstrained Optimization in Two Dimensions;
Constrained Optimization in Two Dimensions; etc..."
Interpolation
"...Bernstein Polynomials;
Taylor Interpolation;
Newton Interpolation;
Error Bounds;
Piecewise Cubic Interpolation; etc..."
Integration and Differentiation
"...Adaptive Quadrature;
Numerical Differentiation;
Richardson Extrapolation;
Romberg Integration; etc..."
Ordinary Differential Equations
"...Trapezoid Method;
Runge-Kutta;
Extrapolation;
Predictor-Corrector;
Galerkin; etc..."
Partial Differential Equations
"...Laplace Equation;
Advection Equation;
Burgers' Equation; etc..."
Fast Fourier Transform
"...Recursive FFT;
Digital Filtering; etc..."
Random Numbers and Simulation
"...Linear Congruential Generators;
Buffon Needle Problem;
Quasi-Random Sequences; etc..."

For more information see Scientific Computing: An Introductory Survey; Michael T. Health's Home Page or the Computational Science and Engineering (CSE) Graduate Option Program

NUMERICAL METHODS IN ENGINEERING - J.J. Westerink, Department of Civil Engineering and Geological Sciences, College of Engineering, University of Notre Dame Multimedia Numerical Methods in Engineering Course - PDF, 250+ Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Numerical Methods in Engineering" Course Lectures include
"...Lecture 2: Direct Solutions to Linear Systems of Algebraic Equations;
Lecture 4: Iterative Solutions to Linear Algebraic Equations;
Lecture 6: Lagrange Interpolation;
Lecture 9: Hermite Interpolating Polynomicals;
Lecture 14: Practical Issues in Applying Finite Difference Approximations;
Lecture 17: Numberical Integration;
Lecture 22: Multi Step Methods; etc..."
For more information see J.J. Westerink's Home Page or the Department of Civil Engineering and Geological Sciences

Graduate Courses, Lectures, etc.

FINITE ELEMENTS IN ENGINEERING - J.J. Westerink, Department of Civil Engineering and Geological Sciences, College of Engineering, University of Notre Dame Multimedia Finite Elements in Engineering (Text & Images). VERY VERY VERY...EXTENSIVE. For more information see J.J. Westerink's Home Page or the Department of Civil Engineering and Geological Sciences

MATHEMATICAL METHODS FOR ENGINEERS II (REAL PLAYER) - Gilbert Strang, Department of Mathematics & the MIT OpenCourseWare, MIT Multimedia Mathematical Methods for Engineers II Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE.
Multimedia Mathematical Methods for Engineers II Course
"...is a continuation of Mathematical Methods for Engineers I. Topics include numerical methods; initial-value problems; network flows; and optimization..."
Examples from over "28" "Mathematical Methods for Engineers" Video Lectures include
"...Comparison of Methods for the Wave Equation Video Lecture;
Second-order Wave Equation Video Lecture;
Finite Differences for the Heat Equation Video Lecture;
Convection-Diffusion/Conservation Laws Video Lecture;
Shocks and Fans from Point Source Video Lecture;
Level Set Method Video Lecture;
Matrices in Difference Equations (1D, 2D, 3D) Video Lecture;
Fast Poisson Solver Video Lecture;
Weighted Least Squares Video Lecture;
Saddle Points/Inf-sup condition Video Lecture; etc..."
For more information see Gilbert Strang's Home Page; Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare

MATHEMATICAL METHODS OF ENGINEERING ANALYSIS - R.J. Vanderbei & E. Cinlar, Department of Operations Research and Financial Engineering, School of Engineering and Applied Science (SEAS), Princeton Universtiy Multimedia Mathematical Methods of Engineering Analysis Textbook, PDF, 119 Pages (Text & Images). VERY VERY VERY...EXTENSIVE.
Examples of "Mathematical Methods of Engineering Analysis" Textbook Chapters include
"...Sets and Functions;
Metric Spaces;
Functions on Metric Spaces;
Differential and Integral Equations;
Convex Analysis;
Measure and Integration; etc..."
For more information see Robert J. Vanderbei's Home Page or the Department of Operations Research and Financial Engineering

Mathematical Physics

RELATED CENTERS

FOR PHYSICS DATABASES, COURSES, TEXTBOOKS, LECTURES, CALCULATORS, SPREADSHEETS, ETC. SEE THE PHYSICS CENTER & ASTROPHYSICS, ASTRONOMY & ASTROBIOLOGY CENTER

SOME EXAMPLES

MATHEMATICAL PHYSICS COURSES

MATHEMATICAL PHYSICS - R.L. Herman, Department of Mathematics and Statistics, University of North Carolina, Wilmington, N.C. Multimedia Mathematical Physics Course (Text & Images). VERY VERY EXTENSIVE.
Mathematical Physics Course Topics
"...are vector analysis, vector spaces, linear algebra, complex variables, power series, ordinary and partial differential equations, Fourier series, Laplace and Fourier transforms, Sturm-Liouville theory, special functions..."
Examples of "Mathematical Physics" Course Lectures include
"...ODEs and SHM;
Linear Algebra;
Harmonics, Fourier Series;
Complex Representations;
Transform Techniques;
Spherical Symmetry; etc..."
For more information see Mathematical Physics (311); Russell L. Herman's Home Page or the Department of Mathematics and Statistics

QUANTUM FIELD THEORY COURSES

QUANTUM FIELD THEORY I - K. Cahill, Department of Physics & Astronomy, University of New Mexico Multimedia Quantum Field Theory I Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE.
Examples from over "26" "Quantum Field Theory" Course Video Lectures include
"...Casimir Effect Video;
Ward-Takahashi Identity Video;
Renormalization Group in Continuum Quantum Field Theory Video;
The Pion as a Nambu-Goldstone Boson, and on Solitons in Two-Dimensional Space-Time Video;
Solitons, Vortices, and Magnetic Monopoles; etc..."
For more information see Kevin Cahill's Home Page or the Department of Physics & Astronomy

STRING THEORY

STRING THEORY FOR UNDERGRADUATES - B. Zwiebach & A. Guth, Department of Physics & the MIT OpenCourseWare, MIT Multimedia String Theory for Undergraduates Course (Text & Images). VERY VERY VERY...EXTENSIVE.
String Theory for Undergraduates Course
"...Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity and basic quantum mechanics. This course develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics..."
Examples from over "24" "String Theory for Undergraduates" Course Lectures include
"...Relativistic Electrodynamics, Gauss' Law, Gravitation and Planck's Length;
Nonrelativistic Strings and Lagrangian Mechanics;
Area Formula for Spatial Surfaces;
Relativistic Strings: Nambu-Goto Action, Equations of Motion and Boundary Conditions;
Solution of the Open String Motion in the Light-cone Gaug;
Closed Strings; etc..."
For more information see Department of Physics; Physics Courses or the MIT OpenCourseWare

Mathematica, JavaView, LiveGraphics3D, 3D-XplorMath

WEBMATHEMATICA & LIVEGRAPHICS 3D IN OPTICS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

WEBMATHEMATICA & LIVEGRAPHICS 3D IN OPTICS - J.C. Wyant, College of Optical Sciences, University of Arizona, Tucson, Arizona VERY VERY VERY...EXTENSIVE.
Examples of "WebMathematica & LiveGraphics3D in Optics" Subject Categories include
"...Zernike Polynomials;
Seidel Aberrations;
Fraunhofer Diffraction;
Fresnel Diffractions; etc..."
For more information see James C. Wyant's Home Page or the College of Optical Sciences

Examples from over "25" webMathematica and LiveGraphics3D Calculators include

Zernike Polynomials Calculator: PSF & MTF (Zernike Polynomials - 36 Terms)

Foucault Knife Edge Patterns for Seidel Aberrations Calculator

Rectangular Aperture Fraunhofer Diffraction Pattern Calculator

Multiple Beam Interference Fringes Calculator

Various Plots and Calculations Calculator

3D-XPLORMATH - VIRTUAL MATH MUSEUM

VIRTUAL MATH MUSEUM - R.S. Palais (Emeritus, Brandeis University) and currently at the Department of Mathematics, University of California, Irvine (UCI) Multimedia Virtual Math Museum (Text & Images). VERY VERY VERY...EXTENSIVE. For more information see 3D-XplorMath; 3D-XplorMath Consortium; Richard Palais Home Page or the Department of Mathematics

JAVAVIEW 3D CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

JAVAVIEW - 3D GEOMETRY (JAVAVIEW) - K. Polthier, Mathematical Geometry Processing, Visualization and Mathematics, Institute of Mathematics, Freie Universität Berlin, Germany VERY VERY VERY...EXTENSIVE.
Visual Geometry Pages
"...are an online geometry book illustrating problems from differential geometry and mathematical visualization using applets, images, animations, and Java software..."
Visual Geometry Calculators include:
"...Platonic Solids Calculator;
Surfaces Calculator;
Curves on Surfaces Calculator;
Minimal Surfaces Calculator;
CMC Surfaces Calculator;
Curvature Properties Calculator;
Harmonic Maps Calculator;
Type a Curve Calculator
"...Type the equations of your favorite curve..."
Type a Surface Calculator
"...Type the equations of your favourite surface..."
Study ODEs Calculator
"...Type and study ordinary differential equations..."
Root Finder Calculator
Find Roots of Real-Valued Functions..."

For more information see Konrad Polthier's Homw Page

Some examples of Visual Geometry Applets include

Curve Calculator

Surface Calculator

JAVAVIEW - INTERACTIVE 3D GEOMETRY AND VISUALIZATION (JAVA APPLETS) - The JavaView Project, Germany VERY VERY VERY...EXTENSIVE. For more information see JavaView

Some examples from over "20" 3D Geometry Calculators include

Geodesic Surveyor: Measure Distances on Polyhedral Surfaces

Harmonic Maps and Minimal Surfaces

Parameterized Surfaces

Visualize Scalar Field on a Surface

Mathematics of Plant Patern Formation

PLANT PATTERN FORMATION CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

PHYLLOTAXIS APPLETS - P. Atela-Cortés & C. Golé, Department of Mathematics & Statistics, Smith College VERY VERY EXTENSIVE.
Phyllotaxis
"...An Interactive site for the Mathematical Study of Plant Pattern Formation..."
For more information see Introduction to Phyllotaxis; Pau Atela-Cortés' Home Page; Christophe Golé's Home Page or the Department of Mathematics & Statistics

Some examples Plant Pattern Formation Calculators & Applets include

Cylinder Lattices Applet
Cylinder Lattices Applet
"...shows all the possible (half) cylindrical lattices..."

Spiral Lattices Applet
Spiral Lattices Applet
"...enables the exploration of all possible spiral lattices and their organization according to their divergence angles, expansion rate, and parastichy numbers..."

Dynamical Model Applet (Centric Representation)
Dynamical Model Applet
"...shows a model of primordia growth (represented by dots) at the apical meristem of a plant. The model is a dynamical system which implements Hofmeister's hypotheses: primordia form periodically, once formed..."

Matrix

FOR MATRIX CALCULATORS & APPLETS SEE LINEAR ALGEBRA: MATRIX CALCULATORS

Mathematics Center

Calculators On-Line Center ~ Home Page