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COMPLEX MATH: N-Z Number Theory (Elementary Number Theory, Algebraic Number Theory, Analytic Number Theory, Graduate Topics in Number Theory, etc.) Numerical Analysis & Numerical Methods ~ Operations Research & Logistics Parametric Equations & Curves ~ Pendulums ~ Poisson Prime Numbers ~ Quantitative Finance Random Numbers ~ Real Analysis ~ Real Functions ~ Real Numbers Representation Theory Sandpiles & Singing Dunes: the Motion of Sand Grains Soap Film & Bubbles ~ Spirograph ~ Splines, Spline Curves Statistical Mechanics Stochastic Processes, Stochastic Analysis, etc. Sudoku ~ Symbolic/Numberic & Inverse Symbolic ~ Tensors & Relativity Mathematics Center Calculators On-Line Center

Number Theory NUMBER THEORY, ALGEBRAIC NUMBER THEORY, ANALYTIC NUMBER THEORY, GRADUATE TOPICS IN NUMBER THEORY COURSES, TEXTBOOKS, LECTURES, ETC. IWASAWA THEORY, p-ADIC DIFFERENTIAL EQUATIONS, ETC. COURSES, TEXTBOOKS, LECTURES, ETC. Undergraduate Number Theory Courses, Textbooks, Lectures, etc. ELEMENTARY NUMBER THEORY - B. Ikenaga, Department of Mathematics, School of Science and Mathematics, Millersiville University, Millersville, PA Multimedia Elementary Number Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Elementary Number Theory" Course Lectures include "...Sums, Products, and Factorials; Divisibility and the Division Algorithm; The Extended Euclidean Algorithm; Elementary Factoring Methods; Fermat Factorization; Congruences and Modular Arithmetic; The Chinese Remainder Theorem; Wilson's Theorem and Fermat's Theorem; Euler's Theorem; the Euler phi Function; Perfect Numbers and Mersenne primes; Quadratic Residues; etc..." For more information see Math Resources; Bruce Ikenaga's Home Page; Bruce Ikenaga's Faculty Home Page or the Department of Mathematics ELEMENTARY NUMBER THEORY - W. Stein, Department of Mathematics, University of Washington Multimedia Elementary Number Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Elementary Number Theory" Course Chapters include "...Prime Numbers; The Ring of Integers Modulo n; Public-Key Cryptography; Quadratic Reciprocity; etc..." For more information see Elementary Number Theory Home Page; William Stein's Teaching; William Stein's Home Page or the Department of Mathematics ELEMENTARY NUMBER THEORY - Jim Hefferon; Department of Mathematics, Saint Michael's College, Colchester, Vermont Multimedia Elementary Number Theory - PDF, 82 Pages (Text & Images). VERY VERY EXTENSIVE. Examples of "Elementary Number Theory" Textbook Chapters & Subchapters include "...Greatest Common Divisor; Bezout’s Lemma; The Fundamental Theorem; Distribution of Primes; Congruence; Residue Classes; etc..." For more information see Jim Hefferon's Home Page or the Department of Mathematics Graduate Algebraic Number Theory Courses, Textbooks, Lectures, etc. ALGEBRAIC NUMBER THEORY - R.B. Ash (Emeritus), Department of Mathematics, University of Illinois, Urbana, Illinois Multimedia Algebraic Number Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Graduate "Algebraic Number Theory" Course Chapters include "...Norms, Traces and Discriminants; Dedekind Domains; Factoring of Prime Ideals in Extensions; The Ideal Class Group; The Dirichlet Unit Theorem; Cyclotomic Extensions; Factoring of Prime Ideals in Galois Extensions; Local Fields..." For more information see Robert B. Ash or the Department of Mathematics ALGEBRAIC NUMBER THEORY - J.S. Milne, Professor Emeritus, Department of Mathematics, College of Literature, Science & Arts, University of Michigan Multimedia Algebraic Number Theory - PDF, 163 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Algebraic Number Theory "... are concerned with algebraic number theory, and the sequel with class field theory...." Examples of Graduate "Algebraic Number Theory" Course Chapters include "...Rings of Integers; Dedekind Domains; Factorization; The Finiteness of the Class Number; The Unit Theorem; Cyclotomic Extensions; Fermat's Last Theorem; Global Fields; etc..." For more information see Course Notes; Mathematics; James Milne's Home Page or the Department of Mathematics Graduate Analytic Number Theory Courses, Textbooks, Lectures, etc. ANALYTIC NUMBER THEORY - K.S. Kedlaya, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Analytic Number Theory (Text & Images). VERY VERY VERY...EXTENSIVE. Analytic Number Theory "...The fundamental questions in analytic number theory, and the ones which we focus on in this course, concern the interplay between the additive and multiplicative structures on the integers. Specifically, it is quite natural to ask questions of an additive nature about constructions which are intrinsically multiplicative..." Examples of "Analytic Number Theory" Course Chapters include "...Dirichlet series and arithmetic functions; Primes in arithmetic progressions; The functional equation for the Riemann zeta function; von Mangoldt's formula; Revisiting the sieve of Eratosthenes; The Selberg sieve; Introduction to large sieve inequalities; The Bombieri-Vinogradov theorem (proof); etc..." For more information see Analytic Number Theory Home Page; Kiran Sridhara Kedlaya's Home Page; Kiran S. Kedlaya's Faculty Home Page; Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare INTRODUCTION TO ANALYTIC NUMBER THEORY (MATH 531) - A.J. Hildebrand, Department of Mathematics, University of Illinois, Urbana-Champaign, Illinois Multimedia Introduction to Analytic Number Theory Course - PDF, 197 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Introduction to Analytic Number Theory" Course Chapters include "...Primes and the Fundamental Theorem of Arithmetic; Arithmetic functions I: Elementary theory; Arithmetic functions II: Asymptotic estimates; Arithmetic functions III: Dirichlet series and Euler products; Distribution of primes II: Proof of the Prime Number Theorem; Primes in arithmetic progressions: Dirichlet's Theorem; etc..." For more information see A.J. Hildebrand's Home Page or the Department of Mathematics Graduate Topics in Number Theory: Iwasawa Theory Courses, Textbooks, Lectures, etc. INTRODUCTION TO IWASAWA THEORY - J.L. Brown, Department of Mathematical Sciences, College of Engineering and Science, Clemson University Multimedia Introduction to Iwasawa Theory Course (Text & Images). Click on "Introduction to Iwasawa Theory". Examples of "Introduction to Iwasawa Theory" Course (PDF, 102 Pages) Chapters include "...Background Material; Some Results on the Sizes of Class Groups; Zp -extensions; The Iwasawa Main Conjecture; etc..." For more information see Jim Brown's Web Page or the Department of Mathematical Sciences Graduate Topics in Number Theory: p-adic Differential Equations Courses, Textbooks, Lectures, etc. TOPCIS IN NUMBER THEORY: p-ADIC DIFFERENTIAL EQUATIONS - K.S. Kedlaya, Department of Mathematics, MIT Multimedia Topics in Number Theory: p-adic Differential Equations - PDF, 190 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Topics in Number Theory: p-adic Differential Equations" Course Parts & Chapters include "...Part 1: Tools of p-adic Analysis; Part 2: Diffenential Algebra; Part 4: Difference Algebra and Frobenius Structures; Chapter 13: Formalism of Difference Algebra; Chapter 14: Frobenius Modules; Chapter 16: Effective Convergence Bounds; etc. Part 5: Areas of Application; etc..." For more information see 18.787: Topics in Number Theory (MIT, Fall 2007); Kedlaya's Course web pages; Kiran Sridhara Kedlaya's Home Page; Kiran S. Kedlaya's Faculty Home Page or the Department of Mathematics NUMBER THEORY CALCULATORS & APPLETS 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) 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..." 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 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 Some examples of other Number Theory Calculators include Gaussian Primes Calculator Gaussian Primes Calculator "...featuring a graphical view of gaussian prime numbers..." Factorization using the Elliptic Curve Method Calculator Factorization using the Elliptic Curve Method Calculator "...can be used to find 20- or 30-digit factors of numbers or numerical expressions up to 1000 digits long. It also computes the number and sum of divisors, Euler's totient and Moebius, and..." Sum of Squares Calculator Sum of Squares Calculator "...can find the decomposition of a number or numerical expression in a sum of up to four squares. It does not need its prime factorization...." NUMBER THEORY (JAVA APPLETS) - J.J. Holt (University of Virginia) & J.W. Jones (Arizona State University) and hosted by the Department of Mathematical Sciences, Michigan Technological University; a W. H. Freeman and Company Production Multimedia Number Theory Lessons (Text & Images). VERY VERY VERY...EXTENSIVE. Number Theory Calculator Subject Categories include: "...Divisibility and Factorization Calculators; The Euclidean Algorithm and Linear Diophantine Equations Calculators; Congruences Calculators; Applications of Congruences Calculators; Solving Linear Congruences Calculators; Primes of Special Forms Calculators; Chinese Remainder Theorem Calculators; Multiplicative Orders Calculators; The Euler phi-function Calculators; Primitive Roots Calculators; Quadratic Congruences Calculators; Representation Problems Calculators; Continued Fractions Calculators; etc..." For more information see the Department of Mathematical Sciences Some examples from over "50" Number Theory Calculators include Chapter 1: Divisibility and Factorization Calculators Chapter 1: Divisibility and Factorization Calculators include: "...Divisors and GCDs Calculator; Divisors and Factorization Calculator; GCDs and Factorization Calculator; The Division Algorithm Calculator; etc..." Chapter 5: Solving Linear Congruences Calculators Chapter 5: Solving Linear Congruences Calculators include: "...Techniques Used with Rationals and Integers Calculator; Multiplicative Inverses Calculator; Linear Congruence Equations Calculator; Cryptanalysis Calculator; etc..." Chapter 8: Multiplicative Orders Calculators Chapter 8: Multiplicative Orders Calculators include: "...Limitations on Orders Calculator; Fermat and Euler Calculator; etc..." Chapter 12: Representation Problems Calculators Chapter 12: Representation Problems Calculators include: "...Sums of Two Squares Calculator; Pythagorean Triples Calculator; Sums of Many Squares Calculator; etc..." NUMBER THEORY (JAVA APPLET)S - Andreas de Vries, Math It, Fachbereich Technische Betriebswirtschaft, Germany In English & German/Deutsch. VERY EXTENSIVE. Number Theory Calculators include: "...Prime Factorization of Numbers Calculator; The Euler Totient Function Calculator; The Carmichael Function Calculator; The Graph of the Riemann zeta function Calculator; Rieman Hypothesis Calculator; etc..." For more information see Math It Mathematical Applets or Math It

Numerical Analysis, Numerical Methods NUMERICAL ANALYSIS COURSES, TEXTBOOKS, LECTURES, ETC. Undergraduate Numberical Analysis Courses NUMERICAL ANALYSIS - P. Olver, School of Mathematics, College of Science & Engineering, University of Minnesota Multimedia Numerical Analysis Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Numerical Analysis" Course Chapters include "...Numerical Solution of Scalar Equations; Review of Matrix Algebra; Gaussian Elimination; Inner Products and Norms; Eigenvalues and Singular Values; Iterative Methods for Linear Systems; Numerical Computation of Eigenvalues; Numerical Solution of Algebraic Systems; Numerical Solution of Ordinary Differential Equations; Numerical Solution of the Heat and Wave Equations; etc..." For more information see Peter Olver's Home Page or the School of Mathematics NUMERICAL ANALYSIS - G. Bal, Department of Applied Physics & Applied Mathematics, The Fu Foundation School of Engineering & Applied Science, Columbia University Multimedia Numerical Analysis Course - PDF, 67 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Numerical Analysis" Course Chapters include "...Finite Differences for Parabolic Equations; Finite Differences for Elliptic Equations Finite Differences for Hyperbolic Equations; Spectral methods; Introduction to finite element methods; etc..." For more information see APAM 6302 - Numerical Methods/PDE Home Page; Guillaume Bal's Teaching; Guillaume Bal's Home Page; Guillaume Bal's Faculty Home Page or the Department of Applied Physics & Applied Mathematics Mathematics of Wavelets INTRODUCTION TO THE MATHEMATICS OF WAVELETS - W. Miller, Program in Applied, Computational & Industrial Mathematics and the Institute for Mathematics and its Applications, School of Mathematics, University of Minnesota Multimedia Introduction to the Mathematics of Wavelets Course - PDF, 294 Pages (Text & Images). Click on "Lecture Notes and Supplementary Notes for the Course". Examples of "Introduction to the Mathematics of Wavelets" Course Chapters include "...Vector Spaces with Inner Product; Fourier Series; The Fourier Transform; Discrete Fourier Transform; Linear Filters; Multiresolution Analysis; Wavelet Theory; The Windowed Fourier transform and the Wavelet Transform; 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 NUMERICAL METHODS COURSES & TEXTBOOKS Graduate Numerical Methods Courses INTRODUCTION TO NUMERICAL METHODS - S.G. Johnson, Applied Mathematics Research, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Introduction to Numerical Methods Course (Text & Images). VERY VERY VERY...EXTENSIVE. Introduction to Numerical Methods "...offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning,..." For more information see Introduction to Numerical Methods Home Page; Steven Johnson's Home Page; Steven G. Johnson's Faculty Home Page; Applied Mathematics Research; Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS - Benjamin Seibold, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Numerical Methods for Partial Differential Equations (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Numerical Methods for Partial Differential Equations" Lecture include "...Laplace and Poisson Equation; Heat Equation, Transport Equation, Wave Equation; Elliptic Equations and Errors, Stability, Lax Equivalence Theorem; Elliptic Equations and Linear Systems; Ordinary Differential Equations; Advection Equation; Conservation Laws; Systems of IVP, wave equation, leapfrog, staggered grids; etc..." For more information see Numerical Methods for Partial Differential Equations Home Page; Department of Mathematics; Mathematics Courses or the MIT OpenCourseWare NUMERICAL ANALYSIS CALCULATORS & APPLETS NUMERICAL ANALYSIS (JAVA APPLETS) - SoftIntegration, Inc. VERY VERY VERY...EXTENSIVE. Examples of "Numerical Analysis" Calculator Subject Categories include "...Data Analysis and Statistics Calculators; Data Interpolation and Curve Fitting Calculators; Minimization or Maximization of Functions Calculators; Polynomials Calculators; Nonlinear Equations Calculators; Ordinary Differential Equations Calculators; Derivatives and Differences Calculators; Integration Calculators; Matrix Analysis Functions Calculators; Matrix Decomposition Calculators; Matrix Functions Calculators; Special Matrices Calculators; Linear Equations Calculators; Eigenvalues and Eigenvectors Calculators; Fast Fourier Transforms Calculators; Convolution and Filtering Calculators; Cross Correlation Calculators; Complex Functions Calculators; Array Functions Calculators; etc..." For more information see Web Services; Numerical Computing or SoftIntegration, Inc. Examples from over "60" "Numerical Analysis" Calculators include Data Analysis and Statistics: Covariance Calculator Data Interpolation and Curve Fitting: Fit a set of data points to a polynomial function Polynomials: Find Coefficients of a Polynomial Based on its Roots Nonlinear Equations: Find zeros of a nonlinear system of equations Integration: Double Integration Calculation Matrix Decomposition: LU factorization of a general n*n matrix Matrix Functions: Orthonormal bases of a matrix NUMERICAL ANALYSIS (JAVA APPLETS) - S.A. Sarra, Department of Mathematics, College of Science, Marshall University VERY EXTENSIVE. Examples of Java Programs for Numberical Analysis include "...Root finding: Bisection, Fixed Point Iteration, Secant Method, Newton's Method Applet; Interpolation Applet; Trapezoid and Simpson's Rules Applet; etc..." For more information see Scott A. Sarra's Home Page or the Department of Mathematics

Operations Research & Logistics

Operations Research Courses & Lectures Operations Research, Logistics, Operations Management Operations Research & Logistics Algorithms P-Median ~ Sorting ~ Traveling Salesman Industrial Engineering: Warehouse & Distribution, Materials Handling, etc.

Operations Research & Logistics OPERATIONS RESEARCH COURSES, LECTURES, TEXTBOOKS, ETC. FOR MORE OPERATIONS RESEARCH CALCULATORS & APPLETS SEE LINEAR & NONLINEAR PROGRAMMING INCLUDING THE SIMPLEX METHOD Operations Research Undergraduate Courses, Textbooks, Lectures, etc. DECISION SCIENCE - MANAGEMENT SCIENCE - OPERATIONS RESEARCH - H. Arsham, Division of Economics, Finance and Management Science, Merrick School of Business, University of Baltimore Multimedia Decision Science, Management Science & Operations Research Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Decision Science, Management Science & Operations Research" Course Chapters include "...Linear Optimization with Sensitivity; Integer Optimization and the Network Models; Tools for LP Modeling Validation; Time Series Analysis and Forecasting; Linear Algebra and LP Connections; Construction of the Sensitivity Region for LP Models; Zero Sagas in Four Dimensions; Systems Simulation; etc..." For more information see Hossein Arsham's Home Page or the Merrick School of Business 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 ADVANCED OPERATIONS RESEARCH TECHNIQUES (IE 316) - T. Ralphs, Computational Optimization Research at Lehigh, Department of Industrial & Systems Engineering, P.C. Rossin College of Engineering and Applied Science, Lehigh University Multimedia Advanced Operations Research Techniques Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Advanced Operations Research Techniques" Course Lectures include "...Extreme Points and Optimality; The Tableau Method; Modeling Languages; The Dual Simplex Method; The Recession Cone, Extreme Rays, and Representation of Polyhedra; Global Sensitivity Analysis; Introduction to Network Flow Problems; The Negative Cost Cycle Algorithm and Maximum Flows; Assignments, Shortest Paths, and Minimum Spanning Trees; Branch and Bound Methods; etc..." For more information see Teaching; Ted Ralphs' Home Page; Computational Optimization Research at Lehigh or the Department of Industrial & Systems Engineering COMPUTATION IN OPERATIONS RESEARCH (IE 495) - T. Ralphs, Computational Optimization Research at Lehigh, Department of Industrial & Systems Engineering, P.C. Rossin College of Engineering and Applied Science, Lehigh University Multimedia Computation in Operations Research Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples from over "25" "Computation in Operations Research" Course Lectures include "...Synthesis; Analyzing Parallel Algorithms; Communication Protocols; Union Find and Hash Tables; Matroid; Introduction to Numerical Algorithms; Solving Systems of Equations; Scaling, Iterative Improvement, and Sparse Systems; etc..." For more information see Teaching; Ted Ralphs' Home Page; Computational Optimization Research at Lehigh or the Department of Industrial & Systems Engineering Operations Research Graduate Courses, Textbooks, Lectures, etc. OPTIMIZATION METHODS IN MANAGEMENT SCIENCE J.B. Orlin, Operations Research Center, Sloan School of Management, & the MIT OpenCourseWare, MIT Multimedia Optimization Methods in Management Science Course (Text & Images). VERY VERY VERY...EXTENSIVE. Optimization Methods in Management Science "...Introduces students to the theory, algorithms, and applications of optimization. Optimization methodologies include linear programming, network optimization, integer programming, decision trees, and dynamic programming. The methods have applications to logistics, manufacturing, transportation, marketing, project management, and finance..." For more information see the Operations Research Center; MIT OpenCourseWare: Sloan School of Management Courses; Sloan School of Management or the MIT OpenCourseWare Linear Programming Graduate Courses, Textbooks, Lectures, etc. 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 Graduate Courses, Textbooks, Lectures, etc. NONLINEAR PROGRAMMING (REAL PLAYER) - R.M. 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 Robert M. Freund's Home Page; Robert M. Freund's Faculty Home Page; Sloan School of Management; MIT OpenCourseWare: Sloan School of Management Courses or the MIT OpenCourseWare OPERATIONS RESEARCH CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS LOGISTICS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS TUTOR: OPERATIONS RESEARCH - Department of Mathematics & Statistics, The University of Melbourne, Australia VERY VERY EXTENSIVE. For more information see World-Wide-Web for Operations Research and Management Science (WORMS) or the Department of Mathematics & Statistics Some examples from over "30" Operations Research Calculators include Matrix Inverse Engine: The Reluctant Inverter Calculator Linear Equations: The Mercyless Equator Calculator Simplex Machine Calculator Transitivity Calculator: Tranzy's Closure Plotty, the Lazy Plotter OPERATIONS RESEARCH AND OPERATIONS MANAGEMENT (JAVA APPLETS) - Operations Research Center, Massachussetts Institute of Technology; Faculty of Business Administration, Memorial University of Newfoundland and the Cambridge Modeling Corporation VERY VERY EXTENSIVE. Operations Research & Operations Management Applet Categories include: "...Queuing and Networks; Forecasting; Inventory; Statistical Process Control..." For more information see the Interactive Learning Center or the Operations Research Center, MIT Some examples from over "14" Operations Research & Operations Management Applets include Queuing and Networks: Shortest Path Algorithms Calculator Forecasting: Forecasting Calculator Inventory: Quantity Discount EOQ Calculator Statistical Process Control: Mean & Range Chart Calculator OPERATIONS RESEARCH & LOGISTICS ALGORITHMS CALCULATORS & APPLETS OPERATIONS RESEARCH & LOGISTICS ALGORITHMS (JAVA APPLETS) - P. Athanasios, D. Nikolaos, & P. Panagiiotis, Univercity Of Patras, Greece VERY VERY EXTENSIVE. For more information see Papagelis Athanasios' Home Page Some examples from over "8" Operations Research & Logistics Applets include Kruskal Algorithm Applet Heuristic Algorithms Applet: Traveling Salesman Problem (T.S.P) Minimum Routes: Dijkstra Algorithm Applet Order Projects by Deadlines Precedence Applet P-MEDIAN CALCULATORS & APPLETS P-MEDIAN SOLVER (JAVA-APPLET) - P.M. Kaminsky, Department of Industrial Engineering and Operations Research (IEOR), U.C. Berkeley P-Median Solver "...the problem of locating P "facilities" relative to a set of "customers" such that the sum of the shortest demand weighted distance between "customers" and "facilities" is minimized..." For more information see P-Median Problem; Philip M. Kaminsky'S Home Page or the Department of Industrial Engineering and Operations Research (IEOR) SORTING CALCULATORS & APPLETS THE XSORTLAB APPLET - D. Eck, Department of Mathematics & Computer Science, Hobart and William Smith Colleges, Geneva, N.Y. VERY EXTENSIVE. xSortLab Applet "...knows five different sorting methods. It has a visual sorting mode, where you can watch as sixteen bars are sorted into increasing order..." For more information see Labs & Applets for the Most Complex Machine or David J. Eck's Home Page TRAVELING SALESMAN CALCULATORS & APPLETS TRAVELING SALESMAN PROBLEM - Author: K. Natasha; Hosted by: Sariel Har-Peled, Algorithms Group, Department of Computer Science, University of Illinois, Urbana-Champaign, Illinois VERY EXTENSIVE. Traveling Salesman Probem - Approximation Algorithms "...A traveling salesman has to travel through a bunch of cities, in such a way that the expenses on traveling are minimized. This is the infamous Traveling Salesman Problem...It belongs to a family of problems, called NP-complete problem..." For more information see Sariel's Research Pages; Sariel Har-Peled's Home Page; Algorithms Group or the Department of Computer Science TRAVELING SALESMAN SOLVER (TSP) (JAVA APPLET) - T. Pederson, Department of Computing Science, Umeå University, Sweden VERY EXTENSIVE. Traveling Salesman Calculator "...is a classical graph-theoretical problem..." For more information see GATTS Information or Thomas Pederson's Home Page

Parametric Equations & Curves PARAMETRIC EQUATIONS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS PARAMETRIC CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS PARAMETRIC CURVE PLOTTER APPLET - P. Kirby VERY EXTENSIVE. For more information see Vector Land or Paul Kirby's Home Page PARMETRIC EQUATIONS - Asian Technology Conference in Mathematics (ATCM) For more information see Calculus; Manipula Math with Java or Math Education and Technology PARAMETRIC FUNCTION GRAPH - Asian Technology Conference in Mathematics (ATCM) For more information see Calculus; Manipula Math with Java or Math Education and Technology PARAMETRIC SPLINE CURVES - D. Gillies, Department of Computing, Imperial College London, U.K. VERY EXTENSIVE. Parametric Spline Curves "...Curves and surfaces can have explicit, implicit, and parametric representations. Parametric representations are the most common in computer graphics..." For more information see Spline Curves and Surfaces; Duncan Gillies' Home Page or the Department of Computing THE PARAMETRIC EQUATIONS APPLET: GRAPHING PARAMETRIC CURVES - R. Miech (Emeritus), Number Theory and Combinatorics, Department of Mathematics, UCLA Parametric Equations Applet "... allows you to graph 2-dimensional parametric curves..." For more information see Java Applets; Ronald Miech's Applets Home Page or the Department of Mathematics Pendulums PENDULUM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS THE PENDULUM LAB - Franz-Josef Elmer, Department of Physics, Institut für Physik, Universität Basel (University of Basel), Switzerland Multimedia Pendulum Lectures & Lessons (Text, Images, Applets & Calculators). VERY VERY VERY...EXTENSIVE. Examples of "Pendulum" Lectures include The Equations of Motion "...The equation of motion of an undamped and undriven pendulum; The equations of motion of damped and driven pendula; The linearized equations of motion..." Oscillations and Resonances "...The harmonic oscillator; Nonlinear oscillations; Nonlinear resonance; Parametric resonance..." Nonlinear Dynamics "...Stability and bifurcation; The nature of deterministic chaos ..." For more information see Home Page of Franz-Josef Elmer or the Department of Physics Examples of Pendulum Calculators & Applets include The Undamped and Undriven Pendulum Applet The Vertically Driven Pendulum Applet THE PIT AND THE PENDULUM: CALCULATOR - The Shodor Education Foundation, Inc. Pendulum Calculator explores "...the differences between a simple pendulum and a physical pendulum, and the effects of the "small angle approximation"..." For more information see The Pit and the Pendulum or The Shodor Education Foundation, Inc. CHAOTIC PENDULUM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS CHAOTIC PENDULUM IN PHASE SPACE CALCULATORS & APPLETS A CHAOTIC PENDULUM IN PHASE SPACE - Applet Author: Hans Kowallik (Landau Research Group); Part of "Applets for A Survey of Computational Physics, Python Edition, Beta2" by R.H. Landau (Oregon State University), M.J. Páez (University of Antinoquia), & C. Bordeianu (University of Bucharest); Hosted by the: Landau Research Group, Department of Physics, College of Science, Oregon State University Multimedia A Chaotic Pendulum in Phase Space (Text & Images). VERY EXTENSIVE. A Chaotic Pendulum in Phase Space Applets include "...Complicated Behavior Applet; Comparison of Two Chaotic Pendula Applet..." For more information see Computational Physics Applets, Movies, etc.; Rubin H. Landau's Home Page or the Department of Physics FINITE DIMENSIONAL MECHANICAL SYSTEMS CALCULATORS & APPLETS LAGRANGE JAVA APPLETS - P. Selinger, Department of Mathematics & Statistics, Dalhousie University, Halifax, Nova Scotia, Canada VERY EXTENSIVE. Lagrange Calculator "...simulates finite dimensional mechanical systems...Here, you see a double pendulum with respective masses..." Other Pendulum Calculators & Applets include: "...Double Pendulum Applet; Double Spring Applet Spring Pendulum Applet..." For more information see Software; Research; Peter Selinger's Home Page or the Department of Mathematics & Statistics

Poisson POISSON CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS POISSON DISTRIBUTION CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FOR RELATED POISSON CALCULATORS & APPLETS SEE STATISTICS CALCULATOR CENTER POISSON PROCESS - K. Siegrist & J. York, Department of Mathematical Sciences, University of Alabama Multimedia Poisson Lessons & Calculators (Text & Applets). VERY VERY EXTENSIVE. The Poisson process "...is one of the most important random processes in probability theory. It is widely used to model random "points" in time and space, such as the times of radioactive emissions, the arrival times of customers at a service center, and the positions of flaws in a piece of material..." Examples of Poisson Lessons & Calculators include "...The Exponential Distribution; The Gamma Distribution; The Poisson Distribution; Splitting a Poisson Process; Bernoulli Trials and the Poisson Process; Higher Dimensional Poisson Processes..." Poisson Calculators include "...Gamma Experiment Calculator; Poisson Experiment Calculator; Two-Type Poisson Experiment Calculator; Two-Dimensional Poisson Process Calculator..." For more information see the Virtual Laboratories in Probability and Statistics or the Department of Mathematical Sciences THE POISSON CALCULATOR - The Poisson Pit, C. Anesi Poisson Calculator "...The Poisson distribution is usually employed for modeling systems where the probability of an event occurring is very low, but the number of opportunities for such occurrence is very high..." For more information see The Anesi Web Site Prime Numbers PRIME NUMBER LESSONS WITH CALCULATORS & APPLETS THE PRIME PAGES - C. Caldwell, Department of Mathematics and Statistics, College of Engineering and Natural Sciences, University of Tennessee, Martin, Tennessee VERY VERY VERY...EXTENSIVE. For more information see Chris Caldwell's Home Page or the Department of Mathematics and Statistics PRIME NUMBER CALCULATORS & APPLETS FACTORIZATION USING THE ELLIPTIC CURVE METHOD - D.A. Alpern, Buenos Aires, Argentina VERY VERY EXTENSIVE. Factorization using the Elliptic Curve Method Calculator "...can be used to find 20- or 30-digit factors of numbers or numerical expressions up to 1000 digits long. It also computes the number and sum of divisors, Euler's totient and Moebius, and its decomposition as a sum of up to 4 perfect squares..." For more information see Calculators or Darío A. Alpern's Home Page PRIME CURIOS!: A PRIMALITY TEST - CALCULATOR - C. Caldwell, Department of Mathematics and Statistics, College of Engineering and Natural Sciences, University of Tennessee, Martin, Tennessee VERY VERY EXTENSIVE. Prime Curios "...Do you have an integer you would like to test for primality?... " For more information see Chris Caldwell's 'The Prime Numbers' or the Department of Mathematics and Statistics PRIME NUMBERS, MERSENNE PRIMES, PERFECT NUMBERS, ETC. - L.C. Noll VERY VERY VERY...EXTENSIVE. For more information see Landon Curt Noll's Home Page or isthe.com PRIME NUMBERS - FACTORIS (ENGLISH) OR FACTORIS (FRANÇAIS) - Xiao Gang, Laboratoire J.-A. Dieudonné, Université de Nice, Nice, France English & Français. VERY VERY EXTENSIVE. Prime Numbers Calculator "...factors a formula into its irreducible or prime components... Such a formula may be an integer, a rational number, a polynomial of one variable x, or a rational function (with integer coefficients)..." For more information see WIMS PRIME NUMBER CALCULATOR - A. Schulman, Santa Rosa, CA VERY EXTENSIVE. Prime Number Calculator "...This is a very simple prime-number calculator, based on a Java applet. "View Source" to see how HTML and JavaScript interact with the Java applet..." For more information see Andrew Schulman's Home Page THE PRIME MACHINE CALCULATOR (JAVA APPLET) - P. Alfeld, Department of Mathematics, University of Utah VERY VERY EXTENSIVE. Prime Machine Calculator "...finds prime numbers using the Sieve of Eratosthenes and lets you study and explore those prime numbers..." For more information see Java Page or Peter Alfeld 's Home Page THE Nth PRIME PAGE (JAVA APPLET) - Author: A. Booker, and hosted by Chris Caldwell's 'The Prime Pages' VERY VERY EXTENSIVE. The Nth Prime Page Calculator "...Enter a value for n, from 1 to 1012, inclusive. The server will return the nth prime number..." Also includes: "...Pi function Calculator & Choose a Random prime..." For more information see The Prime Pages

Quantitative Finance - Advanced Mathematical Finance RELATED CENTERS FOR MORE ADVANCED MATHEMATICAL FINANCE, BUSINESS, MANAGEMENT, CORPORATE FINANCE, ETC. COURSES, CALCULATORS, SPREADSHEETS, ETC. SEE THE BUSINESS, MANAGEMENT & ECONOMICS CENTER QUANTITATIVE FINANCE COURSES TERM STRUCTURE MODELS (SPREADSHEETS OPEN ONLINE WITH EXCEL, iWORK-NUMBERS, IBM LOTUS SYMPHONY, NEOOFFICE, OPENOFFICE CALC, ETC.) - M. Haugh, Department of Industrial Engineering & Operations Research, Columbia University Multimedia Term Structure Models Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Term Structure Models" Course Chapters include "...Lattice Models; Stochastic Calculus; Short-Rate Models; Monte Carlo Methods for Short-Rate Models; Heath-Jarrow-Morton Models; Market Models..." Term Structure Model Spreadsheets include: "...Term Structure Lattices Calculator..." For more information see Martin Haugh's Home Page or the Department of Industrial Engineering & Operations Research QUANTITATIVE FINANCE COURSES, TEXTBOOKS, LECTURES, LESSONS, ETC. WILOTTWIKI QUANTITATIVE FINANCE - Wilmott Multimedia Quantitative Finance Lessons (Text & Images). VERY VERY VERY...EXTENSIVE. WilmottWiki Quantitative Finance "...repository of both received wisdom and cutting-edge research! (Or at least that is what we are aiming for!) This wiki is an ongoing project in which we hope the quant community will contribute so as to establish a convenient and free source of definitions, concepts, model specifications, and original research..." Examples of "WilmottWiki Quantitative Finance" Subject Categories include "...All Articles; Categories; Wanted Pages; Special Pages; etc..." For more information see Wilmott OPTIONS - Wikipedia Multimedia Options Lessons (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Options" Lessons include "...Bear call spread; Binary option; Bond option; Call option; Cliquet; Covered call; Exotic option; Naked call; Naked put; Straddle; Strike price; etc..." For more information see Wikipedia QUANTITATIVE FINANCE CALCULATORS, APPLETS & SPREADSHEETS (XLS) ASX CALCULATORS & TOOLS - Australian Securities Exchange VERY VERY EXTENSIVE. ASX Calculators & Tools "...The values produced by applying the calculators to different products may differ from the current price of those products, due to market conditions. Where an interest rate is specified, the overnight cash rate is used. Inflation expectations are built into this rate..." Examples from over "20" Calculators & Tools include Options Calculators "...Options Profiler Calculator; Covered Call Calculator; Margin Estimator Calculator; etc..." SFE Calculators "...SFE Futures and Options Calculator; 90 Day Bank Bill Strip Calculator; 30 Day Interbank Cash Rate Strip Calculator..." Bond Calculators; Warrants Calculator; etc. For more information see Australian Securities Exchange FOREX CALCULATORS - Oz Forex Foreign Exchange, Australia VERY VERY EXTENSIVE. FOREX Calculators include: Fx Currency Option Pricing Calculator INPUT Values include "...Ccy One; Ccy Two; Spike; Spot; Fwd; Volatility; Principal; Start Date; etc... Historical Rate Roll Calculator (Historical Rate Extensions Calculator - HRE) "...HRRs (Historic Rate Rolls) or HREs (Historical Rate Extensions) are the same thing. If a corporate has a forward contract where the rate on the deal is not at the current market and wants to extend that deal the normal procedure is..." Contract Predelivery Calculator (Pre-Delivery Calculator) "...For pre-delivering FX deals to a date nearer than the current settlement date of the deal. Almost the opposite to an HRE. Again a pre-deilvery is based on the historical rate as opposed to the market rate..." For more information see Oz Forex Foreign Exchange GLOBAL DERIVATIVES SPREADSHEETS (SPREADSHEETS OPEN ONLINE WITH EXCEL, iWORK-NUMBERS, IBM LOTUS SYMPHONY, NEOOFFICE, OPENOFFICE CALC, ETC.) - Global Options VERY VERY VERY...EXTENSIVE. Examples from over "60" Derivatives Calculators include Vanilla Options Calculators "...Black-Scholes-Merton Option Calculator; Binomial Method Option Calculator (Reiner-Leisen); Binomial Method Option Calculator (Cox-Ross-Rubinstein); Jump Diffusion Option Calculator (Merton); Hopscotch Method Option Calculator (Averaging Implicit & Explicit Finite Differences); Roll, Geske, Whaley Option Calculator (Single Dividend); Ju-Zhong Approximation Option Calculator; Exotic Options Calculators "...Geometric Closed Form Option Calculator (Kemna & Vorst); Barrier Option Calculator; Balloon Option Calculator; Cliquet Option Calculator; Double Barrier Option Calculator; Extreme Spread Calculator; Rainbow Option Calculator; Spread Option Calculator; etc..." Currency Derivatives Option Calculators Caplets & Floorlets Option Calculator Equity Linked Forex Option Calculator Quanto Option Calculator Bond Derivatives Option Calculators; Credit Derivatives Option Calculators; etc. For more information see Global Derivatives HOADLEY'S ON-LINE OPTIONS PRICING ANALYSIS CALCULATORS - P. Hoadley VERY VERY VERY...EXTENSIVE. Examples from over "10" Options Pricing & Probability Calculators include: "...Employee Stock Option (ESO) Valuation Calculator; Black-Scholes Pricing Analysis Option Calculator Trinomial Tree Graphical Option Calculator; Barrier Option Calculator Using Trinomial Lattice Calculator Black-Scholes/Binomial Convergence Analysis Option Calculator Dividend Impact Analysis & American & European Option Pricing Comparison Calculator; Stock Price lognormal Distribution Analysis Calculator; Stock Price Probability Calculator..." Hoadley Derivatives Add-in for Excel "...lets you put together spreadsheets & build spreadsheet applications which require the calculation of option prices, hedge parameters ("Greeks"), implied volatility, historical volatility, underlying asset probabilities, trading profitability, futures pricing, identification of optimal early exercise points,..." For more information see Peter Hoadley Some examples of Options Pricing & Probability Calculators include Cox, Ross & Rubinstein: Binomial Tree Option Calculator Cox, Ross & Rubinstein: Binomial Tree Option Calculator INPUT Values include: "...Strike price; Underlying Asset Price; Volatility; Interest rate; Days to Expiration; Dividend; etc..." Trinomial Tree Option Calculator Trinomial Tree Option Calculator INPUT Values include: "...Strike price; Underlying Asset Price; Volatility; Interest rate; Days to Expiration; Dividend; etc..." Black-Scholes/Binomial Convergence Analysis Black-Scholes/Binomial Convergence Analysis Calculator INPUT Values include: "...Strike price; Stock Price; Volatility; Interest rate; Days to Expiration; Option Type; etc..." OPTIONS CALCULATORS - International Securities Exchange (ISE) VERY EXTENSIVE. Options Calculators include: Basic Options Calculation Wizard "...walks newcomers through the process of setting the variables that affect the price of an option..." Advanced Options Calculator "...provides users with variables that affect the price of an option. This version of the calculator has an additional feature that allows users to calculate theoretical options prices and risk parameters..." For more information see the International Securities Exchange (ISE) OPTIONS CALCULATOR & COVERED CALL CALCULATOR - Montréal Exchanges, Canada VERY VERY EXTENSIVE. Trading Tools include "...Options Calculator; Covered Call Calculator..." For more information see the Montréal Exchanges OPTIONS CALCULATOR & COVERED CALL CALCULATOR - The Options Industry Council VERY VERY VERY...EXTENSIVE. 888options "...offers free 20 minute delayed quotes which include Stocks, Options with Indexes, LEAPS, and Historical Volatility information..." 888options Basic Options Calculator "...powered by IVolatility.com, provides fair values and Greeks of any option using our volatility data and previous trading day prices. You may customize all the input parameters (option style, price of the underlying instrument, strike, expiration, implied volatility, interest rate and dividends data) or enter a stock or options symbol and the database will populate all those fields for you!..." Covered Call Calculator "...20 minute delayed options quotes are provided by IVolatility, and NOT BY OCC. OCC makes no representation as to the timeliness, accuracy or validity of the information and this information should not be construed as a recommendation to purchase or sell a security,..." For more information see The Options Industry Council

Random Numbers RANDOM NUMER CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS HOTBITS: GENUINE RANDOM NUMBERS, GENERATED BY RADIOACTIVE DECAY - J. Walker, Fourmilab, Switzerland VERY VERY VERY...EXTENSIVE. Random Numbers "...an Internet resource that brings genuine random numbers, generated by a process fundamentally governed by the inherent uncertainty in the quantum mechanical laws of nature, directly to your computer in a variety of forms. HotBits are generated by timing successive pairs of radioactive decays detected by a Geiger-Müller tube interfaced to a computer..." For more information see Fourmilab LAVARND - Co-inventors: L.C. Noll & S. Cooper; Editor & Adviser: M. Pleasant VERY VERY VERY...EXTENSIVE. LEVARND "...a cryptographically sound random number generator. At its heart, it uses a chaotic source to power the generation of very high quality random numbers..." For more information see Landon Curt Noll's Home Page RANDOM NUMBER (RANDOM INTEGERS) GENERATOR - M. Haahr, Distributed Systems Group, Department of Computer Science, Trinity College, Dublin, Ireland VERY VERY VERY...EXTENSIVE. Random Numbers - Random Integers "...This form allows you to generate random integers. The randomness comes from atmospheric noise, which for many purposes is better than the pseudo-random number algorithms typically used in computer programs..." For more information see Mads Haahr's Home Page or the Random.org Examples of other Random Number Generators include Random Sequence Generator Random Byte Generator ("...Hexadecimal; Decimal; Octal; Binary...") RANDOM NUMER GENERATOR (JAVA APPLET) - P. Alfeld, Department of Mathematics, College of Science, University of Utah VERY VERY VERY...EXTENSIVE. Random Number Generator "...describes how (most) random number generators work and most importantly it lets you design and test your own random number generator..." For more information see Java Page; Peter Alfeld 's Home Page or the Department of Mathematics RANDOM NUMBERS GENERATOR (JAVA APPLET) - Author: J. Beaver & Hosted by K. Pruhs, Department of Computer Science, University of Pittsburgh VERY EXTENSIVE. Random Numbers Generator "...demonstrates random number generation with the Linear Congruential Method..." For more information see Applets; Applet Demonstration; CS 1501; Kirk Pruhs's Home Page or the Department of Computer Science Real Analysis REAL ANALYSIS COURSES & TEXTBOOKS Undergraduate Real Analysis Courses & Textbooks INTERACTIVE REAL ANALYSIS & JAVA TOOLS (JAVA APPLETS) - B.G. Wachsmuth, Department of Mathematics and Computer Science, Seaton Hall University Multimedia Real Analysis Course (Text & Images). VERY VERY VERY...EXTENSIVE. Interactive Real Analysis is "...an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, power series, and more..." Examples of "Real Analysis" Course Chapters include ...Sets & Relations; Infinity and Induction; Sequences of Numbers; Series of Numbers; Topology; Continuity and Differentiation; The Intergral; Sequences of Functions; Metric Spaces..." For more information see Bert G. Wachsmuth's Home Page; Bert G. Wachsmuth's Faculty Home Page; Department of Mathematics and Computer Science or Seaton Hall University Examples of Real Analysis Calculators include Sequencer Calculator Sequencer Calculator "...Lets you draw the elements of a sequence and determine graphically whether it converges..." Continuity Checker Calculator Continuity Checker Calculator "...investigates whether a given function is continuous at a point or uniformly continuous..." ADVANCED REAL ANALYSIS - C.T. McMullen, Department of Mathematics, Faculty of Arts & Sciences, Havard University Multimedia Advanced Real Analysis Course, PDF, 94 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Advanced Real Analysis" Course Chapters include "...Convexity and Locally Convex Topological Vector Spaces; Distributions; Fourier Transforms; Elliptic Equations; The Prime Number Theorem; Banach Algebras; Operator Algebras and the Spectral Theorem; Ergodic Theory..." For more information see Advanced Real Analysis Home Page; C.T. McMullen's Home Page or the Department of Mathematics Graduate Real Analysis Courses & Textbooks REAL ANALYSIS: PART I - W.G. Faris, Department of Mathematics, University of Arizona Multimedia "Real Analysis: Part I" Course - PDF, 150 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples From over "13" "Real Analysis: Part I" Course Chapters include "...Mathematical Proof; Sets; Relations, Functions, Dynamical Systems; Functions, Cardinal Number; Ordered Sets and Completeness; Metric Spaces; Measurable Functions; Integrals and Measures; Fubini’s Theorem; etc..." For more information see William G. Faris: Lecture Notes; William G. Faris's Home Page or the Department of Mathematics REAL ANALYSIS: PART II - W.G. Faris, Department of Mathematics, University of Arizona Multimedia "Real Analysis: Part II" Course - PDF, 119 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples From over "10" "Real Analysis: Part II" Course Chapters include "...Hilbert Space; Differentiation; Conditional Expectation; Fourier Series; Topology; Radon Measures; etc..." For more information see William G. Faris: Lecture Notes; William G. Faris's Home Page or the Department of Mathematics Real Functions REAL FUNCTIONS COURSES, TEXTBOOKS, ETC. REAL VARIABLES AND FUNCTIONAL ANALYSIS COURSES, TEXTBOOKS, ETC. THEORY OF FUNCTIONS OF A REAL VARIABLE - S. Sternberg, Department of Mathematics, Faculty of Arts and Sciences, Harvard University Multimedia Theory of Functions of a Real Variable Course (Book) - PDF, 393 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Click on "Theory of Functions of a Real Variable". Examples of "Theory of Functions of a Real Variable" Course (Book) Chapters include "...The topology of metric spaces; Hilbert Spaces and Compact operators; The Fourier Transform; Measure theory; The Lebesgue integral; The Daniell integral; Wiener measure, Brownian motion and white noise; Haar measure; The spectral theorem; Stone’s theorem; etc..." For more information see Shlomo Sternberg's Home Page; Shlomo Sternberg's Faculty Home Page or the Department of Mathematics Real Numbers REAL NUMBERS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS CONSTRUCTIVE REALS CALCULATORS & APPLETS CONSTRUCTIVE REALS CALCULATOR: IMPLEMENTS CONSTRUCTIVE REAL ARITHMETIC (JAVA APPLET) - Hans-J. Boehm, HP Labs, Hewlett-Packard Company VERY VERY VERY...EXTENSIVE. Constructive Reals Calculator "...operates on constructive real numbers. Numbers are represented exactly internally to the calculator, and then evaluated on demand to guarantee an error in the displayed result that is strictly less than one in the least significant displayed digit..." For more information see About Constructive Real Numbers (aka Recursive or Computable reals); Hans-J. Boehm's Home Page or HP Labs INVERSE SYMBOLIC CALCULATORS & APPLETS INVERSE SYMBOLIC CALCULATOR - Development Team: N. Singer, A. Shouldice, L. Ye, T. Daske, P. Dobcsanyi, D. Manna, O-Yeat Chan & J. Borwein; 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. Inverse Symbolic Calculator "...uses a combination of lookup tables and integer relation algorithms in order to associate with a user-defined, truncated decimal expansion (represented as a floating point expression) a closed form representation for the real number..." For more information see Computer Assisted Research Mathematics and its Applications (CARMA) or the School of Mathematical and Physical Sciences Representation Theory REPRESENTATION THEORY COURSES, TEXTBOOKS, ETC. Representation Theory Courses, Textbooks, etc. REPRESENTATION THEORY - C. Teleman, Department of Mathematics, College of Letters & Science, University of California, Berkeley Multimedia Representation Theory Course - PDF, 60 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Representation Theory" Course Chapters include "...What is Representation Theory?; Representations of a Cyclic Group; Complete Reducibility and Unitarity; Schur’s Lemma; Isotypical Decomposition; The Character of a Representation; The Regular Representation; Integrality in the Group Algebra; The Unitary Group; etc..." For more information see Math; Constantin Teleman's Home Page or the Department of Mathematics INTRODUCTION TO REPRESENTATION THEORY - P. Etingof, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Introduction to Representation Theory Course (Text & Images). VERY VERY VERY...EXTENSIVE. Introduction to Representation Theory "...goal is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces..." Examples of "Introduction to Representation Theory" Course Chapters include "...Basic Notions of Representation Theory; General Results of Representation Theory; Representations of Finite Groups: Basic Results; etc..." For more information see Introduction to Representation Theory; Mathematics Courses; MIT OpenCourseWare or the Department of Mathematics REPRESENTATION THEORY - FINITE GROUP REPRESENTATIONS FOR THE PURE MATHEMATICIAN - P. Webb, School of Mathematics, University of Minnesota Multimedia Representation Theory Book - Finite Group Representations for the Pure Mathematician (Text & Imags). VERY VERY VERY...EXTENSIVE. Chapters 1 thru 8 - PDF, 105 Pages; Chapters 9 to Appendix - PDF, 82 Pages Examples of "Representation Theory Book - Finite Group Representations for the Pure Mathematician" Chapters include "...Representation, Maschke’s theorem and semisimplicity; The structure of algebras for which every module is semisimple; The construction of modules and characters; Pro jective modules for group algebras; Changing the ground ring: splitting fields and the decomposition map; Changing the ground ring: splitting fields and the decomposition map; Brauer characters; Indecomposable modules; etc..." For more information see Peter Webb's Home Page or the School of Mathematics Representations of Finite Groups and Invariant Theory REPRESENTATION THEORY: REPRESENTATIONS OF FINITE GROUPS AND INVARIANT THEORY - D.I. Panyushev, Mathematical College, Independent University of Moscow; and the Institute for Information Transmission Problems, oscow, Russia Multimedia Lectures on Representations of Finite Groups and Invariant Theory - PDF, 49 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Lectures on Representations of Finite Groups and Invariant Theory Chapters include "...Representation theory of finite groups; Invariant theory of finite groups..." For more information see Dmitri I. Panyushev's Home Page

Sandpiles & Singing Dunes: the Motion of Sand Grains SANDPILE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS BTW SANDPILE MODEL CALCULATORS & APPLETS BAK-TANG-WIESENFELD (BTW) SANDPILE MODEL (JAVA APPLET) - S. Maslov & A. Zheludev, Physics Department, Brookhaven National Laboratory (BNL) VERY EXTENSIVE. BTW Sandpile Calculator - Sandpile Applet "...simulates the dynamics of the BTW sandpile model..." For more information see Applets or the Condensed Matter Theory Group CELLULAR AUTOMATA SAND PILE MODEL CALCULATORS & APPLETS CELLULAR AUTOMATA SAND PILE MODEL (JAVA APPLET) - A. Schueller, Department of Mathematics, Whitman College Cellular Automata Sand Pile Model - Sandpile Calculator - Sandpile Applet "...chance to play with sand without getting your hands dirty. The black pipe at the top center is a source of sand grains. The black line at the bottom is the ground..." For more information see My Java Applets or Albert Schueller's Home Page SINGING DUNES: THE MOTION OF SAND GRAINS THE SONG OF THE DUNES AS A SELF-ORGANISED (SELF-SYNCHRONIZED) INSTRUMENT - S. Douady, et.al., Laboratoire de physique statistique, Départment de physique, ENS, Paris, France Multimedia (Text, Images, Videos/Movies & Audio/Sound). VERY VERY EXTENSIVE. The Song of the Dunes as a Self-Organized Instrument "...By comparing several singing dunes and two controlled experiments, one in the laboratory and one in the field, we here demonstrate that the frequency of the sound is the frequency of the relative motion of the sand grains. The sound is produced because some moving grains synchronize their motions..." For more information see Stéphane Douady's Home Page or the Laboratoire de physique statistique Soap Film & Bubbles SOAP FILM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS SOAP FILM INTERFERENCE THICKNESS CALCULATORS & APPLETS SOAP FILM INTERFERENCE THICKNESS CALCULATOR - C.R. Nave, Department of Physics & Astronomy, College of Arts & Sciences, Georgia State University VERY EXTENSIVE. Soap Film Interferenct Thickness Calculator "...The interference colors from a soap film can be related to the thickness of the film by using the interference condition and noting that there is a 180 degree phase change upon reflection..." For more information see Thin Films; Interference Concepts; Light & Vision; HyperPhysics; Carl Rod Nave's Home Page or the Department of Physics & Astronomy SOAP FILM CALCULATORS & APPLETS DEFORMATION RETRACT SOAP FILM CALCULATORS & APPLETS J.F. ADAMS' DEFORMATION RETRACT (JAVA APPLET) - Author: K.A. Brakke, Department of Mathematical Sciences, Susquehanna University & EG-Models, Germany Deformation Retract Soap Film Calculator "...can help visualize the homotopy. It starts with one of the flat disks, the left, say, retracted horizontally along the midplane to the wire, stretching the film behind..." For more information see Deformation Retract Soap Film; EG-Models or Ken Brakke's Home Page or the Department of Mathematical Sciences SOAP FILM CALCULATORS & APPLETS SOAP FILM CONES CALCULATORS & APPLETS SOAP FILM CONES - K. Brakke, Department of Mathematical Sciences, Susquehanna University, Selinsgrove, PA Soap Film Cones "...If one magnifies a point of a soap film, one gets a tangent cone. Recall that a cone is composed of rays..." For more information see Ken Brakke's Home Page or the Department of Mathematical Sciences SOAP FILM CALCULATORS & APPLETS SOAP FILMS ON KNOTS CALCULATORS & APPLETS SOAP FILMS ON KNOTS - K. Brakke, Department of Mathematical Sciences, Susquehanna University, Selinsgrove, PA Soap Films on Knots "...Knotted wires support many interesting soap films. It has recently been proved that every knotted wire supports a soap film that does not touch the entire wire..." For more information see Ken Brakke's Home Page or the Department of Mathematical Sciences Spirograph SPIROGRAPH CALCULATORS & APPLETS SPIROGRAPH (PARAMETRIC EQUATIONS) APPLET - D. Little, Department of Mathematics, Eberly College of Science, Pennsylvania State University VERY EXTENSIVE. Spirograph Applet "...allows you to create all the SpiroGraphs your heart desires by varying the values of R, r and p, as well as..." For more information see Parametric Equations; Java Index; David Little's Home Page or the Department of Mathematics Splines, Spline Curves & Spline Surfaces SPLINES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS SPLINE CURVES CALCULATORS & APPLETS - ALL INCLUSIVE SPLINE SURFACES CALCULATORS & APPLETS - ALL INCLUSIVE CUBIC SPLINE INTERPOLATION UTILITY - AKiTi.ca, David Binner, Vancouver, British Columbia, Canada VERY EXTENSIVE. Cubic Spline Interpolation Utility "...is based on the sub-programs PCHEV and PCHEZ written by David K. Kahaner. These are top-level programs that control several sub-routines from the SLATEC collection..." For more information see Math Functions: Miscellaneous Mathematical Utilities or AKiTi SPLINES: AN INTERACTIVE INTRODUCTION TO SPLINES (JAVA APPLETS) - E. Demidov, Department of Semiconductor Physics, Institute for Physics of Microstructures (IPM), Russian Academy of Sciences (RAS), Russia VERY VERY VERY...EXTENSIVE. In English & Russian. For more information see E-notes Some examples from over "30" Spline Curves Applets & 3D Spline Surface Applets include Interpolating Cardinal and Catmull-Rom splines B-splines: Building cubic B-spline B-splines: Nonuniform B-splines Bézier spline curves Tensor product spline surfaces SPLINE CURVES AND SURFACES (JAVA APPLETS) - D. Gillies, Department of Computing, Imperial College London, U.K. Multimedia Spline Curves & Spline Surfaces Lessons with Applets (Text & Images). VERY VERY EXTENSIVE. For more information see Duncan Gillies' Home Page or the Department of Computing Examples from over "7" Spline Curves and Surfaces Applets include Explicit Spline Curves Calculators Explicit Spline Curves Calculators include: "...Cubic Curve Calculator; Quadratic Curve Calculator..." B-Spline Curves Calculators B-Spline Curves Calculators include: "...Approximate Gaussian Curve Calculator; Free B-Spline Calculator; B-Spline with Clamped Ends Calculator..." Bézier Surfaces CURVES (JAVA APPLETS) - Abteilung Geometrische Datenverarbeitung, Universität Karlsruhe (TH), Germany, (Geometric Design Group, University of Karlsruhe) VERY VERY EXTENSIVE. Curve Applets include: "...B-Splines Applet; Spline Curves Applet; De Boor's Applet; Spline Division Applet; B-Spline Rendering Applet; etc..." For more information see CAGD-Applets: An Interactive Tutorials on Geometric Modeling; CAGD-Applets Home Page or the Abteilung Geometrische Datenverarbeitung (Geometric Design Group)

Statistical Mechanics STATISTICAL MECHANICS COURSES, LECTURES & TEXTBOOKS Statistical Mechanics Textbooks STATISTICAL MECHANICS: ENTROPY, ORDER PARAMETERS, AND COMPLEXITY (PDF) - James P. Sethna, Laboratory of Atomic and Solid State Physics, Department of Physics, Cornell University & Published by Claredon Press, Oxford, 2008 Multimedia Statistical Mechanics: Entropy, Order Parameters, and Complexity Textbook - 371 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Statistical Mechanics: Entropy, Order Parameters, and Complexity "...This text is careful to address the interests and back ground not only of physicists, but of sophisticated students and researchers in mathematics, biology, engineering, computer science, and the social sciences...." Examples of "Statistical Mechanics: Entropy, Order Parameters, and Complexity" Textbook Chapters include "...What is statistical mechanics?; Temperature and equilibrium; Entropy; Free energies; Quantum statistical mechanics; Order parameters, broken symmetry, and topology; Abrupt phase transitions; etc..." For more information see James P. Sethna's Home Page; Laboratory of Atomic and Solid State Physics or the Department of Physics Statistical Mechanics Courses & Lectures STATISTICAL MECHANICS II (PHYSIS 212) - J. Moore, Department of Physics, University of California, Berkeley, & the Materials Sciences Division, Lawrence Berkeley Laboratory Multimedia Statistical Mechanics II Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples from over "20" "Statistical Mechanics II" Course Lectures include Collisional equilibria. Liouville's theorem for Hamiltonian systems; BBGKY hierarchy of evolution equations for n-particle distribution functions; Hydrodynamics; Correlation functions. Intro to rescaling; Landau theory. Ginzburg criterion. Critical exponents. Scaling hypothesis; Scaling hypothesis and rescaling transformations; Blume-Capel model: using RG to guess phase diagrams. 2D Ising self-duality; Gaussian model; etc..." For more information see Joel More's Home Page or the Department of Physics Stochastic Processes, Stochastic Analysis, etc. STOCHASTIC PROCESSES RELATED CENTERS FOR STOCHASTIC PROCESSES RELATED COURSES, CALCULATORS, ETC. SEE THE STATISTICS CENTER STOCHASTIC PROCESSES COURSES, TEXTBOOKS, ETC. STOCHASTIC PROCESSES - A. Dembo, Department of Mathematics & the Department of Statistics, Stanford University Multimedia Stochastic Processes Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Stochastic Processes" Course (PDF, 131 Pages) Chapters include "...Probability, measure and integration; Conditional expectation and Hilbert spaces; Stochastic Processes: general theory; Martingales and stopping times; Markov, Poisson and Jump processes; etc..." For more information see Amir Dembo's Home Page or the Department of Mathematics STOCHASTIC PROCESSES - C.R. Shalizi, Department of Statistics, Marianna Brown Dietrich College of Humanities and Social Sciences (Dietrich College), Carnegie Mellon University Multimedia Stochastic Processes Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Stochastic Processes" Course Lectures include "...Probability kernels and regular conditional probabilities, extendings finite-dimensional distributions defined recursively through kernels to processes (the Ionescu Tulcea theorem)..." One-paramater processes and their representation by shift-operator semi-groups; Kinds of continuity, versions of stochastic processes, difficulties of continuity, the notion of a separable random function; Markov processes as transformed IID noise; Markov processes as operator semi-groups on function space; Generators of homogeneous Markov processes, analogy with exponential functions; Diffusions, Wiener measure, non-differentiability of almost all continuous curves; Examples of stochastic integrals. Ito's formula for change of variables. Stochastic differential equations, existence and uniqueness of solutions. Physical Brownian motion: the Langevin equation, Ornstein-Uhlenbeck processes; Metric transitivity. Examples of ergodic processes. Preliminaries on ergodic decompositions; etc..." For more information see Cosma R. Shalizi's Home Page or the Department of Statistics STOCHASTIC EVOLUTION EQUATIONS - J.M.A.M. van Neerven, Analysis Group, Applied Mathematics, Faculty Electrical Engineering, Mathematics and Computer Science, Delft University of Technology (TU Delft), The Netherlands Multimedia Stochastic Evolution Equations Course - PDF (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Stochastic Evolution Equations" Course Chapters include "...Integration in Banach Spaces; Random Variables in Banach Spaces; Gaussian Random Variables; Stochastic Integration I the Wiener Integral; Linear Equations with Additive Noise I; Conditional Expectations and Martingales; UMD-spaces; Applications to Stochastic PDE; etc..." For more information see Stochastic Evolution Equations Home Page; Courses: Mathmatics; Jan van Neerven's Home Page; J.M.A.M. (Jan) van Neerven's Faculty Home Page; Analysis Group; Applied Mathematics; Faculty Electrical Engineering, Mathematics and Computer Science or TU Delft Online Courses LARGE DEVIATIONS COURSES, TEXTBOOKS, ETC. LARGE DEVIATIONS - A. Dembo, Department of Mathematics & the Department of Statistics, Stanford University Multimedia Large Deviations Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Large Deviations" Course Chapters include "...LDP for Finite Dimensional Spaces; The Finite Dimensional Case; General Principles; Sample Path Large Deviations; etc..." For more information see Amir Dembo's Home Page or the Department of Mathematics Sudoku SUDOKU CALCULATORS & APPLETS SUDOKU - Andrew Stuart, Sudoku Online: Home of the Sudokulist, U.K. Multimedia Sudoku Solver (Text & Images). VERY VERY EXTENSIVE. For more information see Sudoku Online: Home of the Sudokulist SUDOKU SOLVER - Department of Computer Science, Daimi, Faculty of Science, University of Aarhus, Denmark Multimedia Sudoku Solver (Text & Images). VERY EXTENSIVE. For more information see Martin Sponholtz's Home Page or the Department of Computer Science, Daimi SUDOKU SOLVER - SudokuWiki, Andrew Stuart Multimedia Sudoku Solver (Text & Images). VERY VERY EXTENSIVE. For more information see Strategy Families or SudokuWiki SUDOKU HINTS - SOLVER AND ONLINE PUZZLES - David J. Nixon Multimedia Sudoku Solver (Text & Images). VERY VERY EXTENSIVE. Sudoku Hints "...Sudoku puzzles also known as Su Doku or Number Place are easy to learn, but not necessarily easy to solve..." Symbolic/Numberic & Inverse Symbolic NUMERIC & SYMBOLIC CALCULATORS & APPLETS TUSANGA CALCULATOR - NUMERIC & SYMBOLIC CALCULATOR - A. Williams VERY VERY VERY...EXTENSIVE. Tusanga Calculator "...This online, numeric & symbolic calculator and solver enables you to define variables and functions as well as to evaluate expressions containing numbers in any number system from 2 (binary) over 8 (octal), 10 (decimal) and 16 (hexadecimal) to 36, roman numerals, complex numbers, intervals, variables, matrices, function calls,...." INVERSE SYMBOLIC CALCULATORS & APPLETS INVERSE SYMBOLIC CALCULATOR - Development Team: N. Singer, A. Shouldice, L. Ye, T. Daske, P. Dobcsanyi, D. Manna, O-Yeat Chan & J. Borwein; 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. Inverse Symbolic Calculator "...uses a combination of lookup tables and integer relation algorithms in order to associate with a user-defined, truncated decimal expansion (represented as a floating point expression) a closed form representation for the real number..." For more information see Computer Assisted Research Mathematics and its Applications (CARMA) or the School of Mathematical and Physical Sciences Tensors & Relativity GENERAL RELATIVITY, DIFFERENTIAL GEOMETRY, ETC. COURSES, TEXTBOOKS, ETC. RELATIVITY (EINSTEIN LIGHT) - Author: Joe Wolfe, Multimedia Design: George Hatsidimitris, Laboratories in Waves and Sound: John Smith, Department of Environmental and Applied Physics, School of Physics, Faculty of Science, University of New South Wales, Sydney, Australia Multimedia Relativity Lectures (Text, Images, Animations, Videos/Movies & Audio/Sound). VERY EXTENSIVE. Relativity Lectures (Einstein Light) include "...Galileo: Mechanics & Relativity; Maxwell: Electricity & Magnestism; Einstein: Relativity & Constant c; Time Dilation; E = mc2; Beyond Relativity..." For more information see Joe Wolfe's Educational Pages; Joe Wolfe's Home Page; Department of Environmental and Applied Physics; School of Physics or the Faculty of Science GENERAL RELATIVITY LECTURE NOTES - Matthias Blau, Gravity and String Theory Group, Albert Einstein Center for Fundamental Physics - Institute for Theoretical Physics, Université de Neuchâtel, Switzerland Multimedia General Relativity Course Lecture Notes - PDF - 229 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "General Relativity" Course Chapters include "...The Physics and Geometry of Geodesics; Tensor Algebra; Physics in a Gravitational Field; The Lie Derivative, Symmetries and Killing Vectors; The Schwarzschild Metric; Particle and Photon Orbits in the Schwarzschild Geometry; Linearised Gravity and Gravitational Waves; Kaluza-Klein Theory; etc..." For more information see Matthias Blau's Lecture Notes; Matthias Blau's Home Page; Gravity and String Theory Group or the Albert Einstein Center for Fundamental Physics - Institute for Theoretical Physics INTRODUCTION TO DIFFERENTIAL GEOMETRY AND GENERAL RELATIVITY - S. Waner, Department of Mathematics, Hofstra University Multimedia Differential Geometry and General Relativity Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Introduction to Differential Geometry and General Relativity" Course Chapters include "...Smooth Manifolds and Scalar Fields; Contravariant and Covariant Vector Fields; Riemannian Manifolds; Covariant Differentiation; Geodesics and Local Inertial Frames; The Riemann Curvature Tensor; The Stress Tensor and the Relativistic Stress-Energy Tensor; Three Basic Premises of General Relativity; etc..." For more information see Online Utilities & Software - Calculators; Finite Mathematics & Applied Calculus; Stefan Waner's Home Page; Department of Mathematics or Hofstra University DIFFERENTIAL GEOMETRY - VOLUME I: CURVES & SURFACES AND VOLUME II: MANIFOLDS - M. Ghomi, School of Mathematics, Georgia Institute of Technology Multimedia Differential Geometry - Volume II: Manifolds Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Differential Geometry - Volume I: Curves and Surfaces" Course Lectures include "...Definition of curves, examples, reparametrizations, length, Cauchy's integral formula, curves of constant width; General definition of curvature using polygonal approximations (Fox-Milnor's theorem); Osculating circle, Kneser's Nesting Theorem, total curvature, convex curves; Torsion, Frenet-Seret frame, helices, spherical curves; Intrinsic metric and isometries of surfaces, Gauss's Theorema Egregium, Brioschi's formula for Gaussian curvature; The definition of geodesic curvature, and the proof that it is intrinsic; etc..." Examples of "Differential Geometry - Volume II: Manifolds" Course Lectures include Immersions and Embeddings. Proof of the embeddibility of comapct manifolds in Euclidean space; Definition of differential structures and smooth mappings between manifolds; Proofs of the inverse function theorem and the rank theorem; Proof of Whitney's 2n+1 embedding theorem; Various definitions of orientability and the proof of their equivalence. Proof of the nonorientability of the Mobius strip and the nonembeddability of the real projective plane in R3. Proof that RPn is oreintable for n odd and is not orientable for n even; Definition of a Riemannian metric, and examples of Riemannian manifolds, including quotients of isometry groups and the hyperbolic space. The notion of distance on a Riemannian manifold and proof of the equivalence of the metric topology of a Riemannian manifold with its original topology; Riemannian connections, brackets, proof of the fundamental theorem of Riemannian geometry, induced connection on Riemannian submanifolds, reparameterizations and speed of geodesics, geodesics of the Poincare's upper half plane; Exponential map and geodesic flow; etc..." For more information see Differential Geometry I Home Page; Courses; Mohammad Ghomi's Home Page or the School of Mathematics DIFFERENTIAL GEOMETRY (MA3429) - D.R. Wilkins, School of Mathematics, Faculty of Science, Trinity College, University of Dublin, Ireland Multimedia Differential Geometry Course - PDF, 206 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of "Differential Geometry" Course Parts & Sections include Part I (PDF, 63 Pages) "...Topological Spaces and Smooth Manifolds; Tangent Spaces and Derivatives; Submanifolds of Smooth Manifolds; etc..." Part II (PDF, 77 Pages) "...Tensors and Multilinear Algebra; Vector Bundles; Vector Fields, Lie Brackets and Flows..." Part III (PDF, 72 Pages) "...Connections, Curvature, and Torsion; Riemannian and Pseudo-Riemannian Manifolds; etc..." For more information see Courses & Lecture Notes; David R. Wilkins Home Page or the School of Mathematics DIFFERENTIABLE MANIFOLDS (MATH 250A) - Hans Lindblad, Department of Mathematics, University of California, San Diego (UCSD) Multimedia Differentiable Manifolds Course - Differential Geometry Course (Text & Images). Differentiable Manifolds Course "...is roughly vector calculus on manifolds. An example of a manifold is a surface in space when you ignore the rigid structure of space. Many things in geometry and physics, such as Einstein's equations of general relativity, are best stated independent of a particular coordinate system. A manifold together with invariantly defined differential operators is the natural setting for many nonlinear equations of physics..." Example of "Differentiable Manifolds" Course Chapters include "...Differentiability; Inverse and implicit function theorem; Submanifolds of Euclidean space; Topological and smooth manifolds; Tangent space and bundle; Vector fields, existence for ODE, Lie bracket and derivative, Frobenius theorem; Tensors and differential forms; etc..." For more information see Hans Lindblad's Home Page; Hans Lindblad's Faculty Home Page or the Department of Mathematics GEOMETRY OF MANIFOLDS - Denis Auroux, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Geometry of Manifolds Graduate Course (Text & Images). VERY VERY VERY...EXTENSIVE. Geometry of Manifolds Course "...The main emphasis is on the geometry of symplectic manifolds, but the material also includes long digressions into complex geometry and the geometry of 4-manifolds, with special emphasis on topological considerations..." Examples from over "22" "Geometry of Manifolds" Course Lectures include "...Symplectic vector fields, flux; isotopy and deformation equivalence; Moser's theorem; Darboux's theorem; More Floer homology; almost-complex structures; compatibility with a symplectic structure; polar decomposition; compatible triple; Horizontal distributions; metric connections; curvature of a connection: Intrinsic definition; expression in terms of connection 1-form; Nijenhuis tensor; integrability; square of the dbar operator; Newlander-Nirenberg theorem; Kähler manifolds; complex projective space; Symplectic fibrations; Thurston's construction of symplectic forms; symplectic Lefschetz fibrations, Gompf and Donaldson theorems; Symplectic branched covers of symplectic 4-manifolds; etc..." For more information see Geometry of Manifolds Home Page; Denis Auroux's Home Page; Mathematics Courses; MIT OpenCourseWare or the Department of Mathematics GEOMETRY OF MANIFOLDS - T. Mrowka, Department of Mathematics, & the MIT OpenCourseWare, MIT Multimedia Geometry of Manifolds Graduate Course (Text & Images). VERY VERY VERY...EXTENSIVE. Geometry of Manifolds Course is "...analyzes topics such as the differentiable manifolds and vector fields and forms. It also makes an introduction to Lie groups, the de Rham theorem, and Riemannian manifolds..." Examples of "Geometry of Manifolds" Graduate Course Lectures include "...Smooth Maps and the Notion of Equivalence; Vector Bundles and the Differential: New Vector Bundles from Old; Vector Bundles and the Differential: The Tangent Bundle; Sard's Theorem; Stratified Spaces; Smale's Sard Theorem; etc..." For more information see Geometry of Manifolds Home Page; Tomasz Mrowka's Home Page; Mathematics Courses; MIT OpenCourseWare or the Department of Mathematics RIEMANNIAN GEOMETRY (MATH 250B) - Hans Lindblad, Department of Mathematics, University of California, San Diego (UCSD) Multimedia Riemannian Geometry Course - Differential Geometry Course (Text & Images). Riemannian Geometry Course "...Riemannian geometry is designed to describe the universe of creatures who live on a curved surface and who are unaware of space outside and can only measure distances and areas on the surface. This lead to the modern notion of a manifold independent of a surrounding space..." Example of "Riemannian Geometry" Course Chapters include "...Curvature of curves, surfaces and submanifolds of Euclidean space; Riemannian metric on a manifold. Riemannian connection; Geodesics; Curvature, Sectional curvature; Bianchi identities; Jacobi fields; etc..." For more information see Hans Lindblad's Home Page; Hans Lindblad's Faculty Home Page or the Department of Mathematics SEMI-RIEMANN GEOMETRY AND GENERAL RELATIVITY - S. Sternberg, Department of Mathematics, Faculty of Arts and Sciences, Harvard University Multimedia Semiriemannian Geometry Course (Book) - PDF, 251 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Click on "Semi-Riemann Geometry and General Relativity". Examples of "Semi-Riemann Geometry and General Relativity" Course (Book) Chapters include "...The Principle Curvatures; Rules of Calculus; Levi-Civita Connections; The bundle of frames; Connections on principal bundles; Gauss’s lemma; Special relativity; Die Grundlagen der Physik; Submersions; Petrov types; etc..." For more information see Shlomo Sternberg's Home Page; Shlomo Sternberg's Faculty Home Page or the Department of Mathematics DIFFERENTIAL GEOMETRY CALCULATIONS GRTENSOR II DEMONSTRATIONS - P. Musgrave, Astronomy Research Group, Department of Physics, Engineering Physics & Astronomy, Queen's University, Kingston, Ontario, Canada VERY VERY VERY...EXTENSIVE. GRTensorII "...a computer algebra package for performing calculations in the general area of differential geometry. Its purpose is the calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors..." Demonstrations of GRTensorII currently available are in the areas of: "...General Relativity & Geometry; Black Hole Perturbations; The GRJunction Package & Engineering Applications.." For more information see GRTensor II or the Department of Physics, Engineering Physics & Astronomy RELATIVITY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS THE RELATIVITY CALCULATOR - J.T. Mitchell, PHENIX Experimental Group, Relativistic Heavy Ion Collider (RHIC), Brookhaven National Laboratory (BNL) VERY EXTENSIVE. Relativity Calculator "...calculates physical properties at relativistic speeds. You input the speed of the object, its mass, length, and clock time, and the calculator will automatically calculate what the object will look like to you..." For more information see Relativistic; Jeffery Mitchell's RHIClets; Jeffery Thomas Mitchell's Home Page; PHENIX Software Page; PHENIX Experimental Group; Relativistic Heavy Ion Collider (RHIC) or the Brookhaven National Laboratory (BNL) RELATIVITY APPLET - T. Tao, Department of Mathematics, UCLA VERY VERY EXTENSIVE. Relativity Calculator Options include: "...An Inertial Reference Frame; An Inertial Object of Zero Length; A Non-inertial Object of Zero Length; A Inertial Object of Non-zero Length; A Light Ray or An Event..." For more information see Applets; Terence Tao's Home Page or the Department of Mathematics RELATIVISTIC ACCELERATION CALCULATORS & APPLETS TIME DILATION CALCULATORS & APPLETS PROPER-ACCELERATION CALCULATOR CALCULATORS & APPLETS CONSTANT PROPER-ACCELERATION CALCULATOR - P. Fraundorf, Department of Physics & Astronomy, University of Missouri, St. Louis VERY VERY EXTENSIVE. Constant Proper-Acceleration Calculator "...provides students with quantitative tools for dealing with time dilation, relativistic acceleration, and even curved space-time..." For more information see One-Frame Views of Unidirectional Motion; Phil Fraundorf's Home Page or the Department of Physics & Astronomy GENERAL RELATIVITY COURSES, CALCULATORS & APPLETS SPECIAL RELATIVITY COURSES, CALCULATORS, ANIMATIONS & SIMULATIONS GENERAL RELATIVIEY & SPECIAL RELATIVITY - C.R. Nave, Department of Physics & Astronomy, College of Arts & Sciences, Georgia State University VERY VERY EXTENSIVE. Multimedia General Relativity & Special Relativity Course (Text, Images, Simulations & Calculators). For more information see HyperPhysics; Carl Rod Nave's Home Page or the Department of Physics & Astronomy SPECIAL RELATIVITY (JAVA APPLET) - Physics 1, Department of Physics, California Institute of Technology (CIT) VERY EXTENSIVE. Special Relativity Calcaultor "...demonstrates some physical effects of Einstein's Special Relativity..." Special Relativity Calculator Options include: "...Experiment 1: Perpendicular Rods; Experiment 2: Flying Clocks; Experiment 3: A Light Clock; Experiment 4: Moving Michelson-Morley; Experiment 5: Barn & Ladder Paradox; Experiment 6: Car Headlight Experiment;..." For more information see Physics 1 Applet Page or Physics 1b (Analytical): Special Relativity and Electromagnetism

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