CALCULATORS ON-LINE CENTER MATHEMATICS CENTER: E-H

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Sydney, Australia: Sunday, December 29, 2019

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

over “4,420” Courses, Lectures, Manuals, Handbooks,

& “1,000’s” of Movies, Videos, Simulations & Animations

COMPLEX MATH: E-H

Hypercube & N-Dimensional

Mathematics Center

Calculators On-Line Center

Eigenvalues & Eigenvectors

EIGENVALUES AND EIGENVECTORS COURSES, LECTURES, LESSONS, ETC.

EIGENVALUE DEMONSTRATIONS & MINI-LECTURES ON EIGENVALUES (FLASH) – G. Strang,
Department of Mathematics & the
MIT OpenCourseWare, MIT
Multimedia Eigenvalue Demonstrations & Mini-lectures on Eigenvalues
(Text, Images, Videos/Movies & Audio/Sound).
VERY VERY EXTENSIVE.

Examples of “Eigenvalues” Video Lectures include

• • • • “…Eigenvectors and Trace Video Lecture;

• • • • Powers Video Lecture;

• • • • Diagonalization Video Lecture;

• • • • Differential Equations Video Lecture;

• • • • Symmetry Video Lecture;

• • • • Positive Definite Video Lecture; etc…”

For more information see the

Linear Algebra Course 18-06;

Gilbert Strang’s Home Page;

Department of Mathematics;

Mathematics Courses or the

MIT OpenCourseWare

EIGENVALUES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

• • • EIGENVECTORS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

EIGENEXPLORER – J.R. Senning, Department of
Mathematics & Computer Science, Gordon College, Wenham, MA

EigenExplorer

• • • • “…is a Java applet designed to explore the

• • • • the relationships between a matrix A, a vector x, and the

• • • • matrix-vector product Ax…”

For more information see

Linear Algebra Visualization Assistant;

Jonathan R. Senning’s Home Page or the

Department of Mathematics & Computer Science

EIGENVALUES AND EIGENVECTORS – AKiTi.ca, David Binner,
Vancouver, British Columbia, Canada
VERY VERY EXTENSIVE.

Examples of Eigenvalues and Eigenvectors Calculators include

• • • • “…Eigenvalues of a 2 by 2 Matrix Calculator;

• • • • Eigenvalues of a 3 by 3 Matrix Calculator;

• • • • Eigenvalues of a 4 by 4 Matrix Calculator;

• • • • Eigenvalues of a 5 by 5 Matrix Calculator;

• • • • Eigenvalues of a 6 by 6 Matrix Calculator; etc…”

For more information see

Math Functions: Miscellaneous Mathematical Utilities or

AKiTi

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

Click on Eigenvalue Problems

Eigenvalues and Eigenvectors

• • • • “…illustrate properties of eigenvalues and eigenvectors

• • • • of matrices, and demonstrate the behavior of algorithms

• • • • for computing them…”

Eignevalue Applets include:

• • • • “…Power Iteration and Inverse Iteration;

• • • • QR Iteration with Shifts; Jacobi’s Method;

• • • • Gershgorin’s Theorem…”

For more information see

Interactive Educational Modules in Computational Science;

Teaching;

Michael T. Heath’s Home Page or the

Department of Computer Science

EIGENVALUES AND EIGENVECTORS OF MATRICES IN TWO DIMENSIONS

EIGENVALUES AND EIGENVECTORS OF MATRICES
IN TWO DIMENSIONS (JAVA APPLETS) – B. Casselman,
Department of Mathematics,
Faculty of Science,
University of British Columbia, Vancouver, Canada
VERY EXTENSIVE.
For more information see

Topics in Geometry – Mathematics 309;

Bill Casselman’s Home Page or the

Department of Mathematics

EIGENVALUES OF A MATRIX

THE OVALS OF CASSINI AND GERSHGORIN’S CIRCLES – R.S. Verga &
A. Krautstengl, Department of Mathematics & Computer Science,
Kent State University

The Ovals of Cassini and Gershgorin’s Circles

• • • • “…This page presents an interactive introduction

• • • • to some ideas about the location of the eigenvalues of a

• • • • matrix…”

For more information see

Gershgorin-Type Problems;

1999 Abstracts or

Electronic Transactions on Numerical Analysis (ETNA)

EggMath

MATHEMATICS CALCULATORS & APPLETS RELATING TO EGGS

EGG MATH (JAVA APPLETS) – S. Bradlow, J. Sullivan, S. Levy & B. Klamik, Chickscope,
Beckman Institute for Advanced Science and Technology,
University of Illinois, Urbana-Champaign
VERY EXTENSIVE.

Egg Math is

• • • • “…a collection of web modules (including many interactive applets) covering

• • • • different topics in mathematics related to eggs…”

For more information see

Chickscope or the

Beckman Institute for Advanced Science and Technology

• • • • Examples of EggMath Calculators & Simulations include

The Shape of an Egg

The White/Yolk Theorem

Embryo Calculus

Cryptography, Cryptology
& Quantum Cryptography Journals & e-Prints

NIST’s Cryptographic Validation, Algorithm Validation,
Toolkits, FIPS Publications, Computer Security ITL Bulletins, etc.

IACR Publications

Black Hat Technical White Papers

Cryptography
1st & 2nd Year, Intermediate & Graduate
Courses, Lectures, Textbooks, Lessons, etc.

Zero Knowledge Proofs (ZK or ZKP)

Indistinguishability Obfuscation

Lattice-Based Cryptography
Homomorphic Encryption & Lattices

Quantum Cryptography

Steganography & Digital Watermarking
Courses, Textbooks, Lessons, Publications, etc.

Cryptography Calculators, Applets, etc. – All Inclusive
(Quantum Random Numbers, MAGMA, SAGE, Elliptic Curves,
Affine, ElGamal, Least Common Multiple,
Prime Factorization, Viginère Enciphering, etc.)

Electronic Paper & Pencil Cryptography

Enigma Encryption Machine

Reed-Solomon Encryption ~
RSA Encryption

Shift Ciphers

Electrical & Computer Engineering Center:
Computer Engineering, etc.: Computer and Network Security
Courses, Lectures, Textbooks, Calculators, etc.

Electrical & Computer Engineering Center:
Complexity Theory
Courses, Lectures, Textbooks, Calculators, etc.

Cryptography – Quantum Cryptography – Encryption – Steganography & Digital Watermarking

CRYPTOLOGY, CRYPTOGRAPHY, QUNATUM CRYPTOLOGRAPHY JOURNALS & E-PRINTS

Cryptography & Cryptology e-Prints

CRYPTOGRAPHY AND SECURITY E-PRINTS – arXiv.org
Multimedia Cryptography and Security e-Prints (Text & Images).
For more information see

arXiv.org

CRYPTOLOGY E-PRINTS – International Association for Cryptologic Research
Multimedia Cryptology e-Prints (ePrint) (Text & Images).
For more information see the

International Association for Cryptologic Research

QUANTUM PHYSICS E-PRINTS – INCLUDES QUANTUM CRYPTOGRAPHY – arXiv.org
Multimedia Quantum Physics e-Prints – Includes Quantum Cryptography (Text & Images).
For more information see

arXiv.org

Cryptography & Cryptology Journals

DESIGNS, CODES AND CRYPTOGRAPHY – Publisher: Springer Netherlands
Multimedia Designs, Codes and Cryptography Journal (Text & Images).

CRYPTOGRAPHY AND COMMUNICATIONS – Publisher: Springer New York
Multimedia Cryptography and Communications Journal (Text & Images).

CRYPTOLOGIA – Publisher: Taylor & Francis
Multimedia Cryptologia Journal (Text & Images).

JOURNAL OF CRYPTOGRAPHIC ENGINEERING – Publisher: Springer
Multimedia Journal of Cryptographic Engineering (Text & Images).

JOURNAL OF CRYPTOLOGY – International Association for Cryptologic Research
Multimedia Journal of Cryptology (Text & Images).
For more information see the

International Association for Cryptologic Research

NIST’S CRYPTOGRAPHY, CRYPTOGRAPHIC VALIDATION, ALGORITHM VALIDATION, BLOCK CIPHER TECHNIQUES

CRYPTOGRAPHY – Computer Security Resource Center (CSRC),
National Institute of Standards and Technology (NIST)
Multimedia Cryptography Toolkit (Text & Images).
For more information see

Topics or the

Computer Security Resource Center (CSRC)

IACR PUBLICATIONS

IACR PUBLICATIONS – International Association for Cryptologic Research (IACR)
Multimedia IACR Publications (Text & Images).
VERY VERY VERY…EXTENSIVE.
For more information see the

International Association for Cryptologic Research (IACR)

BLACK HAT TECHNICAL WHITE PAPERS

BLACK HAT USA 2014 BRIEFINGS – Black Hat
Multimedia Black Hat USA 2014 Briefings – Technical White Papers (Text & Images).
VERY VERY VERY…EXTENSIVE.
For more information see

Black Hat USA 2014 or

Black Hat

CRYPTOGRAPHY COURSES, LECTURES, TEXTBOOKS, LESSONS, ETC.

First & Second Year Cryptography Courses, Lectures, etc.

INTRODUCTION TO CRYPTOGRAPHY – (CS55N) (2015) – Dan Bonehs,
Applied Crypto Group,
Stanford Security Laboratory,
Department of Computer Science,
School of Engineering,
Stanford University;
Course Hosted by Coursera
Multimedia Introduction to Cryptography Course (Text, Images, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Introduction to Cryptography

• • • • “…This course explains the inner workings of cryptographic primitives and

• • • • how to correctly use them. Students will learn how to reason about the

• • • • security of cryptographic constructions and how to apply this

• • • • knowledge to real-world applications…”

Examples of “Introduction to Cryptography” Course Sections & Lectures include

• • • • Stream Ciphers
        • “…Stream ciphers and pseudo random generators Video Lecture;

• • • • • Attacks on stream ciphers and the one time pad Video Lecture;

• • • • • Real-world stream ciphers Video Lecture;

• • • • • Semantic Security Video Lecture; etc…”

Block Ciphters;

Message Integrity

• • • • • “…Message Authentication Codes Video Lecture;

• • • • • CBC-MAC and NMAC Video Lecture;

• • • • • MAC padding Video Lecture; etc…”

Authenticated Encryption;

Basci Key Exchange; etc.

For more information see

Introduction to Cryptography Home Page;

Cryptography I;

Dan Boneh’s Home Page;

Applied Crypto Group or the

Stanford Security Laboratory

AN INTRODUCTION TO CRYPTOGRAPHY AND CRYPTANALYSIS (2010) – E. Schaefer,
Department of Mathematics & Computer Science,
College of Arts and Sciences,
Santa Clara University
Multimedia An Introduction to Cryptography and Cryptanalysis Book – PDF, 120 Pages (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “An Introduction to Cryptography and Cryptanalysis” Book Parts & Sections include

• • • • Introduction
        • “…Vocabulary;

• • • • • Concepts; etc…”

Cryptography

• • • • • “…Symmetric key cryptography;

• • • • • Self-Synchronizing Stream Ciphers;

• • • • • Modern Block Ciphers;

• • • • • Public Key Cryptography;

• • • • • Diffie Hellman Key Agreement;

• • • • • RSA for Message Exchange;

• • • • • ElGamal Message Exchange;

• • • • • Massey Omura Message Exchange;

• • • • • Elliptic Curve Cryptography;

• • • • • Elliptic Curve Discrete Logarithm Problem;

• • • • • Elliptic Curve Cryptosystems;

• • • • • The MD5 hash function;

• • • • • Schnorr Authentication and Signature Scheme; etc…”

Applications of Cryptography

• • • • • “…Public Key Infrastructure;

• • • • • Certificates;

• • • • • Internet Security;

• • • • • Key Management and Salting 20 Quantum Cryptography;

• • • • • Blind Signatures;

• • • • • Digital Cash;

• • • • • Digital Elections; etc…”

Cryptanalysis

For more information see

Cryptography and Arithmetic Geometry;

Ed Schaefer’s Home Page or the

Department of Mathematics & Computer Science

EXPLORATIONS IN CRYPTOGRAPHY (CCS 130H) (2013) – Ç.K. Koç,
Department of Computer Science,
College of Engineering,
University of California Santa Barbara (UCSB)
Multimedia Explorations in Cryptography Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Explorations in Cryptography” Course Lectures include

• • • • “…Public-Key Cryptography;

• • • • Elliptic Curve Cryptography (ECC);

• • • • Elliptic Curve Digital Signature Algorithm (ECDSA;

• • • • Introduction to DES & AES and Efficient Software Implementations;

• • • • Random Number Generators for Cryptographic Applications;

• • • • Side-Channel Attacks and Countermeasures;

• • • • Cryptographic Algorithms and Key Size Issues; etc…”

For more information see

Teaching;

Çetin Kaya Koç’s Faculty Home Page or the

Department of Computer Science

INTRODUCTION TO CRYPTOGRAPHY (MATH 373/578) (2013) – K.K. Toth,
Department of Mathematics,
West Virginia University
Multimedia Introduction to Cryptography Course (Text & Images).
VERY VERY EXTENSIVE.

Examples of “Introduction to Cryptography” Course Lectures include

• • • • “…Modular Arithmetic;

• • • • Prime Numbers, Unique Factorization, & Finite Fields;

• • • • Discrete Logarithm Problem;

• • • • Diffie-Hellman Key Exchange;

• • • • ElGamal Public Key Cryptosystem; etc…”

For more information see

Introduction to Cryptography Course Home Page;

Krista K. Toth Faculty Home Page;

Intermediate Cryptography Courses, Lectures, etc.

A (RELATIVE EASY TO UNDERSTAND) PRIMER ON ELLIPTIC CURVE CRYPTOGRAPHY (10/24/2013) – CloudFlare, Inc.
Multimedia A (Relatively Easy To Understand) Primer on Elliptic Curve Cryptography Technical Report (Text & Images).

Elliptic Curve Cryptography (ECC)

• • • • “…is one of the most powerful but least understood types of

• • • • cryptography in wide use today…”

For more information see

CloudFlare Blog or

CloudFlare

ELLIPTIC CURVES (18.783) (2017) – A.V. Sutherland,
Department of Mathematics,
Massachusetts Institute of Technology (MIT)
Multimedia Elliptic Curves Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples from over “24” “Elliptic Curves” Course Lectures include

• • • • “…Finite fields arithmetic;

• • • • Isogenies;

• • • • Endomorphism rings;

• • • • Schoof’s algorithm;

• • • • Discrete logarithms;

• • • • Elliptic curve factorization;

• • • • Elliptic curve primality proving (ECPP)

• • • • Endomorphism algebras;

• • • • Elliptic functions, Eisenstein series, Weierstrass p-function;

• • • • Orders, ideals, class groups, isogenies over C;

• • • • The main theorem of complex multiplication; etc…”

For more information see

Elliptic Curves Course Home Page;

Andrew V. Sutherland’s Faculty Home Page or the

Department of Mathematics

PRACTICAL CRYPTOGRAPHIC SYSTEMS (650.445) (2012) – Matthew D. Green,
Security and Privacy Applied Reasearch (SPAR),
Department of Computer Science,
Whiting School of Engineering and the
Information Security Institute (ISI),
Johns Hopkins University
Multimedia Practical Cryptographic Systems Course (Text & Images).

Examples of “Practical Cryptographic Systems” Course Lectures include

• • • • “…Crypto & Physical Security;

• • • • Physical Security;

• • • • Protocols;

• • • • Attacking & Defending RFID Devices;

• • • • Provable Security;

• • • • Reverse Engineering Software; etc…”

For more information see

Practical Cryptographic Systems Home Page;

Matthew Green’s Home Page;

Security and Privacy Applied Reasearch (SPAR);

Information Security Institute (ISI) or the

Department of Computer Science

CRYPTOGRAPHY (CS 433) (2010) – B. Barak,
Microsoft Research New England,
Cambridge, MA
Multimedia Cryptography (Text & Images).
VERY VERY VERY…EXTENSIVE.

• • • • “…This course will be an introduction to modern “post-revolutionary” cryptography

• • • • with an emphasis on the fundamental ideas (as opposed to an emphasis on practical

• • • • implementations)…”

Examples from over “22” “Cryptography” Course Lectures include

• • • • “…Perfect secrecy and its limitations;

• • • • Computational model, computational security;

• • • • Computational indistinguishability, pseudorandom generators;

• • • • The authentication problem, CCA security;

• • • • One way permutations and pseudorandom generators, Goldreich-Levin Theorem;

• • • • Public key cryptography and Rabin encryption;

• • • • Zero knowledge proofs;

• • • • Forward security, identity-based encryption;

• • • • Oblivious transfer, Private information retrieval;

• • • • Secure 2-party and multiparty computation;

• • • • Cramer-Shoup Cryptosystem; etc…”

For more information see

Courses I Taught or Co-taught at the Department of Computer Science, Princeton University

Boaz Barak’s Home Page or

Microsoft Research New England

MODERN CRYPTOLOGY (MATH 5410) (2012) – B. Cherowitzo,
Department of Mathematical & Statistical Sciences,
College of Liberal Arts and Sciences,
University of Colorado, Denver, Colorado
Multimedia Modern Cryptology Course (Text & Images).
VERY VERY EXTENSIVE.

Examples of “Modern Cryptology” Course Lectures include

• • • • “…Redundancy and Information Theory;

• • • • Data Encryption Standard (DES) & Advanced Encryption Standard (AES);

• • • • The extended Euclidean Algorithm;

• • • • The Solovay-Strassen Primality Test;

• • • • The Chinese Remainder Theorem;

• • • • Coding Theory;

• • • • McEliece Cryptosystem; etc…”

For more information see

Modern Cryptology: Math 5410 Home Page;

Teaching Activity;

Bill Cherowitzo’s Home Page or the

Department of Mathematical & Statistical Sciences

CRYPTOGRAPHY AND COMPUTER SECURITY (CS 467) (2013) – M.J. Fischer,
Department of Computer Science,
Yale University
Multimedia Cryptography and Computer Security Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples from over “23” “Cryptography and Computer Security” Course Lectures include

• • • • “…Lecture 4: Block Ciphers
        • Cryptanalysis (Brute Force Attack & Manual Attacks);

• • • • • Building Block Cipher; etc…”

Lecture 7: Stream Cipher from Block Cipher, Active Adversary Attacks, Steganography, etc.;

Lecture 11: Discrete Logarithm; Diffie-Hellman Key Exchange, EIGamal Key Agreement, etc.;

Lecture 16: Hash Function Constructions, Authentication Using Passwords, Chinese Remainder Theorem, etc.;

Lecture 20: BBS Pseudorandom Sequence Generator, Bit-Prediction, Shamir’s Secret Splitting Scheme, etc.;

Lecture 23: Privacy-Preserving Multipary Computation, The Millionaire’s Problems, etc…”

For more information see

Cryptography and Computer Security Course Home Page;

Michael Fischer’s Home Page;

Michael Fischer’s Faculty Home Page or the

Department of Computer Science

Graduate Cryptography Courses, Lectures, etc.

INTRODUCTION TO CRYPTOGRAPHY (GRADUATE COURSE) (2012) – Y. Dodis,
Cryptography Group,
Department of Computer Science,
Courant Institute of Mathematical Sciences,
New York University
Multimedia Introduction to Cryptography Graduate Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Introduction to Cryptography Graduate Course

• • • • “…primary focus of this course will be on definitions and

• • • • constructions of various cryptographic objects, such as

• • • • pseudo-random generators, encryption schemes, digital signature schemes,

• • • • message authentication codes, block ciphers, commitment schemes…”

Examples from over “15” “Introduction to Cryptography” Graduate Course Lectures include

• • • • “…Problem of secret communication. One-time pad and Shannon impossibility result. Modern Cryptography: computationally bounded adversaries…”;

• • • • “Brush-up on number theory. Primes vs. composites, easy and hard problems. RSA, discrete log, factoring…”;

• • • • “Proving the general construction satisfies the next-bit test. Showing that next-bit test implies all statistical tests. Computational Indistinguishability and…”;

• • • • “Symmetric-Key Encryption. One-time definition and scheme. CPA definition and…”;

• • • • “…Commitment Schemes. Definition and properties. Increasing input size: bit-by-bit composition, hash-then-commit technique using CRHF’s…”;

• • • • “…Introduction to Zero-Knowledge (ZK). Proofs and class NP. Interactive protocols and class IP. Importance of…” etc.

• • • • NM Extractors, Condensers, Crooked LHL, Improved LHL;

• • • • Optimality of I.T. Key Derivation, Computational Extractors, Dense Model;

• • • • Robust Extractors and Their Limitations; etc…”

For more information see

Introduction to Cryptography Course Home Page;

Yevgeniy Dodis Faculty Home Page;

Cryptography Group;

Department of Computer Science or the

Courant Institute of Mathematical Sciences

RANDOMNESS IN CRYPTOGRAPHY (GRADUATE COURSE) (2013) – Y. Dodis,
Cryptography Group,
Department of Computer Science,
Courant Institute of Mathematical Sciences,
New York University
Multimedia Randomness in Cryptography Graduate Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples from over “15” “Randomness in Cryptography” Course Lectures include

• • • • “…Role of Randomness in Cryptography;

• • • • One-Time MACs, (XOR) Universal hashing, Min-entropy, Weak Keys;

• • • • Impossibility of Privacy with Weak Sources;

• • • • SV-robust Mechanisms and Bias-Control-Limited Source;

• • • • Encryption => Extraction, Bit-Fixing Source;

• • • • Cryptography with Weak Keys but Perfect Local Randomness;

• • • • NM Extractors, Condensers, Crooked LHL, Improved LHL;

• • • • Optimality of I.T. Key Derivation, Computational Extractors, Dense Model;

• • • • Robust Extractors and Their Limitations; etc…”

For more information see

Yevgeniy Dodis Faculty Home Page;

Cryptography Group;

Department of Computer Science or the

Courant Institute of Mathematical Sciences

ZERO KNOWLEDGE PROOFS (ZK or ZKP)

Zero Knowledge Proofs (ZK or ZKP) Publications

ZERO KNOWLEDGE PROOFS: AN ILLUSTRATED PRIMER – Matthew Green, A Few Thoughts on Cryptographic Engineering
Multimedia Zero Knowledge Proofs [ZK or ZKP]: An Illustrated Primer (Text & Images).
VERY VERY EXTENSIVE.

Zero Knowledge Proofs [ZK or ZKP]: An Illustrated Primer

• • • • “…zero-knowledge proofs are one of the most powerful tools cryptographers have ever devised. But

• • • • unfortunately they’re also relatively poorly understood. In this series of posts I’m going try to

• • • • give a (mostly) non-mathematical description of what ZK proofs are, and what makes them so special.

• • • • In this post and the next I’ll talk about some of the ZK protocols we actually use…”

For more information see

Matthew Green, A Few Thoughts on Cryptographic Engineering

INDISTINGUISHABILITY OBFUSCATION PUBLICATIONS, ETC.

Indistinguishability Obfuscation Overview Articles

PERFECTING THE ART OF SENSIBLE NONSENSE – Author: Erica Klarreich;
Published 1/30/2014,
Computer Science Category,
Quanta Magazine,
Simons Foundation
Multimedia Perfecting the Art of Sensible Nonsense Article (Text & Images).
For more information see

Erica Klarreich’s Home Page;

Computer Science Category;

Quanta Magazine or the

Simons Foundation

Indistinguishability Obfuscation Publications, etc.

CANDIDATE INDISTINGUISHABILITY OBFUSCATION AND FUNCTIONAL ENCRYPTION FOR ALL CIRCUITS (THE FIRST CRYPTOGRAPYIC GENERAL-PURPOSE SOFTWARE OBFUSCATION SCHEME) – S. Garg, C. Gentry,
S. Halevi, M. Raykova, A. Sahai, & B. Waters;
Date Published: 7/21/2013;
Publisher: Cryptology ePrint Archive,
International Association for Cryptologic Research (IACR)
Multimedia Candidate Indistinguishability Obfuscation and Functional Encryption for all circuits Publication (Text & Images).

“Candidate Indistinguishability Obfuscation and Functional Encryption for all circuits” (The First Cryptographic General-Purpose Software Obfuscation Scheme)

• • • • “…In this work, we give new constructions for secure obfuscation. While

• • • • indistinguishability obfuscation is the technical focus of our work, we

• • • • note that we know of no actual attacks on our obfuscation scheme as a

• • • • black- box obfuscator except for the attacks that arise on specific circuit

• • • • classes that are known to be unobfuscatable…”

For more information see the

Cryptology ePrint Archive;

International Association for Cryptologic Research (IACR);

Craig Gentry’s Home Page (Cryptography Research Group, IBM T.J.Watson Research Center);

Shai Halevi’s Home Page (Cryptography Research Group, IBM T.J.Watson Research Center);

Mariana Raykova’s Home Page (Cryptography Research Group, IBM T.J.Watson Research Center);

Brent Waters Home Page (Department of Computer Science, University of Texas, Austin) or

Amit Sahai’s Home Page (Department of Computer Science, UCLA)

HOW TO USE INDISTINGUISHABILITY OBFUSCATION: DENIABLE ENCRYPTION, AND MORE – A. Sahai & B. Waters;
Date Published: 7/23/2013;
Publisher: Cryptology ePrint Archive,
International Association for Cryptologic Research (IACR)
Multimedia How to Use Indistinguishability Obfuscation: Deniable Encryption, and More Publication (Text & Images).

“How to Use Indistinguishability Obfuscation: Deniable Encryption, and More”

• • • • “…We introduce a new technique, that we call punctured programs,

• • • • to apply indistinguishability obfuscation towards cryptographic problems.

• • • • We use this technique to carry out a systematic study of the applicability

• • • • of indistinguishability obfuscation to a variety of cryptographic goals…”

For more information see the

Cryptology ePrint Archive;

International Association for Cryptologic Research (IACR);

Brent Waters Home Page (Department of Computer Science, University of Texas, Austin) or

Amit Sahai’s Home Page (Department of Computer Science, UCLA)

PROTECTING OBFUSCATION AGAINST ALGEBRAIC ATTACKS – B. Barak, S. Garg, Y.T. Kalai, O. Paneth & A. Sahai;
Date Published: 2/4/2014;
Publisher: Cryptology ePrint Archive,
International Association for Cryptologic Research (IACR)
Multimedia Protecting Obfuscation Against Algebraic Attacks Publication (Text & Images).

“Protecting Obfuscation Against Algebraic Attacks”

• • • • “…We describe a simplified variant of this compiler, and prove

• • • • that it is a virtual black box obfuscator in a generic multilinear map model…”

• • • • “…Our result shows that there is a candidate obfuscator that

• • • • cannot be broken by algebraic attacks, hence reducing the task of

• • • • creating secure obfuscators in the plain model to obtaining sufficiently

• • • • strong security guarantees on candidate instantiations of multilinear maps…”

For more information see the

Cryptology ePrint Archive;

International Association for Cryptologic Research (IACR);

Boaz Barak’s Home Page (Microsoft Research New England) or

Amit Sahai’s Home Page (Department of Computer Science, UCLA)

ON THE IMPLAUSIBILITY OF DIFFERING-INPUTS OBFUSCATION AND EXTRACTABLE WITNESS ENCRYPTION WITH AUXILIARY INPUT – S. Garg, C. Gentry, S. Halevi & D. Wichs;
Date Published: 1/13/2014;
Publisher: Cryptology ePrint Archive,
International Association for Cryptologic Research (IACR)
Multimedia On the Implausibility of Differing-Inputs Obfuscation and Extractable Witness Encryption with Auxiliary Input Publication (Text & Images).
For more information see the

Cryptology ePrint Archive;

International Association for Cryptologic Research (IACR);

Craig Gentry’s Home Page (Cryptography Research Group, IBM T.J.Watson Research Center);

Shai Halevi’s Home Page (Cryptography Research Group, IBM T.J.Watson Research Center) or

Daniel Wichs Home Page (Department of Computer Science, Northeastern University)

LATTICE-BASED CRYPTOGRAPHY – HOMOMORPHIC ENCRYPTION AND LATTICES PUBLICATIONS & COURSES

Lattice-Based Cryptography & Homomorphic Encryption and Lattices Courses

ADVANCED CRYPTOGRAPHY: HOMOMORPHIC ENCRYPTION AND LATTICES (GRADUATE COURSE) (2013) – S. Halevi & T.G. Malkin,
Department of Computer Science,
The Fu Foundation School of Engineering and Applied Sciences,
Columbia University
Multimedia Advanced Cryptography: Homomorphic Encryption and Lattices Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Advanced Cryptography: Homomorphic Encryption and Lattices” Course Lectures include

• • • • “…The Hermite normal form;

• • • • Discrete Gaussians, Smoothing Parameter, Leftover Hash Lemma;

• • • • The Gentry-Peikert-Vaikuntanathan SIS-based signatures;

• • • • The lattice trapdoor construction of Micciciancio-Peikert;

• • • • The Gorbunov-Vaikuntanathan-Wee LWE-based Attribute-Based Encryption Scheme;

• • • • Ideal Lattices, The NTRU cryptosystem; etc…”

For more information see

Tal Malkin’s Home Page or the

Department of Computer Science

Lattice-Based Cryptography Pubications

THE GEOMETRY OF LATTICE CRYPTOGRAPHY – D. Micciancio,
Department of Computer Science & Engineering,
Jacobs School of Engineering,
University of California, San Diego (UCSD)
Multimedia The Geometry of Lattice Cryptography – PDF, 20 Pages (Text & Images).

The Geometry of Lattice Cryptography

• • • • “…Interest in lattice cryptography is due to several concurring factors.

• • • • On the theoretical side, lattice cryptography is supported by strong

• • • • worst-case/average-case security guarantees. On the practical side,

• • • • lattice cryptography has been shown to be very versatile, leading to

• • • • an unprecedented variety of applications, from simple…”

For more information see

Papers;

Daniele Micciancio’s Home Page or the

Department of Computer Science & Engineering

HOW TO SHARE A LATTICE TRAPDOOR: THRESHOLD PROTOCOLS FOR SIGNATURES AND (H)IBE – Authors: R. Bendlin, S. Krehbiel & C. Peikert;
Report: 2013/419, Date: 11/13/2013,
Cryptology ePrint Archive,
International Association for Cryptologic Research (IACR)
Multimedia How to Share a Lattice Trapdoor: Threshold Protocols for Signatures and (H)IBE – PDF, 29 Pages (Text & Images).
For more information see the

Cryptology ePrint Archive or the

International Association for Cryptologic Research (IACR)

ASYMPTOTICALLY EFFICIENT LATTICE-BASED DIGITAL SIGNATURE – Authors: Vadim Lyubashevsky and Daniele Miccicancio;
Report 2013/746, Date 11/13/2013,
Cryptology ePrint Archive,
International Association for Cryptologic Research (IACR)
Multimedia symptotically Efficient Lattice-Based Digital Signature – PDF, 20 Pages (Text & Images).
For more information see the

Cryptology ePrint Archive or the

International Association for Cryptologic Research (IACR)

QUANTUM CRYPTOGRAPHY, MEASUREMENT-DEVICE-INDEPENDENT QKD (MDI-QKD), BELL NONLOCALITY,

• • • DETECTION-LOOPHOLE-FREE TEST OF QUANTUM NONLOCALITY, AND APPLICATIONS, ETC.

FOR QUANTUM COMPUTERS, COMPUTATION, QUITS, TELPORTATION, ETC. COURSES, DATABASES & CALCULATORS SEE

QUANTUM COMPUTERS, COMPUTATION, QUITS, TELPORTATION

QUANTUM CRYPTOGRAPHY – arXiv.org, Cornell University Library
Multimedia Quantum Cryptography Publications – PDF, 51 Pages (Text & Images).
For more information see

arXiv.org

Quantum Cryptography

QUANTUM CRYPTOGRAPHY – Hoi-Kwong Lo & Yi Zhao,
Center for Quantum Information and Quantum Control,
Department of Physics and Department of Electrical & Computer Engineering,
Universityof Toronto, Toronto, Canada;
arxiv.org/pdf/0803.2507, April, 2008
Multimedia Quantum Cryptography – PDF, 51 Pages (Text & Images).
VERY VERY VERY…EXTENSIVE.

Quantum Cryptography

• • • • “…is the synthesis of quantum mechanics with the art of code-making (cryptography)…”

• • • • “…quantum cryptography is a branch of quantum information processing, which

• • • • includes quantum computing, quantum measurements, and quantum teleportation. Among

• • • • all branches, quantum cryptography is the branch that is closest to real-life

• • • • applications. Therefore, it can be a concrete avenue for the demonstrations

• • • • of concepts in quantum information processing…”

Examples of “Quantum Cryptography” Course Chapters include

• • • • “…Quantum Key Distribution: Motivation and Introduction;

• • • • Security Proofs;

• • • • Experimental Fundamentals;

• • • • Experimental Implementation of BB84 Protocol;

• • • • Other Quantum Key Distribution Protocols;

• • • • Quantum Hacking; etc…”

For more information see

arXiv: Quantum Cryptography;

arXiv.org or the

Center for Quantum Information and Quantum Control

Measurement-Device-Independent QKD (MDI-QKD)

FOILING QUANTUM HACKERS – Author: Hoi-Kwong Lo,
Centre for Quantum Information and Quantum Control,
Departments of Electrical & Computer Engineering and Physics,
University of Toronto,
Toronto, Ontario, Canada;
Published: 9/23/2013,
Physics 6, 104 (2013),
DOI: 10.1103/Physics.6.104,
Physics – Spotlighting Exceptional Research,
American Physical Society
Multimedia Foiling Quantum Hackers (Text & Images).

“Foiling Quantum Hackers”

• • • • “…Researchers have implemented a new quantum encryption

• • • • method that, in principle, may provide the ultimate security against hackers

• • • • in real-world cryptography applications…”

For more information see

Physics – Spotlighting Exceptional Research

REAL-WORLD TWO-PHOTON INTERFERENCE AND PROOF-OF-PRINCIPLE QUANTUM KEY DISTRIBUTION IMMUNE TO DETECTOR ATTACKS – Authors: A. Rubenok,
J.A. Slater, P. Chan, I. Lucio-Martinez, and W. Tittel;
Published: Week Ending 9/23/2013,
PRL 111, 130501 (2013),
Physics Review Letters,
Selected for a Viewpoint in Physics: Viewpoint: Foiling Quantum Hackers;
Physics – Spotlighting Exceptional Research,
American Physical Society
Multimedia Real-World Two-Photon Interference and Proof-of-Principle Quantum Key Distribution Immune to Detector Attacks (Text & Images).
For more information see

Foiling Quantum Hackers or

Physics – Spotlighting Exceptional Research

EXPERIMENTAL MEASUREMENT-DEVICE-INDEPENDENT QUANTUM KEY DISTRIBUTION – Authors:
Yang Liu, Teng-Yun Chen, Liu-Jun Wang, Hao Liang, Guo-Liang Shentu,
Jian Wang, Ke Cui, Hua-Lei Yin, Nai-Le Liu, Li Li, Xiongfeng Ma,
Jason S. Pelc, M. M. Fejer, Cheng-Zhi Peng, Qiang Zhang, and Jian-Wei Pan;
Published: Week Ending 9/27/2013,
PRL 111, 130502 (2013),
Physics Review Letters,
Selected for a Viewpoint in Physics: Viewpoint: Foiling Quantum Hackers;
Physics – Spotlighting Exceptional Research,
American Physical Society
Multimedia Experimental Measurement-Device-Independent Quantum Key Distribution (Text & Images).

“Experimental Measurement-Device-Independent Quantum Key Distribution”

• • • • “…By assuming a trusted source scenario, our practical system,

• • • • which generates more than a 25 kbit secure key over a 50 km fiber link,

• • • • serves as a stepping stone in the quest for unconditionally secure

• • • • communications with realistic devices…”

For more information see

Foiling Quantum Hackers or

Physics – Spotlighting Exceptional Research

Bell nonlocality

BELL NONLOCALITY – Authors: N. Brunner, D. Cavalcanti, S. Pironio,
V. Scarani, and S. Wehner;
Published: revised 12/18/2013 (this version, v2),
arXiv:1303.2849v2 [quant-ph],
arXiv
Multimedia Bell nonlocality – PDF, 65 Pages (Text & Images).

“Bell nonlocality”

• • • • “…We review the main concepts and tools which have been

• • • • developed to describe and study the nonlocality of quantum theory,

• • • • and which have raised this topic to the status of a full sub-field of quantum information science….”

Examples of “Bell nonlocality” Chapters include

• • • • “…Mathematical characterization of nonlocal correlations;

• • • • Nonlocality and quantum theory;

• • • • Applications of quantum nonlocality;

• • • • Information-theoretic perspective on nonlocality; etc…”

For more information see

Quantum Physics or

arXiv

Detection-Loophole-Free Test of Quantum Nonlocality, and Applications

DETECTION-LOOPHOLE-FREE TEST OF QUANTUM NONLOCALITY, AND APPLICATIONS Authors: B.G. Christensen,
K.T. McCusker, J. Altepeter, B. Calkins, T. Gerrits, A. Lita, A. Miller, L.K. Shalm, Y. Zhang,
S.W. Nam, N. Brunner, C.C.W. Lim, N. Gisin and P. G. Kwiat;
Published: revised 9/26/2013 (this version, v2),
arXiv:1306.5772v2 [quant-ph],
arXiv
Multimedia Detection-Loophole-Free Test of Quantum Nonlocality, and Applications Publication – PDF, 11 Pages (Text & Images).

• • • • “…We present a source of entangled photons that violates a

• • • • Bell inequality free of the “fair-sampling” assumption, by

• • • • over 7 standard deviations…”

• • • • “…we use the source to generate “device-independent” private

• • • • quantum random numbers at rates over 4 orders of magnitude beyond

• • • • previous experiments…”

For more information see

Quantum Physics;

arXiv;

Kwiat Quantum Information Group or

Paul G. Kwiat Faculty Home Page

STEGANOGRAPHY AND DIGITAL WATERMARKING COURSES, LESSONS, TECHNICAL REPORTS, ETC.

STEGANOGRAPHY E-PRINTS – arXiv.org
Multimedia Steganography e-Prints (Text & Images).
For more information see

arXiv.org

WATERMARKING E-PRINTS – arXiv.org
Multimedia Digital Watermarking e-Prints (Text & Images).
For more information see

arXiv.org

SKYDE: A SKYPE-BASED STEANOGRAPHIC METHOD – Authors: W. Mazurczyk,
M. Karas & K. Szczypiorski,
Department of Computer Networks and Switching,
Faculty of Electronics and Information Technology,
Institute of Telecommunications,
Warsaw University of Technology,
Warsaw, Poland;
Published: January, 2013 in the Cryptography and Security subsection,
Computer Science Section, arXiv.org
Multimedia SkyDe: a Skype-based Steganographic Method – PDF, 7 Pages (Text & Images).

SkyDe (Skype Hide)

• • • • “…a new steganographic method that utilizes Skype encrypted packets

• • • • with silence to provide the means for clandestine communication. It is

• • • • possible to reuse packets that do not carry voice signals for

• • • • steganographic purposes because Skype does not use any

• • • • silence suppression mechanism…”

For more information see

Wojciech Mazurczyk;

Department of Computer Networks and Switching or

arXiv.org

JOHNSON’S STEGANOGRAPHY AND DIGITAL WATERMARKING – Neil F. Johnson,
Johnson & Johnson Technology Consultants, LLC.
Multimedia Johnson’s Steganography & Digital Watermarking Lessons, Software, Technical Reports, etc. (Text & Images).

Steganography

• • • • “…applications conceal information in other, seemingly innocent media.

• • • • Steganographic results may masquerade as other file for data types,

• • • • be concealed within various media, or…”

For more information see

Johnson & Johnson Technology Consultants, LLC.

PETITCOLAS’ STEGANOGRAPHY AND DIGITAL WATERMARKING – Fabien Petitcolas
Multimedia Petitcolas’ Steganography & Digital Watermarking Lessons, Software, Technical Reports, etc. (Text & Images).
For more information see

Fabien Petitcolas Home Page

CRYPTOGRAPHY CALCULATORS & APPLETS: ALL INCLUSIVE

• • • ENCRYPTION CALCULATORS & APPLETS: ALL INCLUSIVE

Advanced Cryptography Calculators & Applets

ANU QUANTUM RANDOM NUMBER SERVER – Thomas Symul,
Syed Assad & Ping Koy Lam,
Secure Quantum Communication Group,
Centre for Quantum Computing and Communication Technology,
Department of Quantum Sciences (DQS),
Research School of Physics and Engineering,
The Australian National University,
Canberra,
Australia
VERY VERY VERY…EXTENSIVE.

ANU Quantum Random Number Server

• • • • “…This website offers true random numbers to anyone on

• • • • the internet. The random numbers are generated in real-time in

• • • • our lab by measuring the quantum fluctuations of the vacuum.

• • • • The vacuum is described very differently in the quantum mechanical

• • • • context than in the classical context…”

For more information see the

Secure Quantum Communication Group;

Centre for Quantum Computing and Communication Technology or the

Department of Quantum Science (DQS)

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

PRIMO – Marcel Martin,
Argenteuil,
France
VERY VERY VERY…EXTENSIVE.

Primo

• • • • “…primality proving program based on the ECPP (Elliptic Curve Primality Proving)

• • • • algorithm. With Primo, one can check

• • • • crypto-primes and prove whether they are actually prime…or not…”

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…”

CRYPTOLOGY CALCULATORS – Christel Bach,
Formerly at the Department of Mathematics,
Aarhus University,
Denmark (2010)
VERY VERY VERY…EXTENSIVE.
For more information see

Christel Bach Danish Design Agency

• • • • Examples of Elliptic Curves Calculators include

Elliptic Curve Calculator for any curve

Elliptic Curve Calculator for any curve

• • • • • • “…Elliptic Curve Calculator for elliptic curve E(Fp): Y^2=X^3+AX+B for p prime…”

Point calculation on ECC with Suite B

Point calculation on ECC with Suite B

• • • • • • “…Calculate kP on NIST Curves – recommended curves according to the Suite B standard

• • • • • • Select NIST Curve over Prime Field – P-192, P-224, P-256, P-384 & P-521;

• • • • • • Calculate kP for point you recieve from others…”

ECC – Menezes Vanstone Elliptic Curve ElGamal Cryptosystem

ECC – Menezes Vanstone Elliptic Curve ElGamal Cryptosystem

• • • • • • “…MV Elliptic Curve Cryptosystem;

• • • • • • Select NIST Curve over Prime Field – P-192, P-224, P-256, P-384 & P-521;

• • • • • • Calculate your public key – or type in Qx and Qy – a recived public key;

• • • • • • Encode your message to ASCII decimal value here; etc…”

Examples of other Cryptology Calculators inclulde

Modular multiplikative inverse

Message ASCII encoding/decoding

ELGAMAL CRYPTOSYSTEM INTERACTIVE APPLET – Department of Computer Science and Statistics,
University of Rhode Island
VERY EXTENSIVE.

ElGamal Cryptosystem Interactive Applet

• • • • “…enter P, a prime number in the range of 3..45000 and

• • • • S, a number between 2 and P-1 and then click the ok button…”

For more information see

Cryptology or the

Department of Computer Science and Statistics

Introduction & Intermediate Cryptography Calculators & Applets

IMMERSE YOURSELF IN CRYPTOGRAPHY – Crypto Club,
a collaboration between UIC’s Learning Sciences Research Institute,
Department of Mathematics, Statistics, and Computer Science,
and The School of Art and Design,
University of Illinois,
Chicago,
Illinois
VERY VERY EXTENSIVE.

Imerse Yourself in Cryptography

• • • • “…develops classroom and web-based material to teach

• • • • cryptography and related mathematics,…”

For more information see the

Department of Mathematics, Statistics, and Computer Science

CRYPTOGRAPHY AND NUMBER THEORY – F. Richman,
Department of Mathematical Sciences,
Florida Atlantic University
VERY VERY EXTENSIVE.
For more information see

Fred Richman’s Home Page or the

Department of Mathematical Sciences

• • • • Some examples from over “11” Cryptography Calculators include

Shift Ciphers Calculator

Viginère Enciphering Calculator

Primality Testing with Fermat’s Little Theorem Calculator

MATHEMATICAL CRYPTOGRAPHY CALCULATOR – J.H. Silverman,
Department of Mathematics,
Brown University
VERY EXTENSIVE.
For more information see

Cryptography – Mathematics 1580;

Joseph H. Silverman’s Home Page or the

Department of Mathematics

ELECTRONIC PAPER & PENCIL CRYPTOGRAPHY CALCULATORS & APPLETS

CIPHERCLERK’S APPLET – W.M. Plotz, Austria
VERY EXTENSIVE.

CipherClerk’s Applet

• • • • “…is implementing a collection of

• • • • historic ciphers. Most ciphers are ‘paper & pencil’

• • • • types, e.g. to use them you wouldn’t need more than a

• • • • sheet of paper and something to write….”

For more information see

Wilhelm M. Plotz’s Home Page

• • • • Examples of other Cipher Applets include

Virtual U.S. Army Cipher Device, Model M-94

Major Bazeries Cipher Device

ENIGMA ENCRYPTION MACHINE CALCULATORS & APPLETS

THE ENIGMA MACHINE (JAVA APPLET) – R. Schwager
VERY EXTENSIVE.

The Enigma Machine Applet

• • • • “…has several variable settings

• • • • that affect the operation of the machine. The user must select

• • • • three rotors from a set of rotors to be used in the machine.

• • • • A rotor contains one-to-one mappings of all the letters. Some

• • • • Enigma machines had more than 3 rotors which just added to

• • • • the number of possible encryption combinations…”

REED-SOLOMON ENCRYPTION CALCULATORS & APPLETS

FINITE FIELD CALCULATOR AND REED-SOLOMON SIMULATOR (JAVA APPLET) – E. Soljanin,
Bell Labs,
Alcatle-Lucent,
Murray Hill, New Jersery
VERY EXTENSIVE.

Finite Field Calculator

• • • • “…allows arithmetic over extension fields of GF(2)…”

Reed-Solomon Encoder/Decoder Calculator

• • • • “…A codeword is generated based on a random information

• • • • word. A random set of t errors is generated and added to the

• • • • codeword…”

For more information see

Emina Soljanin’s Home Page or

Bell Labs

RSA ENCRYPTION CALCULATORS & APPLETS

FINDING THE RSA PUBLIC KEY (JAVA APPLET) – Andreas de Vries,
Math It, Fachbereich Technische Betriebswirtschaft, Germany
In English & German/Deutsch.
VERY EXTENSIVE.

Finding the RSA Public Key Simulation

• • • • “…determines the RSA public key (e, n) depending on

• • • • the given secret key (d, p, q)…”

For more information see

Math It Mathematical Applets or

Math It

SHIFT CIPHERS CALCULATORS & APPLETS

SHIFT CIPHERS – 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

Shift Ciphters Calculator

• • • • “…When implementing the shift cipher, each letter of

• • • • the message is shifted a fixed distance down the alphabet…”

For more information see

Applications of Congruences;

Number Theory or the

Department of Mathematical Sciences

Ergodic Theory, Bers Slices, Riemann Surfaces, Teichmüller Theory, Teichmüller Space

ERGODIC THEORY, RIEMANN SURFACES, TEICHMTÜLLER THEORY & TEICHMTÜLLER SPACE COURSES & SEMINARS

ERGODIC THEORY (254A) – T. Tao,
Analysis Group,
Department of Mathematics,
Division of Physical Sciences,
College of Letters and Science,
UCLA
Multimedia Ergodic Theory Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Ergodic Theory” Course Lectures include

• • • • Lecture 8: The mean ergodic theorem;

• • • • Lecture 9: Ergodicity;

• • • • Lecture 10: The Furstenberg correspondence principle;

• • • • Lecture 15: The Furstenberg-Zimmer structure theorem and the Furstenberg recurrence theorem;

• • • • Lecture 16: A Ratner-type theorem for nilmanifolds; etc…”

For more information see

Terence Tao’s Home Page at WordPress.com;

254B;

Terence Tao’s Home Page;

Analysis Group or the

Department of Mathematics

ERGODIC THEORY – K. Petersen,
Department of Mathematics,
University of North Carolina
Multimedia Graduate Ergodic Theory Lectures – PDF, 28 Pages (Text & Images).
VERY VERY EXTENSIVE.
For more information see

Karl Petersen’s Home Page or the

Department of Mathematics

RIEMANN SURFACES, DYNAMICS, GEOMETRY & TEICHMTÜLLER THEORY – C.T. McMullen,
Department of Mathematics,
Faculty of Arts & Sciences,
Havard University
Multimedia Riemann Surfaces, Dynamics, Geometry & Teichmüller Theory Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Riemann Surfaces, Dynamics, Geometry & Teichmüller Theory Course

• • • • “…will concern the interaction between:

• • • • hyperbolic geometry in dimensions 2 and 3;

• • • • the dynamics of iterated rational maps; and

• • • • the theory of Riemann surfaces and their deformations…”

Examples of “Riemann Surfaces, Dynamics, Geometry & Teichmüller Theory” Course Chapters include

• • • • “…Geometric Function Theory;

• • • • Teichmüller Theory;

• • • • Dynamics of Rational Maps;

• • • • Hyperbolic 3-Manifolds;

• • • • Holomorphic Motions and Structural Stability;

• • • • Iteration on Teichmüller Space;

• • • • Geometrization of 3-Manifolds; etc…”

For more information see

Courses;

C.T. McMullen’s Home Page or the

Department of Mathematics

CALCULATORS, APPLETS & SOFTWARE

BEAR: BERS SLICES OF PUNCTURED TORI – D. Dumas,
Department of Mathematics, Statistics, and Computer Science,
College of Liberal Arts & Sciences,
University of Illinois,
Chicago, Illinois
VERY VERY VERY…EXTENSIVE.

BEAR: BERS Slices of Punctured Tori Calculator

• • • • “…is a mathematical research tool for calculating and

• • • • testing discreteness of holonomy representations of complex

• • • • projective structures on punctured tori. It can be used to

• • • • draw pictures of Bers slices and explore the geometry of

• • • • quasifuchsian space in the SL2(C) representation…”

For more information see

David Dumas’ Home Page or the

Department of Mathematics, Statistics, and Computer Science

RANDOM CHORDS APPLET – D. Dumas,
Department of Mathematics, Statistics, and Computer Science,
College of Liberal Arts & Sciences,
University of Illinois,
Chicago, Illinois
VERY EXTENSIVE.

Random Chords Applet

• • • • “…demonstrates a result from the paper

Distribution
of intersection lengths of a random geodesic with a geodesic
lamination

• • • • by…”

For more information see

David Dumas’ Home Page or the

Department of Mathematics, Statistics, and Computer Science

Fault Tolerant Computing

FAULT TOLERANT COMPUTING COURSES, TEXTBOOKS, LECTURES, CALCULATORS, APPLETS, ETC.

FAULT TOLERANT COMPUTING SIMULATOR (JAVA APPLETS) – I. Koren,
Department of Electrical and Computer Engineering,
College of Engineering,
University of Massachusetts
VERY VERY VERY…EXTENSIVE.

Examples of “Fault Tolerant Computing” Subject Categories include

• • • • “…Error Detection and Correction Codes;

• • • • Fault Detection in Encryption Algorithms;

• • • • Reliability Evaluation;

• • • • Networks; etc…”

For more information see

Israel Koren’s Home Page or the

Department of Electrical and Computer Engineering

• • • • Examples from over “27” Fault Tolerant Computing Calculators & Applets include

The Cyclic Code Simulator: Cyclic Encoder/Decoder

Systematic and Standard Cyclic Codes

Arithmetic Encoder/Decoder Applet

Advanced Encryption Algorithm – Detection: Fault Detection in AES Encoder and Decoder Applet

4-state Markov Chain Solver Calculator

Calculation of Terminal Reliability for Two Nodes in a Network Applet

Checkpointing Calculators

Checkpointing Calculators include

• • • • • • Uniprocessor Checkpointing for Multiple Instructions Calculator;

• • • • • • Domino Effect Animation for Distributed Checkpointing Calculator.

Fibonacci Numbers

FIBONACCI COURSES, TEXTBOOKS, LECTURES & LESSONS WITH CALCULATORS & SIMULATIONS

FIBONACCI NUMBERS AND THE GOLDEN SECTION – R. Knott,
and hosted by the Department of Mathematics of Surrey University, U.K.
Multimedia Fibonacci Numbers Lectures & Lessons (Text, Images, Calculators, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Examples of “Fibonacci Numbers and the Golden Section” Lectures & Lessons include

• • • • Fibonacci Numbers and Nature;

• • • • The Mathematical Magic of the Fibonacci Numbers
        • “…looks at the patterns in the Fibonacci numbers themselves:

• • • • • the Fibonacci numbers in Pascal’s Triangle; using the Fibonacci

• • • • • series to generate all right-angled triangles with integers

• • • • • sides based on Pythagoras Theorem…”

Two-dimensional Geometry and the Golden section or Fantastic Flat Facts about Phi; etc.

For more information see

Fibonacci Numbers and the Golden Section or

Ron Knott’s Home Page

FIBONACCI CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

• • • FIBONACCI AND LUCUAS NUMBERS CALCULATORS & APPLETS

FIBONACCI AND LUCUAS NUMBER CALCULATOR – R. Knott,
and hosted by the Department of Mathematics of Surrey University, U.K.
VERY VERY EXTENSIVE.

“…For Fibonacci(i) and Lucas(i) you have a choice of Precision: exact or approximate.

• • • • Exact: the calculator will find Fibonacci(i) and Lucas(i) for i into the thousands…”

• • • • Approximate: Immediate result. The length of the answer decreases as i gets larger…”

For more information see

Fibonacci Numbers and the Golden Section or

Ron Knott’s Home Page

FIBONACCI SERIES CALCULATORS & APPLETS

GENERALISING THE FIBONACCI SERIES – R. Knott,
and hosted by the Department of Mathematics of Surrey University, U.K.
VERY VERY EXTENSIVE.
For more information see

Fibonacci Numbers and the Golden Section or

Ron Knott’s Home Page

• • • • Some examples of Fibonacci Calculators include

General Fibonacci Series Calculator

General Fibonacci Series Calculator

• • • • • • “…is a simple calculator to show you some terms of a General Fibonacci Series…”

Wythoff Array Calculator

Stolarsky Array Calculator

FIBONACCI NUMBER SYSTEM CALCULATORS & APPLETS

A FIBONACCI NUMBERS – Ron Knott,
Department of Mathematics,
Faculty of Electronics and Physical Sciences,
University of Surrey, U.K.
VERY VERY VERY…EXTENSIVE.
For more information see

Ron Knott’s web pages on Mathematics or the

Department of Mathematics

FIBONACCI SEQUENCES CALCULATORS & APPLETS

FIBONACCI SEQUENCES WITH MULTIPRECISION JAVA – F. Richman,
Department of Mathematical Sciences,
Florida Atlantic University
VERY EXTENSIVE.

Fibonacci Sequences Calculator

• • • • “…You can set the initial values, the number of terms

• • • • in the sequence, and the number of decimal places in the ratios…”

For more information see

JavaScripts or

Fred Richman’s Home Page or the

Department of Mathematical Sciences

Fourier Analysis Courses & Lectures

Fourier Transform & Fast Fourier Transform

Discrete Fourier Transform ~
Fourier-Laplace

Fourier Transform Experimentation: Image Processing

Fourier Series ~
Fourier Synthesis

Fourier

FOURIER ANALYSIS COURSES, LECTURES, TEXTBOOKS, MANUALS, ETC.

THE FOURIER TRANSFORM AND ITS APPLICATIONS – B.G. Osgood,
Department of Electrical Engineering;
Engineering Courses Online: Stanford Engineering Everywhere (SEE),
School of Engineering,
Stanford University
Multimedia The Fourier Transform and Its Applications Course (Text, Images, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Examples from over “29” “The Fourier Transform and Its Applications” Video Course Lectures include

• • Lecture 2
    • “…Periodicity; How Sine And Cosine Can Be Used To Model More Complex Functions, Example Of Periodizing A Signal, Discussion Of How To Model Signals With Sinusoids, “One Period, Many Frequencies” Idea In Modeling Signals, Modeling A Signal A,…”

Lecture 6

• • • “…Setup For Fourier Transform Derivation From Fourier Series, Results Of The Derivation: Fourier Transform And Inverse Fourier Transform, Definition Of The Fourier Transform (Analysis), Definition Of Fourier Inversion (Synthesis),…”

Lecture 12

• • • “…Cop Story, Review Of Rapidly Decreasing Functions, Generalized Functions (Distributions) (Delta Function, Etc.), Viewing Delta As A Limit V. Operationally,…”

Lecture 15

• • • “…Application Of The Fourier Transform: Diffraction: Setup, Representation Of Electric Field, Approach Using Huyghens’ Principle, Discussion Of The Phase Change Associated With Different Paths,…”

Lecture: 22

• • • “…FFT Algorithm: Setup: DFT Matrix Notation, One Intuition Behind FFT: Factoring Matrix, Our Approach: Split Order N Into Two Order N/2, Iterate, Notation (To Keep Track Of Powers Of Complex Exponentials),…” etc.

For more information see

Courses;

Stanford Engineering Everywhere (SEE);

Brad Osgood’s Home Page;

Department of Electrical Engineering or the

School of Engineering

FOURIER AND COMPLEX ANALYSIS – R.L. Herman,
Department of Mathematics and Statistics,
College of Arts & Sciences,
University of North Carolina,
Wilmington, North Carolina
Multimedia Fourier and Complex Analysis Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

“An Introduction to Fourier and Complex Analysis with Applications to the Spectral Analysis of Signals”

• • “…This is an introduction to topics in Fourier analysis and

• • complex analysis. It is a course aimed at students majoring in

• • mathematics and science who are at least at their junior level

• • of mathematical maturity. Students are introduced

• • to Fourier series, Fourier transforms, and a basic complex analysis…”

Examples of “An Introduction to Fourier and Complex Analysis with Applications to the Spectral Analysis of Signals” Course Lectures include

• • “…Sequences and Series;

• • Fourier Series;

• • Generalized Fourier Series;

• • Complex Integration;

• • Discrete Transforms;

• • Signal Analysis; etc…”

For more information see

Lectures;

Russell L. Herman’s Home Page or the

Department of Mathematics and Statistics

FOURIER ANALYSIS 1 – Christoph Thiele,
Department of Mathematics,
University of California, Los Angeles (UCLA)
Multimedia Fourier Analysis 1 Lecture, PDF, 48 Pages (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Fourier Analysis 1” Lectures include

• • “…Schwartz Functions;

• • The Space

S

• • (R

ⁿ

• • ) as Frechet Space;

• • The Fourier Transform;

• • Tempered Distributions;

• • Intermediate Banach Spaces, Regularity;

• • The Poisson Summation Formula;

• • Paley Wiener Theroems;

• • Distributions versus Tempered Distributions; etc…”

For more information see

Lectures;

Christoph Thiele’s Home Page or the

Department of Mathematics

FOURIER ANALYSIS 2 – CLASSICAL FOURIER ANALYSIS – Christoph Thiele,
Department of Mathematics,
University of California, Los Angeles (UCLA)
Multimedia Fourier Analysis 2 Lecture, PDF, 51 Pages (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Fourier Analysis 2 – Classical Fourier Analysis” Lectures include

• • “…The Haar Basis;

• • The Calderon Zygmund Decomposition;

• • The Littlewood Paley Square Function;

• • Khintchine’s Inequality;

• • The Space BMO as Function Space;

• • Maximal Truncated Singular Integrals;

• • Paraproducts and a Discrete

T

• • 1 Theorem;

• • The Cotlar-Stein Lemma; etc…”

For more information see

Lectures;

Christoph Thiele’s Home Page or the

Department of Mathematics

FOURIER ANALYSIS: THEORY & APPLICATIONS – D. Jerison,
Department of Mathematics & the
MIT OpenCourseWare, MIT
Multimedia Fourier Analysis: Theory and Applications Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Fourier Analysis: Theory and Applications

• • “…Roughly half of the subject is devoted to the theory of the

• • Lebesgue integral with applications to probability, and

• • half to Fourier series and Fourier integrals…”

Examples of “Fourier Analysis: Theory and Applications” Course Lectures include

• • “…Boolean Rings;

• • Lp Theory;

• • Hilbert Space and Orthonormal Bases;

• • Fourier Series;

• • Fourier Integrals;

• • Fourier Integrals, Measures, and Central Limit Theorem; etc…”

For more information see

David Jerison’s Home Page;

Department of Mathematics;

Mathematics Courses or the

MIT OpenCourseWare

HIGHER ORDER FOURIER ANALYSIS (254B) – T. Tao,
Analysis Group,
Department of Mathematics,
Division of Physical Sciences,
College of Letters and Science,
UCLA
Multimedia Higher Order Fourier Analysis Graduate Course – PDF, 221 Pages (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Higher Order Fourier Analysis” Graduate Course Chapters & Subchapters include

• • Chapter I: Higher Order Fourier Analysis
    • “…Equidistribution of polynomial sequences in tori;

• • • Roth’s theorem;

• • • Equidistribution of polynomials over finite fields;

• • • The inverse conjecture for the Gowers norm I. The finite field case;

• • • The inverse conjecture for the Gowers norm II;

• • • The integer case Linear equations in primes; etc…”

Chapter II: Related Articles

• • • “…Ultralimit analysis and quantitative algebraic geometry;

• • • Higher order Hilber spaces; etc…”

For more information see

Higher Order Fourier Analysis;

254B;

Terence Tao’s Home Page;

Analysis Group or the

Department of Mathematics

HARMONIC ANALYSIS – W. Schlag,
Department of Mathematics,
Division of Physical Sciences,
University of Chicago
Multimedia Harmonic Analysis Textbook – PDF, 93 Pages (Text & Images).
VERY VERY VERY…EXTENSIVE.

Examples of “Harmonic Analysis” Textbook Chapters include

• • “…Fourier Series: Convergence and Summability;

• • Harmonic Functions on the Disk and Poisson Kernel;

• • L

¹

• • bounded analytic functions and the F. & M. Riesz theorem;

• • The Conjugate Harmonic Function;

• • Calderon-Zygmund Theory of Singular Integrals;

• • Almost Orthogonality; Schauder Estimates;

• • L

^P

• • -multipliers, Mikhlin theorem and Littlewood-Paley theory;

• • Restriction of the Fourier transform, Stein-Tomas theorem, Strichartz estimates;

• • The endpoint for the Stein-Tomas theorem and Strichartz estimates;

• • Some pointwise questions for Fourier series: the case of L

¹

• • (T); etc…”

For more information see the

Wilhelm Schlag’s Home Page or the

Department of Mathematics

FOURIER TRANSFORM CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

• FOURIER CALCULATORS & APPLETS

• FOURIER TRANSFORMS CALCULATORS & APPLETS

• FFT ALGORITHM CALCULATORS & APPLETS

• FFT CALCULATORS & APPLETS

FAST FOURIER TRANSFORM (FFT) FOR POLYNOMIAL MULTIPLICATION (JAVA APPLET) – Author: J. Beaver &
Hosted by K. Pruhs, Department of Computer Science, University of Pittsburgh
VERY VERY EXTENSIVE.

Fast Fourier Transform for Polynomial Multiplication Calculator

• • “…includes a description of the algorithm, a description of the Roots of Unity,

• • a step feature which allows the user to see what is going on in the algorithm,

• • and a multimedia section…”

For more information see

Applets;

Applet Demonstration;

CS 1501;

Kirk Pruhs’s Home Page or the

Department of Computer Science

FAST FOURIER TRANSFORM CALCULATOR – J. Clymer, Cincinnati, Ohio
VERY EXTENSIVE.

Fast Fourier Transform (FFT) Calculator

• • “…performs Fourier Transforms, and DHTML to produce graphs of functions…”

For more information see

Jeffrery Clymer’s Home Page

FOURIER (JAVA APPLET) – R. E. Williamson & S. Schwarz,
Dartmouth University
VERY EXTENSIVE.

Fourier Calculator

• • “…Computes Fourier coefficients of a function,and plots the function and the

• • Fourier approximation of degree at most 20…”

For more information see

Interactive Math Programs or the

Department of Mathematics

FOURIER TRANSFORMS (FT) OF A GIVEN POINTSET (JAVA APPLET) – S. Weber
VERY EXTENSIVE.

Fourier Transform on Periodic Point Sets Calculator

• • “…calculates Fourier transforms (FT) of a given pointset.

• • The pointset is generated by the plane space groups (see Project 22). You may transform all points…”

For more information see

Java Applets;

Steffen Weber’s Home Page or

JCrystal

FOURIER TRANSFORMS (FT) OF QUASIPERDIODIC POINT SETS (JAVA APPLET) – S. Weber
VERY EXTENSIVE.
For more information see

Java Applets;

Steffen Weber’s Home Page or

JCrystal

DISCRETE FOURIER TRANSFORM CALCULATORS & APPLETS

DISCRETE FOURIER TRANSFORM: FFT OF “BIT PATTERN” APPLET
& FFT OF ARBITRARY FUNCTION APLET – Bert G. Wachsmuth,
Department of Mathematics and Computer Science,
Seton Hall University
VERY VERY EXTENSIVE.

Fast Fourier Transform of “Bit Pattern” Calculator

• • “…illustrates what happens when trying to

• • send bits representing a character (coded as the 8-bit ASCI code)

• • though a wire that includes a “low-pass” filter, i.e. frequencies

• • above a certain point are filtered out…”

Fast Fourier Transform of Arbitrary Function Calculator

• • “…lets you enter an arbitrary function and decompose it into its Fourier coefficients…”

For more information see

MathCS or the

Department of Mathematics and Computer Science

FOURIER-LAPLACE CALCULATORS & APPLETS

FOURIER-LAPLACE CALCULATOR – Xiao Gang, Laboratoire J.-A. Dieudonné,
Université de Nice, Nice, France
VERY EXTENSIVE.

Fourier Laplace Calculator

• • “…computes the Fourier transform or

• • Laplace transform of a function, and their inverse transforms…”

For more information see

WIMS

FOURIER TRANSFORM EXPERIMENTATION CALCULATORS & APPLETS – IMAGE PROCESSING

INTERACTIVE FOURIER TRANSFORM EXPERIMENTATION – IMAGE PROCESSING (JAVA APPLET) – R. Fisher, S. Perkins,
A. Walker and E. Wolfart,
School of Informatics,
University of Edinburgh, Edinburgh, Scotland, U.K.

• VERY VERY EXTENSIVE.

• For more information see

Interactive Experimentation

• ;

HIPR2: Hypertext Image Processing Reference

• ;

Robert Fisher’s Home Page

• or the

School of Informatics

FOURIER SERIES CALCULATORS & APPLETS

FOURIER SERIES (JAVA APPLET) – F. Embacher & P. Oberhuemer,
Universität Wien, Austria

Fourier Series Calculator:

• • “…the user may choose the first 21 coefficients of

• • a Fourier series by means of scroll bars and to look at the graph of

• • the resulting function…”

For more information see

Applets or

Maths Online

FOURIER SERIES APPROXIMATION (JAVA APPLET) – Project Director: W.J. Rugh,
Department of Electrical and Computer Engineering,
Whiting School of Engineering,
Johns Hopkins University

Fourier Series Calculator allows you to

• • “…explore the Fourier series approximation, select

• • a labeled signal, use the mouse to sketch one period of a signal,

• • or use the mouse to modify a selected signal. Specify the number

• • of harmonics, N, and…”

For more information see the

Signals, Systems & Controls or the

Department of Electrical and Computer Engineering

FOURIER SERIES CALCULATION FOR TYPICAL DIGITAL WAVEFORMS – EE Circle
VERY EXTENSIVE.

Fourier Series Calculator for Typical Digital Clock Waveforms

• • “…Computes complex Fourier series coefficients (harmonics) of

• • rectangular, triangular or trapezoidal shaped waveform &

• • Plots both the time-domain waveform and the magnitude

• • of the coefficients…”

For more information see

EE Applets or

EE Circle

FOURIER SERIES SIMULATION (JAVA APPLET) – P. Falstad
VERY EXTENSIVE.

Fourier Series Calculator

• • “…is a method of expressing an arbitrary periodic function as a

• • sum of cosine terms. In other words, Fourier series can

• • be used to express a function in terms of the frequencies…”

For more information see

Math, Physics & Engineering Applets or

Paul Falstad’s Home Page

FOURIER SYNTHESIS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

FOURIER SYNTHESIS (JAVA APPLET) – M. Thole, Institut für Netzwerktheorie
und Schaltungstechnik, Braunschweig, Bundesrepublik Deutschland (Germany)
VERY EXTENSIVE.

Fourier Synthesis Calculator

• • “…A periodic signal can be described by a Fourier decomposition as a

• • Fourier series, i. e. as a sum of sinusoidal and cosinusoidal

• • oscillations…”

For more information see

Schaukasten

FOURIERSYNTHESE (JAVA APPLET) – M. Thole, Institut für Netzwerktheorie
und Schaltungstechnik, Braunschweig, Bundesrepublik Deutschland (Germany)
VERY EXTENSIVE.

Fourier Synthesis Calculator

• • “…Ein periodisches Signal kann durch eine

• • Fourierzerlegung mathematisch…”

For more information see

Schaukasten

Fractals & 3D Fractals

3D FRACTALS WITH TEXT, IMAGES, VIDEOS/MOVIES & AUDIO/SOUND

MATHEMATICAL IMAGERY – Jos Leys
Multimedia Mathematical Imagery (Text, Images, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Mathematical Imagery Categories include

• • • • “…3D Fractals Movies;

• • • • Hybrid 3D Fractals Gallery
        • “…produced as hybrids between the Mandelbox and Mandelbulb formulas…”

Virtual Vases Created by Inverse Stereographic Projection;

4D Polychora and Hyperbolic Space Gallery;

True 3D Limit Sets of Kleinian Groups Gallery; etc…”

ULTRA FRACTAL: ADVANCED FRACTAL SOFTWARE FOR WINDOW & MAC OS X – Frederik Slijkerman

Ultra Fractal Software

• • • • “…With Ultra Fractal, you can choose from thousands of fractal types and coloring algorithms, zoom in as far as you want, use gradients to add color, and…”

ANATOMY OF MANDELBROT AND JULIA SETS LESSONS, LECTURES, CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

“ANATOMY” OF THE MANDELBROT AND JULIA SETS (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.

• • • • “…A virtual investigation with interactive pictures…”

For more information see

E-notes

• • • • Some examples from over “40” Mandelbrot & Julia Sets Applets include

Iterations of real quadratic functions

Critical points and Fatou theorem

Attracting Fixed point and Period 2 orbit

Misiurewicz points and the M-set self-similarity

FRACTAL COURSES, LECTURES, CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

FRACTAL GEOMETRY (MATH 190) – Michael Frame, Benoit Mandelbrot (1924-2010) & Nial Neger,
Department of Mathematics,
Yale University
Multimedia Fractal Geometry Course (Text, Images, Applets, etc.).
VERY VERY VERY…EXTENSIVE.

Fractals Applets are a

• • • • “…series of simulators for teaching Fractal Geometry…”

For more information see the

Department of Mathematics

FRACTALS (JAVA APPLETS) – G. Booth
VERY VERY EXTENSIVE.
For more information see

Ginger Booth’s Home Page

PATTERNS IN NATURE (JAVA APPLET) – P. Trunfio & G. McGath, Center for Polymer Studies,
Department of Physics, Boston University
VERY EXTENSIVE.

Patterns in Nature consists of

• • • • “…a number of hands-on activities, laboratory experiments,

• • • • and interactive visualization programs for which encourage

• • • • students to explore how fundamentally random microscopic events can

• • • • give rise to fractal macroscopic patterns…”

For more information see

Center for Polymer Studies or the

Department of Physics

• • • • Examples of Fractal Applets include

Diffusion Limited Aggregation Applet (Aggregation: Growing Fractal Structures)

Fractal Coastlines Applet

The Anthill and Molecular Motion Applet

FRACTAL MODELING CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

• • • FRACTAL GALLERIES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

FRACTALS: 3D STRANGE ATTRACTORS AND SIMILAR OBJECTS – T. Stilson,
Center for Computer Research in Music and Acoustics, Stanford University
VERY VERY EXTENSIVE.
For more information see

Tim Stilson’s Welcome Page or the

Center for Computer Research in Music and Acoustics

JULIA SETS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

• • • MANDELBROT SETS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

JULIA AND MANDELBROT SET GENERATION – D.E. Joyce,
Department of Mathematics and Computer Science,
Clark University,
Worcester, Massachusetts
VERY EXTENSIVE.
For more information see

Dave’s Geometric Pix Gallery;

David Joyce’s Home Page;

David Joyce’s Faculty Home Page or the

Department of Mathematics and Computer Science

• • • • Examples of Related Applets include

Quilted Millefiori with parameters

Kaleidoscope

Newton Basin Generation

MANDELBROT APPLET – P. Alfeld, Department of Mathematics,
University of Utah
VERY EXTENSIVE.
For more information see

Java Page or

Peter Alfeld ‘s Home Page

MANDELBROT EXPLORER – Panagiotis Christias, Department of Electrical and Computer
Engineering, National Technical University of Athens (NTUA), Greece
VERY EXTENSIVE.
For more information see the

National Technical University of Athens (NTUA)

MANDELBROT AND JULIA SET EXPLORER – D.E. Joyce,
Department of Mathematics and Computer Science,
Clark University
VERY EXTENSIVE.
For more information see

David Joyce’s Home Page;

David Joyce’s Faculty Home Page or the

Department of Mathematics and Computer Science

Basic Geometry & Trigonmetry Lessons & Calculators
Middle School – High School

Geometry Courses, Textbooks, Lectures & Lessons
with Calculators & Applets

Euclid’s Elements

Pythagorean & Pythagorean Triples

Geometry Calculators & Applets by Various Categories

Advanced Geometry
(
(Differential Geometry, Geometry of Manifolds, Geometric Folding Algorithms,

Riemannian Geometry, Mirror Symmetry, Holomorphic Curves, etc.))

Computational Geometry

Geometry

MIDDLE SCHOOL – HIGH SCHOOL GEOMETRY & TRIGONMETRY COURSES, LESSONS, CALCULATORS & APPLETS

Geometry Courses, Lessons, Calculators, etc.

GEOMETRY – Kan Academy,
Mountain View,
California
Multimedia Geometry Course (Text, Images, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Browse down to Geometry

Examples from over “60” Geometry Video Lectures include

• • • • “…Measuring Angles in Degrees Video Lecture;

• • • • Using a Protractor Video Lecture;

• • • • Angles at the intersection of two lines Video Lecture;

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

• • • • Congruent Triangle Video Lecture;

• • • • Triangle Area Proofs Video Lecture;

• • • • Area of Koch Snowflake Video Lecture;

• • • • Pythagorean Theorem Proof Using Similarity Video Lecture;

• • • • Area and Perimeter Video Lecture;

• • • • Cylinder Volume and Surface Area Video Lecture;

• • • • Triangle Medians and Centroids Video Lecture;

• • • • Inradius Perimeter and Area Video Lecture; etc…”

For more information see the

Kan Academy Team

GEOMETRIC FORMULAS – Web page design, diagrams, and applets by S. Seastone,
Ask Dr. Math, The Math Forum, Swarthmore College
Multimedia Geometry Lessons with Applets (Text & Images).
VERY VERY VERY…EXTENSIVE.

Geometric Lessons & Formulas for Perimeter, Area, Volume, etc. includes

• • • • Two-dimensional Figures
        • “…also called a plane or planar figure, is a set of line segments

• • • • • or sides and curve segments or arcs, all lying in a single plane. The sides

• • • • • and arcs are called the edges of the figure. The edges are one-dimensional,

• • • • • but they lie in the plane, which is two-dimensional…”

Three-dimensional Figures

• • • • • “…sometimes called a solid figure, is a set of plane regions

• • • • • and surface regions, all lying in three-dimensional space. These surface regions

• • • • • are called the faces of the figure. Each of them is two-dimensional. The arcs of

• • • • • curves that are the edges of the faces of the figure are called the edges

• • • • • of the figure…”

Geometric Lessons, Formulas & Applets include

• • • • “…Triangles; Quadrilaterals; Regular Polygons; Circles; etc…”

For more information see

Formulas;

Ask Dr. Math FAQ or

The Math Forum

GEOMETRY (JAVA APPLETS) – Asian Technology Conference in Mathematics (ATCM)
VERY VERY VERY…EXTENSIVE.

Geometry Applet Subject Categories include:

• • • • “…Angles and Pararell Applets;

• • • • Congruent Figures and Triangles Applets;

• • • • Quadrilaterals and Conservation Applets;

• • • • Similar Figures Applets;

• • • • Circle Applets;

• • • • Pythagorean Theorem Applets; etc…”

For more information see

Manipula Math With Java or

Math Education and Technology

• • • • Examples of Categories which include more than ’90’ Geometry Applets

Angle and Parallel Lines Applets

Congruent Figures and Triangles Applets

Circle Applets

GEOMETRY APPLETS – National Library of Virtual Manipulatives,
Utah State University
VERY EXTENSIVE.

Available in English, French & Spanish.

For more information see the

National Library of Virtual Manipulatives

Trigonometry Courses, Lessons, Calculators, etc.

TRIGONOMETRY – Kan Academy,
Mountain View,
California
Multimedia Trigonometry Course (Text, Images, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Browse down to Trigonometry

Examples from over “40” Trigonometry Video Lectures include

• • • • “…Basic Trigonometry Video Lecture;

• • • • Using Trig Functions Video Lecture;

• • • • Graph of the sine function Video Lecture;

• • • • Graphing trig functions Video Lectures;

• • • • Trigonometric Identities Video Lecture;

• • • • Law of cosines Video Lecture;

• • • • Polar Coordinates Video Lecture; etc…”

For more information see the

Kan Academy Team

TRIGONMETRY CALCULATORS & APPLETS – Asian Technology Conference in Mathematics (ATCM)
VERY VERY VERY…EXTENSIVE.

Examples form over “24” Trigonmetry Calculators & Applets include:

• • • • “…Sine Function Box;

• • • • Tangent Function Box;

• • • • Cosine Function Box;

• • • • Graph of y=sin ax;

• • • • The Law of Cosines;

• • • • Law of Sines; etc…”

For more information see

Manipula Math With Java or

Math Education and Technology

GEOMETRY COURSES, TEXTBOOKS & LESSONS WITH CALCULATORS, APPLETS, ANIMATIONS SIMULATIONS

GEOMETRY – Alexander Bogomolny
Multimedia Lessons with Calculators & Applets (Text & Images).
VERY VERY VERY…EXTENSIVE.

Geometry

• • • • “…Geometry is a branch of mathematics that is concerned with the properties of configurations of geometric objects – points, (straight) lines, and circles being the most basic of these…”

For more information see

Interactive Mathematics Activities or

Interactive Mathematics Miscellany and Puzzles

• • • • Examples from over “700” “Geometry” Subject Categories include

Archimedes’ Book of Lemmas

Napoleon’s Theorem

The Butterfly Theorem

Arbelos – the Shoemaker’s Knife

EUCLID’S ELEMENTS CALCULATORS, APPLETS, ANIMATIONS SIMULATIONS

EUCLID’S ELEMENTS (JAVA APPLETS) – D.E. Joyce,
Department of Mathematics and Computer Science,
Clark University,
Worcester, Massachusetts
Euclids Elements Course (Text, Images, Applets & Simulations).
VERY VERY VERY…EXTENSIVE.

Euclid’s Elements

• • • • “…form one of the most beautiful and influential works of science in

• • • • the history of humankind. Its beauty lies in its logical development of geometry and

• • • • other branches of mathematics. It has influenced all branches of science but none so

• • • • much as mathematics and the exact sciences. The Elements have been studied 24 centuries

• • • • in many languages starting, of course, in the original Greek, then in Arabic, Latin,

• • • • and many modern languages…”

For more information see the

David Joyce’s Home Page;

David Joyce’s Faculty Home Page or the

Department of Mathematics and Computer Science

• • • • Some examples from the 13 Books with “100’s” of “Euclid’s Elements” Applets include

Book I: The Fundamentals of Geometry: Theories of Triangles, Parallels, and Area

Book VII: Foundations of Ratios and Proportions

EUCLID’S ELEMENTS: TRANSLATION OF JOYCE’S “EUCLID’S ELEMENTS” INTO SPANISH & CATALAN (JAVA APPLETS) – JDL euclides.org &
Development Network Services Presence with permission from
D.E. Joyce,
Department of Mathematics and Computer Science,
Clark University, Worcester, Massachusetts
Euclids Elements Course (Text, Images, Applets & Simulations).
VERY VERY VERY…EXTENSIVE.
For more information see the

Joyce’s Euclid’s Elements

EUCLID’S ELEMENTS OF GEOMETRY (JAVA APPLETS) – B. Casselman,
Department of Mathematics,
Faculty of Science,
University of British Columbia,
Vancouver, Canada
Multimedia Euclid’s Elements of Geometry Lessons, Calculators & Applets (Text & Images).
VERY VERY VERY…EXTENSIVE.

Euclid’s Elements of Geometry includes

• • • • “…The integrated text (Byrne, Joyce, and Heath) at UBC: Book I thru Book XIII;

• • • • A local collection of proofs of Pythagoras’ Theorem in Java;

• • • • On Erhard Ratdolt, publisher of the 1482 edition of Euclid (the very first, based on the somewhat faulty medieval edition produced by Campanus); etc…”

For more information see

Bill Casselman’s Home Page or the

Department of Mathematics

PYTHAGOREAN CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

• • • PYTHAGOREAN TRIPLETS CALCULATORS & APPLETS

GENERATING PYTHAGOREAN TRIPLES (JAVA APPLET) – N. Exner,
Office for Mathematics, Science & Technology Education,
University of Illinois, Urbana-Champaign

Pythagorean Triples Calculator

• • • • “…generates non-trivial

• • • • Pythagorean Triples of increasing value. It can be used

• • • • to locate Pythagorean Triples of significant

• • • • size…”

For more information see

Geometry;

MSTE Online Resources or the

Office for Mathematics, Science & Technology Education

PYTHAGOREAN EXPLORER (JAVA APPLET) – The Shodor Education Foundation, Inc.
For more information see

Interactive Activities or

The Shodor Education Foundation, Inc.

GEOMETRY CALCULATORS & APPLETS BY VARIOUS CATEGORIES

GEOMETRY DEMONSTRATIONS USING CINDERELLA (JAVA) – Cinderella,
Jürgen Richter-Gebert & Ulrich Kortenkamp, Germany
VERY VERY EXTENSIVE.

“…The Interactive Geometry Software Cinderella…”

For more information see

Cinderella, The Interactive Geometry Software

• • • • Some examples from over “30” Geometry Applets include

Light going through a Lens Applet

A Conchoid in Elliptic Geometry Applet

AN INTERACTIVE PROFF OF PYTHAGORAS’ THEOREM – J. Morey,
Department of Mathematics,
Faculty of Science,
University of British Columbia,
Vancouver, Canada

An Interactive Proof of Pythagoras’ Theorem

• • • • “…shows a geometrical proof of Pythagoras’ Theorem…”

For more information see

Interactive Math or the

Department of Mathematics

Advanced Geometry
Courses, Textbooks, Lectures & Lessons

Differential Geometry ~
Geometry of Manifolds

Geometric Folding Algorithms: Linkages, Origami, Polyhedra

Semi-Riemann Geometry and General Relativity

Topics in Geometry: Mirror Symmetry

Advanced Geometry Calculators & Applets

High Performance
Calculators for Advanced Geometry

3D Geometry

Periodic Billiard Paths in Triangles

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ADVANCED GEOMETRY COURSES, TEXTBOOKS, LECTURES & LESSONS

Differential Geometry

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

Geometry of Manifolds

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

Geometric Folding Algorithms: Linkages, Origami, Polyhedra

GEOMETRIC FOLDING ALGORITHMS: LINKAGES, ORIGAMI, POLYHEDRA – E. Demaine,
Department of Electrical Engineering and Computer Sciences,
MIT
Multimedia Geometric Folding Algorithms: Linkages, Origami, Polyhedra Course (Text, Images, Videos/Movies & Audio/Sound).
VERY VERY VERY…EXTENSIVE.

Examples from over “22” “Geometric Folding Algorithms: Linkages, Origami, Polyhedra” Course Video Lectures & Lecture Notes include

• • “…Single-vertex Crease Patterns Video Lecture;

• • Artistic Origami Design Video Lecture;

• • Folding Motions Video Lecture;

• • Rigidity Theory Video Lecture;

• • Polyhedron unfolding Video Lectures;

• • Protein Folding Video Lecture;

• • Maekawa and Kawasaki’s Theorems Revisited and Extended Video Lecture; etc…”

For more information see

Erik Demaine’s Home Page or the

Department of Electrical Engineering and Computer Science

Semi-Riemann Geometry and General Relativity

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 or the

Department of Mathematics

Topics in Geometry: Mirror Symmetry

TOPICS IN GEOMETRY: MIRROR SYMMETRY – Denis Auroux,
Department of Mathematics,
& the MIT OpenCourseWare, MIT
Multimedia Topics in Geometry: Mirror Symmetry Course Course (Text & Images).
VERY VERY VERY…EXTENSIVE.

Topics in Geometry: Mirror Symmetry Course is

• • “…This course will focus on various aspects of mirror symmetry.

• • It is aimed at students who already have some basic knowledge in

• • symplectic and complex geometry..”

For more information see

Mathematical Courses;

MIT OpenCourseWare or the

Department of Mathematics

ADVANCED GEOMETRY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS

CONVERTING TRIANGULATIONS TO QUADRANGULATION (JAVA APPLET) – Sam Sanjabi, Rachel Potvin,
The Computational Geometry Lab, School of Computer Science, McGill University
VERY VERY EXTENSIVE.

Converting Triangulations to Quadrangulations Calculator:

• • “…We obtain a variety of characterizations for when a

• • triangulation admits a quadrangulation without the use

• • of (or with a bounded number of) Steine r points. We also

• • examine the effects of demanding that the Steiner points

• • be added in the exterior of a triangulated simple polygon…”

For more information see

Projects;

Teaching Activities or

The Computational Geometry Lab

HIGH PERFORMANCE CALCULATORS FOR GEOMETRY

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