math.gif (2730
                          bytes) Mathematics

Contents

A. Reference D. Functions G. Wavelets
B. General & Miscellaneous E. Fourier Analysis, FFTs H. Cryptography
C. Numerical Methods F. Fractals and Chaos  

also see efg's Delphi Math Info and Links, Delphi Math Functions, Math Projects


A. Reference

Calculators The Calculator Home Page.  Calculator.org has a number of calculator related resources, including an online scientific calculator, units conversion and constants database, and other information.   www.calculator.org 
Geometry

Geometry Algorithms
http://geometryalgorithms.com 

Geometry
http://mathworld.wolfram.com/topics/Geometry.html

Géométrie
http://perso.wanadoo.fr/jpq/geometrie/index.htm 

Famous Curves
http://www-groups.dcs.st-and.ac.uk/~history/Curves/Curves.html 

2D Curves
www.2dcurves.com 

Geometry, Solid geomlogo.gif (987 bytes)The 5 Platonic Solids and the 13 Archimedean Solids
www.scienceu.com/geometry/facts/solids
Mathematics Library/Archive

Front for the XXX Mathematics Archive
UC Davis seach engine of xxx mathematics archives at Los Alamos
http://front.math.ucdavis.edu

Math Stuff Library by Don Lancaster.  Included are such topics as Fourier Series,  linear  algebraic equations, nonlinear graphic transforms, chain codes, digital filters, halftone techniques, and similar subjects.  http://www.tinaja.com/math01.shtml

Mathematics Archives WWW Server
http://archives.math.utk.edu/newindex.html

Mathematics links, www.alcyone.com/max/links/maths.html 

Sloane's On-Line Encyclopedia of Integer Sequences Look up a number sequence in the database
http://oeis.org
WebMath Students, get help with your homework
www.webmath.com
World of Mathematics Eric Weisstein's World of Mathematics
The Web's Most Extensive Mathematics Resource
(offline now because of a legal fight between CRC Press and Eric Weisstein)

http://mathworld.wolfram.com

B. General & Miscellaneous

American Mathematical Society www.ams.org
Boids Coordinated animal motion such as bird flocks and fish schools
www.red3d.com/cwr/boids 
Decision Tree for Optimization Software http://plato.la.asu.edu/guide.html  
Forensic Mathematics Mostly about DNA identification
http://dna-view.com 
Four-Color Theorem

Four-Color Theorem
http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/The_four_colour_theorem.html 
www.math.gatech.edu/~thomas/FC/fourcolor.html   

The Four Color Map Problem
www.math.utah.edu/~alfeld/math/4color.html 

Fun with Mathematics Harry J. Smith's page:  Pi, Tesseract, Gaussian Primes, Fibonacci, Ackermann's Function, Encyrption, Perfect Numbers, Mersenne Primes, Quaternions,  much more
http://www.geocities.com/hjsmithh/
Graphics for the Calculus Classroom www.math.psu.edu/dna/graphics.html
Geometry

Computational Geometry Algorithms Library.  The CGAL project is a collaborative effort to develop a robust, easy to use, and efficient C++ software library of geometric data structures and algorithms. www.cgal.org 

Geometric Paper Folding
www.sgi.com/grafica/huffman

Geometry in Action
www.ics.uci.edu/~eppstein/geom.html

Paper and Plotter: A 3D Surface
www.sgi.com/grafica/surf/index.html

Polyhedra Database
www.netlib.org/polyhedra/index.html

Geometery Junkyard
www.ics.uci.edu/~eppstein/junkyard/all.html

Klein Bottle Shown here is a glass "Klein Bottle" made in the 70s by the late Mitsugi Ohno (Mr. Ohno died on Oct. 22, 1999 from cancer), an expert glass blower at Kansas State University. A Klein Bottle is a 3D Möbius Strip. See the article "Glass Klein Bottles" in the March 1998 Scientific American "Mathematical Recreations" section (pp. 100-101) for more information. 

Mitsugi Ohno is truly a master artist.

Math Software http://dmoz.org/Science/Math/Software
Mathematical Experiences through Image Processing www.cs.washington.edu/research/metip/metip.html
Mathematical Markup Language A low-level specification for describing mathematics as a basis for machine to machine communication. It provides a much needed foundation for the inclusion of mathematical expressions in Web pages. www.w3.org/Math  Specification: www.w3.org/TR/REC-MathML
Mathematics & Science www.sco.com/skunkware/rr/math.html
Mathematics Renderers Comparative Review of World-Wide-Web Mathematics Renderers
http://hutchinson.belmont.ma.us/tth/mmlreview
Maths Is Fun www.mathsisfun.com 
Pi

Buffon.gif
                    (1033 bytes)   efg's Calculate Pi Using Buffon's Needles Lab Report

On the computation of the n'th decimal digit of various transcendental numbers
www.lacim.uqam.ca/plouffe/Simon/articlepi.html

Prime Numbers The Prime Pages
www.utm.edu/research/primes

The First 10,000 Primes
www.utm.edu/research/primes/lists/small/10000.txt

Great Internet Mersenne Prime Search (26,972,593 - 1 is prime)
www.mersenne.org

On August 31, 1998, Ray Ballinger has found a new largest known
twin primes record with "Proth" written by Yves Gallot:
835335*239014-1 and 835335*239014+1 (11751 digits).
For more details, see www.utm.edu/research/primes/largest.html

David Kuestler's UseNet Post with Prime Numbers Generator C code "erato"
(sieve of Eratosthenes for up to 2^32 by Jim Gillogly)

Ram's Horn Cardboard model of a logarithmic spiral or maybe helix would be a better word

Ram's Math

Random Numbers Server on the Theory and Practice of Random Number Generators
http://random.mat.sbg.ac.at

Papers by Pierre L'Ecuyer about random number generation

Rounding Rules On the Standard Rounding Rule for Multiplication and Division www.angelfire.com/oh/cmulliss/round1.htm
Significant Figures Significant Figures and Rounding Rules
www.angelfire.com/oh/cmulliss/index.html
Sound of Mathematics www.geocities.com/Vienna/9349
Slide Rule Universe www.sphere.bc.ca/test/sruniverse.html
Statistics & Probability Engineering Statistics
www.itl.nist.gov/div898/handbook 

VassarStats:  Web Site for Statistical Computation
http://vassarstats.net/

Stony Brook Algorithm Repository
Comprehensive collection of algorithm implementations of
fundamental problems in combinatorial algorithms.
www.cs.sunysb.edu/~algorith

Symbolic Computation JACAL is an interactive symbolic mathematics program. JACAL can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions.
http://www-swiss.ai.mit.edu/~jaffer/JACAL.html

C. Numerical Methods

Also see
  www.numerical-methods.com
NIST Guide to Available Mathematical Software

ACM Collected Algorithms from Transactions on Mathematical Software Nearly 40 years of ACM publications on mathematical algorithms.

.GZ file Format:
http://www.acm.org/calgo/contents

ASCII Format:
http://www.netlib.org/toms
Approximation Series Approximation Techniques
http://perso.wanadoo.fr/jean-pierre.moreau/c_series.html 
Complex Roots http://perso.wanadoo.fr/jean-pierre.moreau/c_complex.html 
Electronic Library (eLib) for Mathematical Software http://elib.zib.de
GAMS: Guide to Available Mathematical Software U.S. National Institute of Standards and Technology (NIST).
A cross-index and virtual repository of mathematical and statistical software components for use in computational science and engineering. http://math.nist.gov
MAGIC "My Alternate Graphics and Image Code" by Dave Eberly. Includes several programs about numerical methods including eigensystems, integration, ordinary differential equations, root finders, minimizers,  linear system solvers, and special functions.
www.magic-software.com
Matrices http://perso.wanadoo.fr/jean-pierre.moreau/c_matrices.html 
Netlib Repository Collection of mathematical software, papers, and databases.
www.netlib.org

Netlib Master Index www.netlib.org/master/expanded_liblist.html
Numerical Recipes (Book) Home Page:  http://numerical.recipes/

Roots

Roots of a Real Function
http://perso.wanadoo.fr/jean-pierre.moreau/c_roots.html 

Template Numerical Toolkit The Template Numerical Toolkit is a collection of mathematical libraries for numeric computation in C++. Its fundamental classes include vectors, matrices, and multidimensional arrays.
http://math.nist.gov/tnt

D. Functions
Also see efg's Delphi Math Functions Pages

Wolfram's Functions Site

Approximations Functional Approximations
http://perso.wanadoo.fr/jean-pierre.moreau/c_function.html 
Bessel Functions Bessel Programs
http://perso.wanadoo.fr/jean-pierre.moreau/c_bessel.html 

Bessel Function
http://www.2dcurves.com/gamma/gammabs.html

Symbolic and Numerical Computation on Bessel Functions of Complex Argument and Large Magnitude, http://www.cs.engr.uky.edu/~jzhang/pub/BESSEL/Symbolic.html

Complex

The Scientist and Engineer's Guide to Digital Signal Processing
Book Home Page:  www.dspguide.com/pdfbook.htm including PDF files

Exponents www.sisweb.com/math/algebra/exponents.htm
gamma

www.sisweb.com/math/integrals/more/gammafun.htm (with graph)

Trigonometry www.sisweb.com/math/trig/identities.htm

Books about Mathematical Functions

An Atlas of Functions by Spanier and Oldham. Hemisphere Publishing, 1987.

CRC Handbook of Mathematical Curves and Surfaces, CRC Press, 1990.  (out of print)

CRC Standard Mathematical Tables, CRC Press, any version.

Handbook of Mathematical Functions by Abramowitz and Stegun. Dover Publications, 1972.

Numerical Recipes in C: The Art of Scientific Computing (Second Edition), William H.Press, et al, Cambridge University Press, 1992. (Also available in Pascal, FORTRAN, and Basic programming languages.)

Special Functions & Their Applications, Lebedev. Dover Publications, 1972.

Tables of Functions, Jahnke and Emde. Dover Publications, 1945.


E. Fourier Analysis, FFTs

Books Chapter 5, Processing Images in Frequency Space
The Image Processing Handbook
Complex Fast Fourier Transform The Scientist and Engineer's Guide to Digital Signal Processing
www.dspguide.com/pdfbook.htm
Cross Correlation sci.image.processing post by Chris Russ (29 Sept 99):  "Cross correlation in the Fourier domain is really the same as convolution with a 180 degree rotated pattern in the spatial domain.  If you're looking for speed and that is the reason you're interested in an FFT-based implementation of cross-correlation, you may want to consider this equivalence."

"A small spatial convolution (say under 13x13) is less numerically intensive (and usually faster) than two forward FT's a complex multiplication with the phase reversed and an inverse FT."

Fast Fourier Transform Code and Information www.fftw.org/links.html
Fast Fourier Transform Algorithm www.cs.cf.ac.uk/Dave/Vision_lecture/node20.html#SECTION00141500000000000000
FFT code and related stuff www.jjj.de/fxt
FFT Demystified http://www.eptools.com/tn/T0001/INDEX.HTM 
FFTW FFTW is a C subroutine library for computing the Discrete Fourier Transform (DFT) in one or more dimensions, of both real and complex data, and of arbitrary input size. We believe that FFTW, which is free software, should become the FFT library of choice for most applications.  Developed at MIT.   [Winner of 1999 Wilkinson Prize for Numerical Software -- awarded by Argonne Nat'l Lab (U.S.),   National Physical Laboratory (UK), Numerical Algorithms Group (UK)]  www.fftw.org
Fourier www.sisweb.com/math/advanced/fourier.htm
Fourier Theory www.cs.cf.ac.uk/Dave/Vision_lecture/node17.html#SECTION00141200000000000000
Fourier Transform in 2D www.vislab.usyd.edu.au/CP3/Four4/mod1.html
Fourier Transform in 2 dimensions http://robotics.eecs.berkeley.edu/~sastry/ee20/vision2/node1.html
HpW Works The HpW Works is spectrum Analyzer for MS Windows on the Intel platform. The Analyzer uses the Fast Fourier Transformation (FFT) technique to transform the sampled data to the frequency domain. It is a way of representing a very complicated sampled data pattern in terms of its linear projection onto sinusoids of various frequency. The FFT spectrum is a power frequency graph which shows quantitatively how much of the original pattern is composed by each of the frequencies.
www.hpw-works.com
Image Transforms Chapter 3, pp. 81-159
Digital Image Processing
, 2nd edition
Signal Proecessing FFT, Butterworth Filter, ...
http://perso.wanadoo.fr/jean-pierre.moreau/c_signal.html 
TFastFourier Delphi Component, www.lohninger.com/fourier.html

F. Fractals and Chaos
Also see efg's Fractals and Chaos Projects Page

general Dr. G. A. Edgar
www.math.ohio-state.edu/~edgar
 
3D Fractal Landscapes www.midnightbeach.com/jon/pubs/3D_Fractal_Landscapes.html
Animated GIFs http://sprott.physics.wisc.edu/fractals/animated
Bifurcation www.exploratorium.edu/complexity/CompLexicon/bifurcation.html
Chaos Theory www.chaos-theorie.de (Auf Deutsch)
Clifford Pickover's Web Page. Check out descriptions of Cliff's many books.
www.pickover.com

http://sprott.physics.wisc.edu/pickover/home.htm
Dynamical Systems The Dynamical Systems and Technology Project at Boston University
http://math.bu.edu//DYSYS
FAQ Fractal Frequently Asked Questions and Answers
www.faqs.org/faqs/fractal-faq 
Generating Random Fractal Terrain www.gameprogrammer.com/fractal.html
IFS Iterated Function Systems

IFS Fractals Digital Encyclopedy   (English or French)
www.chez.com/fractals

Nonlinear Iterated Function Systems
www.cg.tuwien.ac.at/research/vis-dyn-syst/nifs/nlinifs.html  

Keplerian Fractals Koch Snowflake -- very interesting variations
http://clowder.net/hop/Keplrfrct/Keplrfrct.html
Links Fractal Music
Several dozen links in UseNet Post by Paul N. Lee
Julia and Mandelbrot Sets On Gaston Julia's birthday on 3 Feb 2004, Google showed this logo on their search page:

Gaston Maurice Julia
http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Julia.html

http://aleph0.clarku.edu/~djoyce/julia/wwwrefs.html

The Mandelbrot and Julia sets Anatomy Contents
www.people.nnov.ru/fractal/MSet/Contents.htm

  efg's Fractals Show 2 Lab Report
Create Mandelbrot and Julia sets for a number of complex math functions, including z2, zn, zx, zz, exp(z), cos(z), sin(z), cosh(z), sinh(z), I0(z), J0(z), tan(z), tanh(z), sec(z), sech(z), csc(z), csch(z), cot(z), coth(z), gamma(z).

Les Paysages Fractals IFS
http://perso.wanadoo.fr/wronecki/alexandre/francais/tipe.htm
Lyapunov Exponents lyapunov.gif (16030 bytes) efg's Lyapunov Exponents Lab Report
This project describes how to compute and display the Lyapunov exponents of the logistic map with periodic forcing (and to compute and display some very interesting graphics images).
Meus Fontes em Pascal LSM, TCAOS, Logic Chaos, Fractal.EXE
www.schulers.com/jpss/pascal/fontes.htm
Mandelbrot Benoit Mandelbrot's Home Page
www.math.yale.edu/mandelbrot 
Mandelbrot Sets See Julia and Mandelbrot Sets (above)

"The Area of the Mandelbrot Set" by John H. Ewing and Glenn Schober
Numerische Mathematik, 61, 59-72 (1992).

Pi and the Mandelbrot Set
www.math.ohio-state.edu/~edgar/piand.html  

Multifractal Walk Down Wall Street by Benoit B. Mandelbrot
Scientific American, February 1999, pp. 70-73
Sierpinski Gasket Triangle Sierpinski.gif (2621 bytes)   efg's Sierpinski Triangle Lab Report
This project shows how to create a Sierpinksi gasket, a "holey" triangle, by recursively cutting holes in a triangle.
Sprott's Fractal Gallery http://sprott.physics.wisc.edu/fractals.htm
von Koch Curve VonKochSnowflake.gif (1087 bytes) efg's von Koch Curve Lab Report
This project shows how to create a von Koch curve, including a von Koch snowflake.

G. Wavelets

Algorithms Wavelets offer an attractive alternative when it comes to image compression. Steven gives us a practical guide to image compression via wavelets, and compares the results to more familiar techniques, such as JPEG. Dr. Dobb's Journal, August 1999.
Amara's Wavelet Page www.amara.com/current/wavelet.html
Books Wavelet Analysis with Application to Image Processing

Wavelets for Computer Graphics

Chapter 7, Wavelets
Algorithms for Image Processing and Computer Vision

MR/1 Software Package for Multiresolution Analysis
www.multiresolution.com 

Book:  Image and Data Analysis: The Multiscale Approach, Cambridge University Press, 1998.

Wavelet Digest and E-Mail newsletter
www.wavelet.org
Wavelet NetCare www.math.wustl.edu/wavelet
Wavelets Library By Don Lancaster
www.tinaja.com/wave01.html

H. Cryptography
Also see efg's Delphi Cryptography and Multiple-Precision Arithmetic Page

general sci.crypt FAQ
ftp://rtfm.mit.edu/pub/usenet/news.answers/cryptography-faq/ 

Cypherpunks, Cryptography & Hackers
www.activism.net/cypherpunk

Crypto Drop Box www.und.nodak.edu/org/crypto/crypto
Government Encryption Standard DES Takes a Fall www.lubbockonline.com/news/062097/amateurs.htm
Congratulations, Rocke!
Great Internet Mersenne Prime Search www.mersenne.org
Microsoft's Cryptography Research page
www.microsoft.com/en-us/research/group/cryptography-research/
Quadralay's Cryptography Archive www.austinlinks.com/Crypto
Two Fish The Twofish Encryption Algorithm, Dr. Dobb's Journal, December 1998.
Wassenaar Arrangement Agreement of 33 member countries to restrict exports of 56-bit general encryption products, www.wassenaar.org

Updated 18 Oct 2016
Since 1 Nov 1998