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
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 Geometry Géométrie Famous Curves 2D Curves 
Geometry, Solid  The
5 Platonic Solids and the 13 Archimedean Solids www.scienceu.com/geometry/facts/solids 
Mathematics Library/Archive 
Front for the XXX Mathematics Archive Mathematics Archives WWW Server Mathematics links, www.alcyone.com/max/links/maths.html 
Sloane's OnLine 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 
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://dnaview.com 
FourColor Theorem 
FourColor Theorem The Four Color Map Problem 
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 Geometry in Action Paper and Plotter: A 3D Surface Polyhedra Database Geometery Junkyard 
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. 100101) for more information. 
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 lowlevel 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/RECMathML 
Mathematics & Science  www.sco.com/skunkware/rr/math.html 
Mathematics Renderers  Comparative Review of
WorldWideWeb Mathematics Renderers http://hutchinson.belmont.ma.us/tth/mmlreview 
Maths Is Fun  www.mathsisfun.com 
Pi 
efg's Calculate Pi Using Buffon's Needles Lab Report On the computation of the n'th decimal digit of
various transcendental numbers 
Prime Numbers  The Prime Pages www.utm.edu/research/primes The First 10,000 Primes Great Internet Mersenne Prime Search (2^{6,972,593}
 1 is prime) On August 31, 1998, Ray Ballinger has found a new
largest known David Kuestler's UseNet
Post with Prime Numbers Generator C code "erato" 
Ram's Horn  Cardboard
model of a logarithmic spiral or maybe helix would
be a better word 
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 Stony Brook Algorithm Repository 
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://wwwswiss.ai.mit.edu/~jaffer/JACAL.html 
Also see
www.numericalmethods.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/jeanpierre.moreau/c_series.html 
Complex Roots  http://perso.wanadoo.fr/jeanpierre.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 crossindex 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.magicsoftware.com 
Matrices  http://perso.wanadoo.fr/jeanpierre.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 
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
Approximations  Functional Approximations http://perso.wanadoo.fr/jeanpierre.moreau/c_function.html 
Bessel Functions  Bessel Programs http://perso.wanadoo.fr/jeanpierre.moreau/c_bessel.html Bessel Function 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

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. 
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 FFTbased implementation of
crosscorrelation, 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.hpwworks.com 
Image Transforms  Chapter 3, pp. 81159 Digital Image Processing, 2nd edition 
Signal Proecessing  FFT, Butterworth Filter, ... http://perso.wanadoo.fr/jeanpierre.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.ohiostate.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.chaostheorie.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/fractalfaq 
Generating Random Fractal Terrain  www.gameprogrammer.com/fractal.html 
IFS  Iterated Function Systems
IFS Fractals Digital Encyclopedy (English or
French) Nonlinear Iterated Function Systems 
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://aleph0.clarku.edu/~djoyce/julia/wwwrefs.html The Mandelbrot and Julia sets Anatomy Contents efg's Fractals
Show 2 Lab Report 
Les Paysages Fractals  IFS http://perso.wanadoo.fr/wronecki/alexandre/francais/tipe.htm 
Lyapunov Exponents  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 Pi and the Mandelbrot Set 
Multifractal Walk Down Wall Street  by Benoit B. Mandelbrot Scientific American, February 1999, pp. 7073 
Sierpinski Gasket Triangle  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  efg's von Koch
Curve Lab Report This project shows how to create a von Koch curve, including a von Koch snowflake. 
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 
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 EMail 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 MultiplePrecision Arithmetic Page
general  sci.crypt FAQ ftp://rtfm.mit.edu/pub/usenet/news.answers/cryptographyfaq/ Cypherpunks, Cryptography & Hackers 
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/enus/research/group/cryptographyresearch/ 
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 56bit general encryption products, www.wassenaar.org 
Updated  18 Oct 2016 
Since  1 Nov 1998 