# What's New on the Mathematics Archives---April 1996

On this page you will find a chronicle of additions and changes of the items contained on the Mathematics Archives which were made during the month of April, 1996.

## April 30, 1996

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 29, 1996

The following link has been added to the Mathematics Archives' page of JAVA and Other Interactive WWW Pages:

A Calculator to Merge Two Samples
Use this form to get combined statistics from two sets of sample statistics. Note: This form uses JavaScript and requires Netscape 2.0 or later.

This JAVA Applet graphs scaling functions and wavelets with two parameters even and odd. If you are interested, there is a discusiion of the mathematics behind the Applet. The applet shows the graph of the scaling function or wavelet, which is defined on [0,3], on top and the parameter space below.

We have added the following links to our WWW page on Other Software Sites:

MIX Software
MIX software fits mixture distributions to grouped data by the method of maximum likelihood. Mixtures of up to 15 components can be fitted, and the data can be grouped over as many as 80 intervals.

This collection of pages is intended to provide a clearinghouse for information regarding using the Macintosh for statistical analysis. The emphasis here is on statistical analysis as used in marketing and other social science research. It may also be relevant for engineering and hard science applications but that's not its main focus.

UnitCalc - A calculator that keeps track of units
UnitCalc is a Reverse Polish Notation calculator which does all arithmatic with the numbers and the units.

WaveLab
WaveLab .701 is a library of MATLAB routines for wavelet analysis, wavelet- packet analysis, cosine-packet analysis and matching pursuit. WaveLab has been used in teaching courses in adapted wavelet analysis at Stanford and at Berkeley.

The following links were added the Mathematics Archives' page Sites with K-12 Teaching Materials in Mathematics:

Challenger Center for Space Science Education
Challenger Center for Space Science Education is a not-for-profit organization committed to promoting science, math and technology education. Partnering with museums, science centers, schools, universities and communities across North America, Challenger Center uses the theme of space exploration to: create positive learning experiences, foster interest in math, science and technology, and motivate young people to explore.

Ontario Science Centre
The Educational Programs section at the Ontario Science Centre, "your partner in math, science and technology education", is offers quality programs and workshops which have been presented to millions of students and teachers since their opening in 1969.

We have added the following link to our WWW page on Numbers:

Fun with PI
This page contains some methods to calculate PI to a lot of decimals. It also contains some programs you can use to try it yourself, all of these programs were written and tested on my home LINUX-system. I used one of the programs on this page to calculate 1.000.000 decimals of PI. (It took 12 hours on my Pentium-60 !) If you are really interested, you can get the file that contains all the decimals here.

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 28, 1996

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:
The following entry was added to the research section of the Mathematics Archives' page for For Undergraduates:

Reed College's Recent Senior Theses in Mathematics.

## April 25, 1996

The following link was added the Mathematics Archives' page Sites with K-12 Teaching Materials in Mathematics:

Teacher Talk Forum - Math Section

Teacher's Edition Online - Math Section

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers: The following entry was expanded:

## April 24, 1996

We have added the following link to our WWW page on Other Software Sites:

Neufeld & Associates
Publishers of The UNDERSTANDING MATH Programs, collection of programs for interactive learning for grades 6-10. Topics include algebra, equations, exponents, geometry and integers. Software is available in both English and French. Demos are available. The company also provides lessons plans related to these packages and organizes workshops.

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 23, 1996

The following link has been added to the Mathematics Archives' page of JAVA and Other Interactive WWW Pages:

Pythagoras' Theorem
This page shows an animated geometrical proof of Pythagoras' Theorem. The three buttons, NEXT, BACK, RESTART, allow you to go through the steps of the proof.

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 22, 1996

The following link was added to the Mathematics Archives' page on POPMathematics:

A Visual Dictionary of Special Plane Curves
Do you know what is a Nephroid? Check out information about this curve and many other curves. Many graphs are drawn and there are mathematica and geometry sketchpad notebooks for sketching these curves.

The following link has been added to the Mathematics Archives' page of JAVA and Other Interactive WWW Pages:

Interactive Linear Programming
In addition to providing information and links concerning linear programming, this page lets the user submit a linear programming problem which it then solves.

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 19, 1996

We have added the following links to our collection of Mathematics Institutes, Centers and Laboratories:

Center for Approximation Theory
The Center for Approximation Theory (CAT) was founded in September, 1981, by Charles K. Chui, L. L. Schumaker, and J. D. Ward. During the past fourteen years, it has grown into a preeminent center of research in approximation theory and related areas, notably wavelet analysis. The research interests of the various center members have covered a wide range of topics; the thrust of current research is in the areas of splines, computer aided geometric design (CAGD), radial basis functions, and wavelets.

CMAP - Centre de Mathématiques Appliquées

IREM - Institut de Recherche sur l'Enseignement des Mathématiques

We have added the following link to the WWW page on Lessons, Tutorials and Lecture Notes:

Statistics - The Study of Stability in Variation
This is a statistics textbook which is being written by Jan de Leeuw on the WWW. It includes demos which use Xlisp-Stat and includes a number of pages which have interactive calculators.

We have added the following links to our collection of Professional Societies:

Gesellschaft für Didaktik der Mathematik (GDM)
This German society has as its major theme the teaching of mathematics.

SMAI - Société de Mathématiques Appliquées & Industrielles
The objectives of this society, formed in 1983, are to contribute to applied mathematical research, applications in industries and the training of researchers and engineers.

SMF - Société Mathématique de France

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 18, 1996

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 17, 1996

The following link has been added to the Mathematics Archives' page of JAVA and Other Interactive WWW Pages:

Calculators On-Line - Mathematics
This the mathematics section of a collection of links to various calculators on the WWW. Many of the linked pages employ JAVA applets.

The following links were added to the Mathematics Archives' pages on POPMathematics and Images and Mathematics:

The KnotPlot Site
Here you will find a collection of knots and links, viewed from a (partly) mathematical perspective. The images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions.

Knots on the Web
This page contains a collections which are divided into three sections: Knot Tying, Knot Theory, and Knot Art. But knot lovers will understand that these distinctions are artificial. For example, a good practical knot is both a nugget of hard-won technology and a thing of beauty. Decorative knotting can be useful, and in any case requires uncommon dexterity and practical tying ability.

We have added the following link to our WWW page on Other Software Sites:

Knot
Knot lets you create large 3-D color animations and stills of beautiful abstract knots. You design the knot's form, colors, motion, backgrounds and lighting - or design and render entire animations automatically. It's an endless source of gorgeous moving backgrounds and photocollage elements for your work.

MING - The MD-Energy of Knots
The problem about computation of knot energy is to find the minimal energy among all knots isotopic to a given knot. "ming" is the a program which will try to find the minimal energy by pushing the knot along the direction of its "energy gradient".

The following link was added to the Mathematics Archives' page on Lessons, Tutorials and Lecture Notes:

A Knot Theory Primer

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 16, 1996

Journal for Research in Mathematics Education
The Journal for Research in Mathematics Education, an official journal of the National Council of Teachers of Mathematics, is devoted to the interests of teachers of mathematics and mathematics education at all levels--preschool through adult. The JRME is a forum for disciplined inquiry into the teaching and learning of mathematics. It encourages the submission of a variety of high-quality manuscripts: reports of research, including experiments, case studies, surveys, philosophical studies; articles about research, including literature reviews and theoretical analyses; brief reports of research; critiques of articles and books; and brief commentaries on issues pertaining to research.

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 15, 1996

The following link has been added to the Mathematics Archives' page of JAVA and Other Interactive WWW Pages:

The Vector Cross Product - A JAVA Interactive Tutorial
This JAVA applet lets the user explore the cross product of two vectors when one of the vectors is changed.

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

We have added the following link to our WWW page on Other Software Sites:

Interactive Mathematics
INTERACTIVE MATHEMATICS is a new series of college-level, interactive multimedia courses being developed by Academic Systems in collaboration with faculty from colleges and universities around the country. Interactive Mathematics is also the first series of courses that take advantage of an advanced computer-mediated instructional approach, called Mediated Learning, which provides a faculty-guided, learner-centered environment for improving student academic achievement. Each course in the Interactive Mathematics series provides comprehensive mathematics instruction using an engaging and challenging interactive multimedia environment.

## April 14, 1996

We have added the following link to our WWW page on Other Software Sites:

Solutions
Solutions is a symbolic mathematics software built for engineers and scientists. Solutions will provide you with 20 classes of functions from Algebra to Statistics. It will plot and print your work. You can even program it if you need more power!

## April 13, 1996

We have added the following link to our WWW page on Other Software Sites:

William K. Bradford Publishing Company, Inc
This page is the Mathematics section of the On-Line K-12 Software Catalog which an extensive listing of the publisher's offerings for all levels from elementary schools through AP calculus.

## April 11, 1996

The following link has been added to the Mathematics Archives' page of JAVA and Other Interactive WWW Pages

Java Geometry Explorer
This is the first of a promised K-12 Educational Series programmed by Cliff Pickover to simulate students and teachers of art and math. This JAVA applet draws the locus of points obtained by moving a chord around a circle. Other similar pictures are also drawn depending upon the input of the reader.

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

# JAVA and Other Interactive WWW Pages

You will need a browser which supports JAVA to view most of the pages listed on this page.
We have added the following link to our WWW page on Other Software Sites:

Broderbund Software, Inc.
The above-mentioned page is a link to the "Kids' software" products. The software titles are sorted by various categories, one of which is mathematics. Two of the packages listed are James Discovers Math and Math Workshop.

The following links were added to the Mathematics Archives' list of Mathematics Departments WWW, Gopher and Anonymous FTP Servers:

## April 9, 1996

We have added the announcement about the following workshop to the Mathematics Archives' page Conferences and Workshops for Faculty:

Faculty Enhancement Workshops
Teaching Differential Equations Using a Dynamical Systems Perspective
Boston University, June 2-5
Oberlin College, June 16-19

Vladimir Podnos has upgraded his MSDOS field simulation package QuickField(TM), formerly known as ELCUT.

The following link was added to the Mathematics Archives' page on POPMathematics:

Euler's Formula: V-E+F=2 - Ten Proofs
This page lists proofs of the Euler formula: for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. Symbolically F-E+F=2.

We have added the following links to our WWW page on Other Software Sites:

Amos
Amos implements the general approach to data analysis known as structural modeling, analysis of covariance structures, or causal modeling. This approach includes as special cases many well known conventional techniques, including the general linear model and common factor analysis.

KASH
KANT is a software package for mathematicians interested in algebraic number theory. For those KANT is a tool for sophisticated computations in number fields. With Kash you are able to use the powerful KANT V4 functions within a shell and you don't need to know anything at all about programming in C. The main features of the current release are: computations in number fields, ideals in number fields, relative extensions of number fields, lattices.

SpaceStat
SpaceStat, a software program for the analysis of spatial data, originally developed by National Center for Geographic Information and Analysis, at the University of California, Santa Barbara, is now available from the Regional Research Institute at West Virginia University.

Tera Analysis Co.
The chief product of Tera Analysis is QuickField - a PC-oriented Computer Aided Engineering (CAE) package for design of Electro-Mechanical devices. With QuickField's multi-disciplinary analysis capabilities, you can optimize electrical, thermal and mechanical features of your designs, all within one package! In addition, the results of different finite element analyses can easily be linked together which makes it ideal for simulating multi-field coupling effects. A shareware version of QuickField is available from the Mathematics Archives.

WesVarPC
WesVarPC is a software package that computes estimates and replicate variance estimates for data collected using complex sampling and estimation procedures.

We have added the following link in our listing of Professional Societies:

The Bernoulli Society for Mathematical Statistics and Probability
The Bernoulli Society was founded in 1973. It is an autonomous section of the International Statistical Institute, ISI. According to its statutes, the object of the Bernoulli Society is the advancement, through international contacts, of the sciences of probability (including the theory of stochastic processes) and mathematical statistics and of their applications to all those aspects of human endeavour which are directed towards the increase of natural knowledge and the welfare of mankind.

## April 7, 1996

We have added the following link to our WWW page on Fractals:

Chaos and Fractals
CeVis is well known for its many documents concerning Chaos Theory and Fractal Geometry. Several books are available which offer an easy-to-understand introduction to these topics. Besides that, there are several video films available, which are entirely computer generated (e.g. "Fraktale in Filmen und Gesprächen").

The following link was added to the Mathematics Archives' page on POPMathematics:
• The Mathematics of Fermat's Last Theorem
A whirlwind tour of number theory and related mathematical fields that are relevant to FLT and the concepts that have turned out to be fundamental to its proof.

The following link was added to the Mathematics Archives' page on Lessons, Tutorials and Lecture Notes:

MultiMedia Statistics Page
The purpose of this page is to illustrate some statistical concepts using QuickTime movies.

We have added the following link in our listing of Professional Societies:

Association of Christians in the Mathematical Sciences

## April 4, 1996

LMS Undergraduate Project Archive is a site established by the London Math. Society to make available to hard-pressed academics a good stock of topics for undergraduate project work that have been used successfully in other institutions. Ideally this would mean, for each project, a clear description of the work involved in the project, a good set of appropriate references and some indication of the length, level and prerequisites of the project.

We have added the following link in our listing of Professional Societies:

Dansk Matematisk Forening (Danish Mathematical Society)
Dansk Matematisk Forening was founded in 1873 with the purpose of acting for the benefit of mathematics in science and education.

The following link was added to the Mathematics Archives' page on Lessons, Tutorials and Lecture Notes:

xwb : X-Workbench
The program xwb was designed by M. Arbesmeier. xwb is an educational tool for teaching and experimenting with multigrid algorithms. It features a powerful graphical user interface (based on InterViews (177kB compressed Postscript) and Unidraw) with the possibility to manipulate the algorithms interactively.

We have added the following links to our WWW page on Other Software Sites:

QMG: mesh generation and related software
The QMG package does finite element mesh generation in two and three dimensions. The package includes geometric modeling software, the mesh generator itself, and a finite element solver. The software is written primarily in C++ and matlab.

The Multigrid Workbench
This version of the multigrid workbench is a WWW resource providing information about multigrid methods. The workbench teaches the basic principles of multigrid by explaining the steps of a prototype multigrid method giving graphical representations of all intermediate results. The workbench can be used for a self-guided tour through multigrid, but it may also contain useful information for instructors looking for material to use in mathematics or science courses.

## April 3, 1996

We have added the following links to our WWW page on Other Software Sites:

Cabri-géomètre
Cabri-geometry is the product of research activity at the Université Joseph Fourier de Grenoble and at CNRS, in the laboratoire de Structures Discrètes et de Didactique. From the Mathematics Archives pages on Cabri-geometry: Cabri-geometre is an Interactive Notebook to Teach and Learn Geometry. With this package, you perform ruler-compass constructions and then pose questions. You can ask whether lines are parallel or perpendicular. You can compare measures of objects (area, length, angular measurement). An especially nice feature is the ability to move points used as references in constructions and the figure changes appropriately. With this you can examine the trace of a point to find the locus of points, say equidistant from a given point and a given line.

CABRI GEOMETRY II
The interactive software for Geometry - Alter geometric figures on the screen. Students can see patterns, make conjectures, and draw their own conclusions. Discover geometric dependencies in the figures students construct. Display the equations of basic geometric objects including lines, circles, ellipses, and coordinates of points.

## April 2, 1996

The following link was added to the Mathematics Archives' page on POPMathematics:

John Conway's Game of Life - Patterns, Programs, and Links
A page of odds and ends about Conway's Game of Life. This page now contains descriptions of files which are made available for ftp, links to Life resources available elsewhere on the Internet, new results and patterns not archived elsewhere, and a browsable hypertext catalog of Alan Hensel's archive of Life patterns, including a hypertext version of his Life glossary. All the patterns except those in the glossary are Java-animated.

## April 1, 1996

The following link was added to the Mathematics Archives' page on Lessons, Tutorials and Lecture Notes:

New Mexico State University

The following link was added to the Mathematics Archives' page on POPMathematics:

Pentominoes
Learn about pentominoes and the patterns they create and what pentominoes have to do with Escher, Penrose, Logic,Impossible Objects, Mathematics and Art.

The following link was added to the Mathematics Archives' page on Bibliographies:

The following links were added to the Mathematics Archives' page on Images and Mathematics.

These are animations of a two dimensional vibrating circular membrane (I prefer just "drumhead", actually). The equation is a standard problem in partial differential equations, and I have used these animations to successfully (I think) explain atomic orbitals.

Fermat Project
Images used in a popularized introduction to Fermat's Last Theorem, a famous recently solved problem in number theory. Three dimensional mathematical depictions are used in the beginning of the film to illustrate the meaning of the mathematical ideas involved. The second half of the film makes a transition to show a remarkable family of four dimensional surfaces related to Fermat's theorem, and projects them to three dimensions for display using standard rendering and shading techniques.

Fluid.Dynamics Project
Images from an animation which was created by Thierry Dubois and Jacques Laminie of the Institute for Scientific Computing and Applied Mathematics at Indiana University using AVS on fluid dynamics computations and was recorded to video tape at CICA. The flow considered here is a two-dimensional homogeneous flow where the governing equations are the Navier-Stokes equations, supplemented with periodic boundary conditions in both spatial directions.

4Dice Project Movies
An MPEG movie of the 4Dice animation from the Center for Innovative Computer Applications. A glimpse into the fourth dimenion depicting a four-dimensional die with its 3D faces and dots.

Hyperbolic Motion, Fractal Octupus, etc.
MPEG animations by Yoshiaki Araki.

We have added the following links to our WWW page on Other Software Sites:

cGOP
cGOP is a package for rigorously solving nonconvex optimization problems to epsilon-global optimality. The package implements the GOP algorithm (Floudas and Visweswaran, 1993) which is a primal-dual decomposition algorithm applicable to general constrained biconvex problems, using a set of C subroutines to solve these problems using decomposition and branch-and-bound techniques.

Poliplus Software
Poliplus Software is a Canadian company specializing in Applied Computer Algebra and Geometry. It is the publisher of two packages : Formulae 1, which is a powerful, yet very easy to use Computer Algebra System (CAS) designed specifically for the teaching and exploration of mathematics and Euclid which provides functionality similar to that of Cabri II Geometry and uses the same symbolic engine as Formulae 1, thereby allowing new features to be designed based on Symbolic Computation.

The following link was added the Mathematics Archives' page Sites with K-12 Teaching Materials in Mathematics:

Educational Standards and Curriculum Frameworks for Math
Developing Educational Standards is an annotated list of Internet sites with K-12 educational standards and curriculum frameworks documents, maintained by Charles Hill and the Putnam Valley Schools in New York.

The Math Tutor
This is Calgary's Math Tutor. We are still under construction, but the long term plan is to develop a site that contains thousands of worked out examples taken from student queries. Each will be catagorized according to grade level and topic. Since Calgary's Math Tutor is just going online many of the links you see are non-functional, or lead to small numbers of examples. You can change this! Online queries are free! Response times can not be fully guaranteed, but we expect 24 hrs will be the usual turn around time.

Chronicles for the previous month: