Mathematics Resources on the Internet

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Mathematics Resources on the Internet

An electronic guide prepared by Pam Bishop for the workshop on Teaching Materials for Engineering Mathematics within the IMA Conference on the Mathematical Education of Engineers, 26-28 April 2000

This is a guide to some of the ways in which the World Wide Web can be used as a resource for teachers and learners of mathematics. Browsing the Internet can be very time-consuming, so the following selection has been made to save time during this workshop. Many of the descriptions have been taken or modified from the documents themselves; some are tutorials or interactive materials, others are mathematical tools.

Some of these sites use special browsers or plug-ins which can be installed as part of Netscape or Internet Explorer. This has been done in advance at Loughborough to save time. If you want to take advantage of such facilities on machines in your institution, you will have to download and install them. Some are dependent on the platform used. The sites below are classified into two sections - the earlier ones can be viewed from a simple platform such as Windows 3, while the more sophisticated ones require Windows 95 or better.

Many sites are listed on the Mathematics Gateway page originally set up by CTI Mathematics. These represent resources of all kinds, including links to departments, organisations and projects developing Web resources for research, teaching and learning. If you find sites of interest that are not included in our pages, please send us details.

Selection of North American sites containing tutorial materials

Mathematics Archives - Lessons and Tutorials: Very useful list of links to lessons and tutorials from all over the world, which was used in compiling this selection.
Engineering Mathematics - Math 293 at Cornell University: The Math 293 course site includes the text of a series of 41 lectures in engineering mathematics, covering vectors, ODEs (Ordinary Differential Equations), and linear algebra.
Course Notes: Engineering Dynamics, Engineering Statics and Mathematics Needed for Mechanics: These notes, for courses run in Department of Engineering Mechanics at the University of Nebraska, cover statics, dynamics and maths needed for mechanics.
The Wavelet Tutorial: The Wavelet Tutorial was compiled by Robi Polikar from the Departments of Electrical Engineering and Biomedical Engineering at Iowa State University to address his perception that most, if not all, wavelet material was written by maths people for maths people in a language difficult to follow.
The World Lecture Hall - Mathematics: The World Lecture Hall based at the University of Texas contains links to pages created by academics worldwide who are using the Web to deliver class materials. For example, you will find course syllabi, assignments, lecture notes, exams, class calendars, multimedia textbooks, etc. In practice nearly all contributions are based in North America.
Classified list of Web resources for undergraduate teaching: A newly created service function in the Mathematics Department, University of Colorado at Denver, aimed at helping their staff to use the World Wide Web to support their teaching.
Finite Mathematics and Calculus Applied to the Real World: Online tutorials and utilities developed at Hofstra University
Simon Fraser - Organic Mathematics Home Page: This contains some useful tutorials and a number of specialised Maple Web interfaces so that you can use the Maple engine without having the package on your own machine.
Calculus&Mathematica: Developed at the University of Illinois at Urbana-Champaign and the Ohio State University, Calculus&Mathematica presents calculus, differential equations, and matrix theory. Students are no longer bound to the traditional classroom setting, nor do they even need to be on a college campus to gain valuable hands-on experience in practical calculus problems with the help of Mathematica. Instead of using rote memorization, students in Calculus&Mathematica use experimentation and real-time visualization to learn fundamental calculus concepts and ideas.
Graph Theory Tutorials: The home page for a series of short interactive tutorials introducing the basic concepts of graph theory developed by Chris K Caldwell (C) 1995, University of Tennessee at Martin. You can register online to look at the tutorials, which are designed with the needs of future high school teachers in mind and are currently being used as a supplement to a Mathematical Modeling course.
Interactive Real Analysis: An online, interactive textbook for Real Analysis and Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, and more. The text is changing constantly, and comments are very welcome.
Online Exercises: Online Exercises provide automatically generated computer-graded smart exercises for instruction via the Web. HTML documents with graphs, links, and complex formulas are created individually for every student. The system supports answers as numerical or algebraic formulas, true-false, and multiple choice. Based at University of Cinncinnati
Studies in Mathematics: This is the home page for Bryan Clair's Math 110-111 course at the University of Chicago. He is no longer running this particular course, but the resources are still available, and provide lots of examples as to how the Web can be used. "This page is meant as a resource for the students in the class. You can download homework or old exams, get additional resources, check your grades, or talk to Bryan, the TA's, or other students. Using this page is not a course requirement, but hopefully it can be of great help to you."
Mathwright Library: This is a set of books written in the MathWright authoring language, which has already been downloaded for your use - you will need to download the book of your choice. The Mathwright Library is currently being developed with the support of the National Science Foundation as the ILI project: Library for the Interactive Study of Mathematics, directed by James E White and Ladnor D Geissinger. Many of the Library books that were developed during the years 1992-96 were built under the auspices of the MAA sponsored Interactive Mathematics Text Project (co-directed by Jerry Porter and James White), and with major funding from the IBM Corporation, and the National Science Foundation.

Selection of UK Sites containing tutorial materials

Geomaths MathHelp project: Based at University College London, this is a joint Geological Sciences/Mathematics project funded by the HEFCE as part of the Fund for the Development of Teaching and Learning (FDTL) program
Heriot-Watt WebTest Home Page: WebTest is a system for delivering assessment tests via the web. Originally designed to provide self-assessments in mathematics, it has now been extended to other subjects and is used to provide tests for Heriot-Watt students on a variety of courses.
Optimization IB 1998: This is the home page for a course of 12 lectures to first and second year Cambridge mathematics students in spring 1998
Mathematical Assessment on the Web: Part of the MARBLE project funded by the Use of MANs Initiative (UMI), this page delivers a multiple choice mathematical test
Fibonacci Numbers and the Golden Section: Here you can find out who Fibonacci was, look at the Fibonacci series of numbers and some of their numerical properties and all the places that it turns up in nature. There is another page on some puzzles where the answers all seem to involve the Fibonacci numbers and a page to show where the Fibonacci numbers have been used in art, in architecture and in music. Compiled at the University of Surrey.
Learning modules online with Mathematica: Here are some online demonstrations of the experiment-based modules to be found in the book Experiments in Undergraduate Mathematics published by the METRIC project at Imperial College.
Using Computers for Scientific Work: Web mathematics teaching material developed at UMIST, which includes Mathematica worksheets
WANDA project at Dundee: This project developed hypertext pages of use to staff and students in mathematics-related subjects at Dundee, St Andrews and Arbertay Universities. The main features include a numerical analysis web site and interactive tutorials for widely-used software packages (Matlab, Maple and LaTeX).
History of Mathematics: Award-winning archive based at the University of St Andrews

Standard Packages - educational sites

MathSoft's educational site: Mathcad educational files, including the MathBrowser for reading Mathcad files on the Web
MathSource: Wolfram Research archive of materials using Mathematica, including the MathReader
CyberMath: Educational material written in MathView, previously known as Theorist or MathPlus
Maple educational resources: This page is maintained by the Computer Algebra Information Network. CAIN Europe is a server providing all kinds of information about Symbolic and Algebraic Computation which is set up by eight teams in the framework of the European SAC Network maintained by CAN / Riaca (Computer Algebra Nederland)
Universal Technical Systems Inc: Universal Technical Systems specialises in software solutions for mechanical, chemical, electrical, civil and structural engineering, financial analysis, chemistry, and engineering education. The site includes technical bulletin boards, an online UTS Gear On-line Bulletin with archives, an academic resource centre, and product information. An example of their products is TK Solver for simple equation solving and complex mathematical modelling.

Other sites with a substantial collection of maths resources

Mathematics Archives (Tennessee): A wonderful collection of classified resources, including a searchable database of teaching materials, software and WWW links organized by Mathematical Topics. The software section on public domain and shareware software is now available from the UK Mirror Service.
Geometry Center (Minnesota): Funded by the US National Science Foundation, this Science and Technology Center has a unified mathematics computing environment supporting math and computer science research, mathematical visualization, software development, application development, video animation production, and K-16 math education.
CSC (Scientific Computing, Finland): Resources which include examples of mathematical visualisations and animations
MATH Database 1931-1996: A service of the European Mathematical Society providing a bibliographic search facility
Visual Index of all Uniform Polyhedra: from the pages of Prof. Dr. Roman Maeder in Switzerland
The Mathematical Modellers Database: An international catalogue of people who are involved in mathematical modelling, developed at the University of Ulster as part of the MathSkills project.
Electronic Catalogue of teaching innovations: Again developed at Ulster, the aim is to provide a searchable database on the MathSkills' web pages which mathematics lecturers can use to obtain ideas and advice on new methods of teaching or assessment, not necessarily relating to the use of technology.
Math Forum: A Center for Math Education on the Internet funded by the National Science Foundation. The goal of Math Forum is to build a community that can be a center for teachers, students, researchers, parents, educators, citizens at all levels who have an interest in mathematics education.
Math in the Movies: A Guide to Major Motion Pictures with Scenes of Real Mathematics
MegaMath Home Page: MegaMath is a project of the Computer Research and Applications Group of Los Alamos National Laboratory.; It is intended to bring unusual and important mathematical ideas to elementary school classrooms so that young people and their teachers can think about them together.
Collection of maths cartoons: A collection of some math related comics and cartoons, displayed here for enjoyment and educational use.
Favorite Mathematical Constants: All numbers are not created equal; that certain constants appear at all and then echo throughout mathematics, in seemingly independent ways, is a source of fascination. Just as physical constants provide "boundary conditions" for the physical universe, mathematical constants somehow characterize the structure of mathematics.
Internet Center for Mathematics Problems: MathPro Press searches journals and other media to set up this page, which identifies and lists all sources of mathematics problems on the Internet and related information.
On-line Mathematics Dictionary: Another service from the MathPro Press.
Eric's Treasure Trove of Mathematics: A very useful and popular online maths dictionary originally produced at the University of Virginia and now sponsored by Wolfram Research
Spreadsheets in Maths, Science and Statistics Education (Austria): This page tries to collect some information about spreadsheets with an emphasis on mathematics and statistics education.
WWW Virtual Library: Mathematics
Yahoo - Science: Mathematics
MathSearch (Sydney): The last three sites are created by Web search engines, and consist of searchable collections of documents relating to mathematics.

Sites which use Java (not currently available under Windows 3)

An Introduction to Power Series - interactive lectures on Power Series developed for electronic engineering at the University of Birmingham
Non-Euclidean Geometry - part of the Clyde Virtual University
Vector Cross Product - JAVA Interactive Tutorial
CalMaeth - Computer Aided Assessment and Learning of Mathematical Methods
Pythagoras' Haven
Euclid's Elements, Introduction
Martindale's 'The Reference Desk: Calculators On-Line'
A Short Course in Linear Programming

The future of maths on the Web

The workshop Putting Mathematical Notation on the Web took place last year, but a lot of the material referred to in the report is still valid. It included a very valuable hands-on session on techexplorer from Francis Wright, Queen Mary and Westfield College.

Learning and Teaching Support Network Centres for Engineering and for Maths, Stats and OR