Mathematics Archives

Abstract Algebra On Line

This site contains many of the definitions and theorems from the area of mathematics generally called abstract algebra.

Advanced Linear Programming

This course by Harvey J. Greenberg goes deeper into linear programming, starting from having had a graduate course in LP and some introduction to graph theory. Topics include sensitivity analysis, model simplification, graphs of linear programs, embedded and hidden structures, sparse matrix techniques for simplex and interior methods.

Algorithms and Complexity

The links to this book by Herbert Wilf are on his home page.

Algorithms Course Materials on the Net

A large collection of links.

Analysis WebNotes by John Lindsay Orr, University of Nebraska, Lincoln

Applied Computational Methods

These are course notes developed by Bruno D. Welfert, Arizona State University.

Arithmetic Properties of Binomial Coefficients

Binomial Coefficients is an on-line dynamic survey, available on the World Wide Web, and accessible from various mathematical sites and e-journals. It is an edited document, in HTML, and can and will be edited as new developments arise. Content is at the discretion of the editors. We wish to make HyperLinks to other sites where pre-prints about Binomial Coefficients are available. Editors are Andrew Granville and Richard Witt.

California State University, San Bernardino, Notes on logic, proofs, and set theory at CSUSB

CALCULUS I WITH MAPLE V, North Carolina State University

Calculus&Mathematica, University of Illinois, Urbana-Champaign

Calculus Modules OnLine, PWS Publishing Company

Calculus Modules OnLine is an experimental repository of interactive Case Studies, exercises, problems, laboratory projects and applications of Calculus.

Internet Calculus, University of Pittsburgh

CALM - Computer Aided Learning in Mathematics

Initially, the CALM Project built a computerised tutorial system to enhance the teaching of calculus to students of the Heriot-Watt University.

Cellular Automata

A tutorial by David G. Green, Charles Sturt University.

Citadel - Course Materials

Classical and Quantum Chaos (lecture notes, P. Cvitanovic et al.)

Clemson University Course Materials

Colgate University Course Materials

The home page of the department contains links to materials for two courses on probability and statistics.

Combinatorics Topics for K-8 Teachers

Information and materials from a course taught by Roger Day at Illinois State University.

Computation Science Education Project

An introduction to High Performance Computing issues as a preparation for research and studies in computational science and computational engineering. The intended audience are students in science and engineering at the advanced undergraduate level and higher. Mirrored at the following sites:

• Vanderbilt University, Nashville
• Colorado State University, Ft. Collins
• University of Kentucky, Lexington
• Drexel University, Philadelphia
• Tampere University of Technology, Finland
• National University of Singapore, Singapore
• University of Giessen, Germany
• Universitaet Tuebingen, Germany
• Edinburgh University, UK

Computer-based Calculus, Old Dominion University

Cornell University - Engineering Mathematics

Course materials for a linear algebra and differential equations course.

DIANA Probability Module

The DIANA probability module (revisions in progess) is the first module in a series of modules to be used in an introductory undergraduate statistics course. DIANA is a World-Wide Web facility that enables teachers to assess the knowledge base of their class (facets) while providing valuable instructional feedback (prescriptions) to students.

Differential Equations Resource Center

The DE Resource Center has a page on On-line Courses and Course Notes which contains links to sites with DE materials.

Differential Equations Lab Manual

This WWW page by Eric R. Kaufmann contains samples of class room examples and some labs from the differential equations manual. There will be two basic types of labs. The first, applications labs, will focus on data collection and the employment of differential equations to understanding physical phenomena. The second type of lab will use Maple V and focus on problem solving and theory of ordinary differential equations.

Dynamical Systems and Fractals Lecture Notes, David J. Wright.

Dynamical Systems and Technology Project

This project is a National Science Foundation sponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process. At this point, there are several interactive papers available. These are designed to help teachers understand the mathematics behind such topics as iterated function systems (the chaos game) and the Mandelbrot and Julia sets.

Elementary Linear Algebra

Lecture notes for a course on elementary linear algebra by Keith Matthews.

Elementary Numerical Analysis

Lecture notes for a course on elementary numerical analysis by G.W. Stewart.

An Electronic Primer on Geometric Constraint Solving

Geometric constraint solving has applications in many different fields, such as molecular modeling, Computer-Aided Design, tolerance analysis, and geometric theorem proving. In this primer, a solution to the problem of finding a configuration for a set of geometric objects which satisfies a given set of constraints between the geometric elements is detailed. We have provided four different "tours" through the material in order to allow different types of users easy access to the information appropriate to their needs.

Emory University Course Materials

Entropy of Compact Group Automorphisms

Exploring Chaos and Fractals

Exploring Chaos and Fractals is an electronic textbook which includes full text, work sheets, sound, video and animation. Parts of the material have been placed on a Web server as an experiment in electronic publishing of hypertext based material. Exploring Chaos and Fractals covers the subject of chaos theory and its closely related field of fractal geometry.

Exploring the Space of Cellular Automata

Here you can explore the space of cellular automata (CA). using a sequence of interactive pages for generating CA with certain properties, by tuning some parameters .

The Fibonacci Numbers

Finite Rank Torsion Free Modules Over Dedekind Domains

Fortran 90 for the Fortran 77 Programmer

This tutorial is written in order to ease the transition from the very common and popular programming language Fortran 77 to the more modern Fortran 90.

Forum Web-based Units and Lessons

This page from the Math Forum present some examples from their experiment of the use of the WWW for instruction. Included are:

• Algebra and Calculus Sketches
• Hypercard, HyperStudio, and Tessellations
• Introduction to Vectors
• Limits
• Tangent Planes

Fractals and Scale

A tutorial by David G. Green, Charles Sturt University.

Fract-Ed

Fract-Ed is an course on fractals for high school or college students.

Fuzzy Systems - A Tutorial

A tutorial by James F. Brule.

Game Theory: An Introductory Sketch

Geometry and the Imagination

Notes and handouts for an innovative geometry course developed at Princeton and the Geometry Center by John Conway, Peter Doyle, Jane Gilman and Bill Thurston.

George Mason University - Course Materials

Graduate Algebra Course, E. L. Lady, University of Hawaii.

Graph Theory Tutorials

This is the home page for a series of short interactive tutorials by Chris K. Caldwell introducing the basic concepts of graph theory. They 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.

Graphical Data Analysis

The Department of Mathematical Sciences at Montana State University is offering an online version of Statistics 438, Graphical Data Analyisis. This course is about graphical data analysis, how we can use graphics to explore data and present results to others. The course explores topics ranging from human visual perception and computer vision to conditional expectation and empirical distributions. There is a special off campus page to help Internet visitors get started.

Hilbert Space Methods for Partial Differential Equations by R. E. Showalter

Hypercard, HyperStudio, and Tessellations

Imperial College London, Transitional Mathematics Project

Contains self-study modules (Mathematica notebooks) covering the mathematics topics that students need for university courses in mathematics. In addition to a WWW link, there is also a gopher link to the original site in London and there is a mirror on the Mathematics Archives

Indiana University - Purdue University, Indianapolis, Course Materials

InterQuest Calculus project

The InterQuest Calculus project is developing a web-based version of first term Differential Calculus. Our course is designed to meet pedagogic imperatives listed on the page, many of which are enhanced or made possible by the new teaching medium in which we are working.

Introduction to Factor Analysis

Factor analysis is a mathematical tool which can be used to examine a wide range of data sets. It has been used in disciplines as diverse as chemistry, sociology, economics, psychology and the analysis of the performance of race horses. This tutorial is designed to provide a basic understanding of the principles underlying factor analysis. The focus of the tutorial is the analysis of a 'factor space' or 'data space'. It was written to introduce the undergraduate chemistry major to the basic concept of a 'data space' and to demonstrate how factor analysis can be used to study a 'data space'. As an aid to conceptualization a geometric approach is used wherever possible and the actual linear algebra involved is illustrated.

An Introduction to Fourier Theory

Introduction to Math and Spreadsheets

Introduction to Quantitative Methods

A Basic Statistics Course in the College of Education at Arizona State University written by Gene Glass.

Introductory notes on Seifert fibered 3-manifolds

These are notes for a one semester course written by Matt Brin. They are available in two formats: compressed DVI file and compressed postscriptfile.

Introductory Numerical Analysis

This material is provided for students enrolled in a numerical analysis class required of Computer Science majors taught by James Carr at Florida State University.

The Interactive Physics Problem Set

This web page contains almost a hundred practice problems for physics students which are accompanied by detailed solutions, interactive computer experiments (which only run on Macintosh computers that have Interactive Physics II installed) and many MPEG movies. Useful for calculus class.

Interactive Real Analysis

This hypertext project, Interactive text book for Real Analysis, was developed by Bert G. Wachsmuth and supported by a grant from Seton Hall University. This undergraduate level text book contains standard text, interactive exercises, and laboratory programs. All definitions and theorems that are necessary for an exercise can be looked up. Some exercises contain Maple programs which can be run on systems which have Maple installed.

Interdisciplinary Course in Chemistry, Mathematics and Physics

The original TeX document for this course was written by Dennis DeTurck and Larry Gladney at the University of Pennsylvania.

Introduction to Fractal Geometry

Alexandre Kirillov offered this course at the University of Pennsylvania as a technical introduction to fractal geometry. The focus of the course was to develop the mathematical tools to characterize a given set as fractal, "a set whose Hausdorff-Beskovitch dimension strictly exceeds its topological dimension. (Mandelbrot)" The first half of the course covered point set topology and the second half focused on measure theory. Also available are a number of programs used to illustrate concepts in this course.

Introduction to Vectors

Gene Klotz has created a web-based lesson on vectors using Geometry Sketchpad. This is an experiment in creating useful online classroom materials.

Iowa State University - Home pages for courses

Ito Calculus - minicourse by Mitchell Feigenbaum (Postscript file)

Johannes Gutenberg-Universität Mainz - Nonlinear Dynamics Group - Lecture Notes

JPCalculus

The Java Powered Calculus Project is an effort to exploit the resources of the World Wide Web and especially the programming language Java to actively engage students in learning calculus. We take a "lean and lively" approach, which emphasizes conceptual understanding and problem solving over mechanical skills.

A Knot Theory Primer

L Systems

A tutorial by David G. Green, Charles Sturt University.

The Language of Mathematics

Purpose: To teach essential language concepts which have been underemphasized in the usual mathematics curriculum. To emphasize the basic patterns of mathematical expression and thought.

Laurentian University - Course Notes in Mathematics and Computer Science

Two items are (1)Course notes and Maple programs for the solution of linear systems of equations using gaussian elimination and the LU decomposition and (2)A maple program complete with graphs to illustrate that higher and higher order interpolating polynomials oscillate wildly near the end points of the interpolation interval, thus giving bad approximnations to the function.

The Limits of Mathematics

This book features a definitive reformulation of algorithmic information theory with new more constructive definitions of program-size complexity. It is a revised version of the course notes given to the participant at the limits of mathematics short course, University of Maine, Orono, Maine, June 1994.

Linear Algebra WebNotes

This is the cover page of Mark V. Sapir's Linear Algebra WebNotes. This is a complete undergraduate Linear Algebra course including the text of lectures, homework assignments and tests with solutions, a discussion page, Maple examples, etc.

Linear Programming

Information on a fundamental course for students specializing in operations research and/or optimization. Topics include model formulation, solution methods, duality and sensitivity analysis.

Maple Examples from the University of Utah.

Maple in Action from North Carolina State University.

Massachusetts Institute of Technology - Course Materials

Math Link

Math Link is a website based at the University of Illinois that is designed to deliver professional development opportunities and classroom resources to teachers of mathematics, statistics and related subjects at the high school and lower division college levels.

Mathematica Courseware

This page, maintained by Wolfram Research, Inc., contains a few schools that have developed and implemented Mathematica courseware.

Mathematics Education

This is the home page of Jim Wilson at the University of Georgia and contains links to web pages for courses in Mathematics Education. Included are the results of many student projects.

Math Link - Classroom Resources for Mathematics Teachers - Probability and Statistics

Includes:

Three Door Puzzle

Descriptive Statistics (introduction to Mode, Median, and Mean)

Linear Regression

Chi-Square

Exponential Fit

Guessing Correlations

Buffon's Needle

Mathwise

The UK Mathematics Courseware Consortium is a project in the Teaching and Learning Technology Programme. It is producing Computer Based Learning modules in Mathematics, especially for Science and Engineering students.

Mathwright Library

The Mathwright Library is a collecion of Mathwright Books which have been produced by the authoring system, Mathwright. This WEBsite makes available for downloading a Mathwright Library Player which may be used as a viewer for the WorkBooks in this Mathwright Library. However, it is capable of reading only the WorkBooks supplied through this WEBsite. There is a commercial version of Mathwright Library Player which has many additional features. Among the many topics covered in this library are Area Between the Graphs, Bernoulli Trials, Chaotic Pendulum, Curves in Art and Nature, Difference Equations, Dynamical Systems, Eigenvector, Factoring Polynomials, Golden Ratio, Lunar Lander, Matrix Calculator, Periodic Functions, Pool Game, Polar Graphs, Space Filling Curve, and Work Problems.

MATLAB in Education

Site established by Mathworks, publisher of MATLAB, which contains links to colleges, universities and high schools which have course materials using MATLAB.

Matlab Tutorial from the University of Utah.

MCP Project - Toolbook Mathematics Examples

Materials developed at the University of North Carolina at Wilmington for Calculus and Differential Equations.

Mentor Project

The Mentor Project is a Teaching and Learning Technology Project (backed by the Committee of Professors in Operational Research) whose aim is to produce 16 computer based modules in a variety of commonly taught Operational Research subjects. The modules contain hypertext, still/interactive graphics, animations, video and technique software integrated in a complete learning environment.

Middlebury College

Minority Science & Engineering Program at the University of Washington (Seattle, USA).

MultiMedia Statistics Page

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

New Mexico State University

• Projects and themes in calculus, discrete mathematics and linear algebra
• From Projects to Themes: The Evolution of Calculus Classes at New Mexico State University
• Teaching With Original Sources

Newton's Method

Let this site find roots of equations by Newton's method for you.

North Georgia College - Course Materials

These are course materials provided by Paul Patten for Introductory Statistics, Precalculus, College Algebra and Linear Algebra.

Northern Michigan University - Course Materials

Numerical methods for 1 D compressible flows

In this manual, M. Manzini gives a short presentation of some numerical methods for the solution of 1D compressible fluid flow problems. This is a title in the CRS4 Active-Books Library.

NWU Differential Equations Labs

These labs were developed at Nebraska Wesleyan University as part a two and a half year NSF/ILI grant awarded in the Spring of 1995. The labs use Mathematica and will be class tested for the first time in the Spring of 1996.

ODE Labs

These labs were created by Rick Wicklin at the Geometry Center at the University of Minnesota.

Online Exercises

Online exercises is an ongoing project to design and implement automatically generated and computer-graded exercises administered through the Web. We use the Internet and innovative software to remove a large portion of the routine exercises from the classroom, and to tailor the exercises to large and diverse student populations. HTML documents which include graphs and mathematical expressions are created from LaTeX-based templates. Templates may be remotely installed through Web interface. The system supports answers in the multiple choice format as well as numerical and algebraic formulas.

Optimization

Notes and materials for a course on Optimization taught for first and second year students at the University of Cambridge by Richard Weber.

OSU Math Ed Center: Electronic Library - Bookshelves

This page contains a collection of various items including:

• Uses of Technology in the Mathematics Curriculum by Benny Evans and Jerry Johnson
• Fresh Perspectives on Old Topics by Benny Evans and Jerry Johnson

Penn State University

• Graphics for the calculus classroom
• Calculus

Practicum in Numerical Analysis (for Maple V)

"Practicum in Numerical Analysis (PNA)" is a set of laboratory tasks designed to be a supplement to the course of numerical analysis. The exercises illustrate the basic numerical methods, show their advantages and limitations and help to understand the behavior of numerical solutions.

Prime Numbers

These pages were written by Kevin Coombes as an experiment to aid students to better understand proofs of theorems. From an email message: It seems to me that one of the main difficulties that students of (higher) matematics encounter stems from the insistence on getting all the logical prerequiesites set up before trying to explain anything interesting. (Of course, this style of presentation goes back at least as far as Euclid.) Hypertext should make it possible to explain the ideas behind a proof before writing down the proof formally, and it should also allow you to link to the lemmas so that they can be read only as needed when trying to understand more details in a proof.

Probability Theory - The Logic of Science

Project CALC - Bowdoin College

Projects from the 1994-95 UMTYMP Calculus III Course

Taught by Frederick J. Wicklin and Davide P. Cervone at the University of Minnesota. This course was an experimental course that emphasized the geometric aspects of calculus, and included a strong computer-based laboratory component. At the end of the course, students generated their own hypertext documents and labs, of which several are presented here.

QUERCUS - CAL Tools in Statistics and Modelling

The objective set in this first strand to this project is to design software which would make the laboratory work much more effective and more efficient. Initially this was to be based in a service class for Bioscience students but a further development is to make available the authoring resources as tools for other lecturers so that they can piece together their own tutoring system simply by modifying existing applications. The second strand to the project is to develop materials which could be used in statistical modelling. This would link in the capabilities of computer algebra package together with a tutoring system. The aim is to encourage students to develop their understanding of statistical modelling using graphical presentations. Most of the mathematical methods would be handled by the computer algebra package.

Rensselaer Polytechnic Institute - Course Materials

Royal Melbourne Institute of Technology - Maple Worksheets

Many of these Maple worksheets were prepared as part of the project MATHWEB that was funded by RMIT as a Strategic Proposal for Technology in Teaching and Learning. The Mathematics Department gratefully acknowledges this grant as well as money obtained from the Faculty of Applied Science's Quality Assurance committee to support the introduction of Maple into the teaching and learning programmes of large enrolment subjects. These worksheets include a number of animated movies.

Rutgers University - Course Materials

Scarborough College, University of Toronto Courseware

Solving the Quintic with Mathematica

This page is based on the material which appears in the Solving the Quintic with Mathematica poster, and allows you to solve fifth-degree polynomial equations using several programs written in Mathematica by Michael Trott and Victor Adamchik. The notebooks containing the programs are available on MathSource.

Splus Tutorial

Springfield Technical Community College - Calculus Labs

Stanford Testing Systems, Inc.

Stanford Testing Systems, Inc. is the publisher of software to help prepare students for various standardized tests including SAT, ACT, GRE, LSAT, MCAT, GMAT, TOEFL and MAT. In addition, the practice test for SAT is available online together with review lessons.

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.

Statistics - Teaching Resources

This is a substantial listing of resources for the teaching of Statistics which has been organized by Juha Puranen, Department of Statistics, University of Helsinki.

The STEPS Project

The STEPS project brings together nine departments in seven universities throughout the UK to develop problem based teaching and learning materials for statistics. The materials being produced are based around specific problems arising in Biology, Business, Geography and Psychology. It is intended that students will discover that statistical issues arise from these problems as important natural parts of the process of reaching conclusions. The role of the computer is to assist in the exploration of the problem and to provide support materials for the statistical ideas encountered. Graphical illustration plays a major role. A glossary of statistical terms is provided, and, where appropriate, problem modules can be operated in parallel with standard packages.

Studies In Mathematics

A home page for this freshman level class at the University of Chicago by Bryan Clair which has lots of links and some interactive demos on number theory and geometry.

SUNY Institute of Technology at Utica/Rome - Course Materials

SURFSTAT australia

An online introductory statistics book at The University of Newcastle.

Symmetry and the Shape of Space

Teach Modules - Teaching Statistical Concepts to Undergraduate Students

This is a collection of instructional modules from Iowa State University designed to illustrate concepts, provide important insights, and lead to more meaningful experiences and assignments with real or realistic problems of data analysis and inference. The software components of these modules use a combination of state-of-the-art computing hardware, statistical programming languages, high resolution color graphics, simulation, and a highly interactive user interface. The modules are independent of specific courses.

Technology Tools for Secondary School mathematics

Materials developed by Roger Day at Illinois State University.

TRANSMATH - A CBL Mathematics Tutor

Transmath is a computer-based mathematics tutor designed to strengthen and consolidate the basic mathematical knowledge of students commencing numerate degree courses. Topics include: Introduction to Differentiation, Techniques of Differentiation, Introduction to Indefinite Integration, Techniques of Indefinite Integration, Definite Integration, Ordinary Differential Equations, Matrices, Vectors, etc.

Triton College - Math Courses Review Modules

Undergraduate Computational Engineering and Science Archive

The primary goal of UCES is the creation of an archive of high quality educational materials in undergraduate computational science. Materials are divided into four categories:

• Classes: includes Methods and Analysis in UCES, a course in Computational Numerical Analysis
• Modules: includes Variable Mass Rocket, Monte Carlo Methods in Physics, Oscillations and Differential Equations, Exponential Growth, etc.
• Problems: under construction.
• Resources: includes Conic Sections, Trigonometry - A Review, Taylor Series, etc.

United States Naval Academy, Course Materials

The University High School WAVE Project

The Illinois WAVE Project provides Mathematica notebooks for use in the high school mathematics curriculum.

University of Birmingham, Course Materials

University of California, Berkeley

• Courseware
• Lecture Notes

University of Delaware, Course Materials

University of Florida, Course Homepages

University of Illinois at Chicago, Course Materials

University of Hawaii, Calculus Computer Lab

University of Miami, Course materials

The University of Minnesota Calculus Initiative

University of North Dakota Mathematics Computer Lab Units

University of Notre Dame, Course Materials

University of Oklahoma Course Materials

The University of Pittsburgh Calculus Labs

University of Rochester, Course Materials

University of South Carolina, Course Materials

University of Washington, Course Materials

University of Wisconsin, Marathon Center

Notes and Examples for College Algebra and Geometry by M. Maheswaran

Vanderbilt University, Course Materials

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 WAVELET Tutorial by Robi Polikar

Western Kentucky University - Instructional Materials

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