Lessons, Tutorials and Lecture Notes

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

Algorithms and Complexity

Algorithms Course Materials on the Net

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

Calculus&Mathematica, University of Illinois, Urbana-Champaign

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.

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

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.

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.

Entropy of Compact Group Automorphisms

Finite Rank Torsion Free Modules Over Dedekind Domains

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:

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

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.

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.

Hypercard, HyperStudio, and Tessellations

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.

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

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.

Maple Examples from the University of Utah.

Massachusetts Institute of Technology - Course Materials

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.

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.

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

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.

OSU Math Ed Center: Electronic Library - Bookshelves
• 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

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.

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.

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.

University of Delaware, Course Materials

University of Florida, Course Homepages

University of Hawaii, Calculus Computer Lab

The University of Minnesota Calculus Initiative

University of Rochester, Course Materials

University of South Carolina, Course Materials

University of Wisconsin, Marathon Center
Notes and Examples for College Algebra and Geometry by M. Maheswaran

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.

Acknowledgment: Many of the descriptions were taken from and/or modified from the documents from the listed site.