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Mathematics Archives - Lessons and Tutorials
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.
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
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
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.)
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
University of Kentucky,
Lexington
Edinburgh University,
UK
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.
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.
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
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. There is
a mirror on the Mathematics
Archives
Indiana University
- Purdue University, Indianapolis, Course Materials
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.
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 Vectors
Gene Klotz has created a web-based lesson on vectors using Geometry Sketchpad.
This is an experiment in creating useful online classroom materials.
Johannes
Gutenberg-Universität Mainz - Nonlinear Dynamics Group - Lecture
Notes
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.
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.
Massachusetts Institute
of Technology - Course Materials
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.
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
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.
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.
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.
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.
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.
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.
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
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
University
of Delaware, Course Materials
University of Florida,
Course Homepages
University
of Hawaii, Calculus Computer Lab
The University
of Minnesota Calculus Initiative
University
of North Dakota Mathematics Computer Lab Units
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
Acknowledgment: Many of the descriptions were taken from and/or modified
from the documents from the listed site.
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