OzMATH:

LEARNING MATHEMATICS WITH Mathematica

May 1994

This folder contains sample OzMATH NoteBooks.  You can copy and run them if you have Mathematica.  If you don't then you can read the Notebooks non-interactively by opening them with MathReader.  You can download MathReader from this folder via ftp.

The OzMATH NoteBooks are expressly designed to enhance the learning of mathematics and its applications.  Typically a student can work through a Notebook in less than one hour.  The bulk of the work is in coming to grips with mathematical content and assumed knowledge of Mathematica is minimal.   The amount of typing needed to do an exercise or problem is normally no more than a few characters.  Plenty of help is offered for Mathematica novices.

Each Notebook addresses a particular mathematical topic and can be used independently of the others.  In some cases a sequence of Notebooks may pursue a topic in greater depth.

OzMATH aims to cover a wide range of topics in undergraduate mathematics.  From time to time the sample OzMATH Notebooks in this folder are replaced by others.  OzMATH Notebooks also appear regularly in the electronic journal Mathematica World.

USING OzMATH IN A FRESHMAN CALCULUS COURSE

The standard first year calculus course at the University of Tasmania, with an enrolment of about 250 including all engineering students, integrates serious use of Mathematica with the standard lecture and tutorial approach.  We have created and are currently testing a suite of Mathematica Notebooks to enhance the teaching and learning of basic mathematics and calculus and its applications.  The  Notebooks are expressly designed for independent use in the Mathematics Computing Laboratory as an integral part of their course by students of a standard large first calculus course.  No change to the normal lecture format is required.

After an initial intensive hands-on laboratory session, students work through one OzMATH Notebook per week, in their own time and largely unsupervised.  Most students take less than1 hour to do this.  The bulk of the work is in coming to grips with mathematical content.   The amount of typing needed to do an exercise or problem is normally no more than a few characters.  The completed Notebooks are submitted and graded by tutors on line without any printing.  Standard homework is reduced slightly to compensate for time spent on Mathematica assignments.  Students are free to copy and retain Notebooks on floppy disk, and indeed to work on them outside the Mathematics Laboratory if they wish.

ACCESS TO OzMATH COURSE MATERIALS

Expressions of interest are sought from Mathematics Departments wishing to test  OzMATH course materials, including utilities for administering their use by a large class on a networked system.   A large number of Notebooks in the uniform OzMATH format can be made available to participating lecturers, and they also have the opportunity to write more of their own if they wish.   A directory includes a brief statement of the topic, level of difficulty and pre-requisites for each Notebook.  The Notebooks are largely independent of one another and lecturers are free to assign Notebooks on whichever topics they find most useful.   Those which are not assigned as homework may made be made available to students for optional use.   Some help in setting up a networked Mathematica  system, either Macintosh or IBM compatible, may be available to Departments wishing to try out the project materials in 1994-95.  Subsequent to 1995 a charge may be made for use of OzMATH materials in courses.

CONTRIBUTING TO OzMATH

Anyone is welcome to contribute to OzMATH.  All you need to do is write a NoteBook that adheres to the OzMATH Guidelines and submit it by email to the address below.  It will be refereed, changes may be suggested, and when the Notebook is accepted it will be added to the OzMATH world.  Copyright remains with the author and the Notebook may subsequently be withdrawn if the author wishes.  We expect there to be a continuing evolution of OzMATH and the uses that are made of it, and authors will be kept in touch with developments.

OzMATH GUIDELINES

OzMATH Notebooks conform to a uniform Mathematica Notebook style.  Currently there is only one standard style, designed for its suitability for Mathematica-naive users.  To compose a Notebook in this style, simply start with an existing OzMATH Notebook.  Note the use of the Special 2 and Special 4 styles.

Each Notebook addresses a single mathematical topic.  Notebooks normally include Exercises that require only a few keystrokes but substantive mathematical thought to answer.  The idea is that a student with the assumed background should be able to work through the Notebook, answering all the exercises in about an hour.  A Notebook may also contain more difficult optional problems or open-ended projects.  Though Notebooks may deal specifically with Mathematica features, the primary emphasis must be on mathematical content.  Shorter Notebooks that treat a topic briefly and in an entertaining way are also acceptable.

The aim of an OzMATH Notebook is to enrich the mathematical world of the user.  An hours work must result in some new knowledge or skill being acquired.   If that can be done more easily or more quickly by reading a book then there is no reason to use a computer.  The reader of an OzMATH Notebook must be more than a reader: it must be actively engaged in dialogue with Mathematica.

Acknowledgment.

Preparation of Notebooks and other materials for a standard first calculus course in 1993 was funded by an Australian National Teaching Development Grant.

Your comments and questions are welcome.  Please address them to