OzMATH

OzMATH is a library of Mathematica Notebooks and utilities designed to enhance the learning of mathematics and its applications.  It aims to cover a wide range of topics in undergraduate mathematics.  

Anyone with appropriate mathematical background should be able to work through an OzMATH 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.

Sample OzMATH Notebooks

This special Education Today issue of Mathematica World contains sample OzMATH Notebooks that should give a good idea of the OzMATH approach.  

The three Notebooks Function Iteration 1, 2  and 3 address a topic that students do not usually greet with enthusiasm: convergence of numerical sequences.  

We try to use Mathematica to enliven the topic.  We use a couple of different ways of picturing convergence that require some mental effort to grasp.  We do not shrink from proof.  We usually provide built-in feedback that will immediately tell the student if its answer to an exercise was wrong.  We try to elicit alertness and concentration from our students.  For some of them the current Notebook may be the longest piece of consecutive text thay have ever read!

Mathematica's ease of use makes it feasible to introduce levels of complexity that would normally be left to a later course, and we do that.  But it is unrealistic and even counter-productive to expect average freshman mathematics students to write Mathematica code, and we do not ask our students to do so.  They do pick up knowledge of Mathematica  as they work through the OzMATH Notebooks, but that is secondary to the main game: learning mathematics.  

We try to write Mathematica code that is mathematically neat and we don't worry about programming issues such as efficiency.  We don't aim for the kind of bullet-proof, slick code that would normally be expected in a finished package.  We leave that to a subsequent Mathematica programming course.  We hope that our students will be motivated to take such a course. 

We've also included a Notebook Questionnaire which summarizes the response of a 1993 calculus class to questions about the use of Mathematica in their course.  You'll see that Function Iteration 3, which introduces the notion of chaos, is one of the most popular Notebooks.

More about OzMATH

OzMATH Notebooks appear regularly in the electronic journal Mathematica World.  There are also sample Notebooks in the OzMATH folder at the University of Tasmania Gopher node.  From time to time the samples are replaced by others.  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 via ftp.

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 use of Mathematica with the standard lecture and tutorial approach.  OzMATH Notebooks are used by students independently in the Mathematics Computing Laboratory as an integral part of the 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 style can be made available to participating lecturers, and they also have the opportunity to write more of their own if they wish.   With the author's permission Notebooks that conform to the OzMATH Guidelines can be added to the OzMATH Library.

Each Notebook includes an indication of its topic, level of difficulty, pre-requisites and author.  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 may be available to Departments wishing to try out OzMATH materials in 1994-95.

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

Desmond Fearnley-Sander
OzMATH
Department of Mathematics, University of Tasmania 
GPO Box 252C, Hobart, Tasmania 7001, AUSTRALIA.
EMAIL:  dfs@hilbert.maths.utas.edu.au