Teaching and Learning Technology Resource

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DESCRIPTION OF INNOVATION:

This computational physics course consists of a suite of computational "experiments", implemented using interactive Mathematica Notebooks. The course is a "hands-on" laboratory style course consisting of 9 x 3 hour laboratory sessions with continuous assessment. The course Notebooks are available from

http://www.pd.uwa.edu.au/Physics/Courses/
Third_Year/Computational_Physics.html

After completing the course, students are given two weeks to work on a "take-home" examination to see how well they can apply the computational methods they have learnt during the course to new problems.

REASONS FOR DEVELOPMENT/INTRODUCTION OF THE INNOVATION:

"The purpose of computing is insight, not numbers" (Richard Hamming)

In traditional computational courses, simulation and modelling are taught by stressing numerical techniques, whilst visualisation often requires a range of specialised software tools. This course uses Mathematica as both a presentation environment and a computational tool. Programs like Mathematica have the potential to revolutionize teaching and learning in a range of computational disciplines because their hypertext "Notebook" interface provides an environment for computation (including linking to external fortran or C code), a high-level programming language, text, graphics, animation, and sound. At the same time Mathematica is capable of, and used for, high-level computation by physicists making it, in some ways, an ideal computer assisted learning tool.

Computational physics is taking its place alongside the traditional disciplines of theoretical and experimental physics as a third paradigm for doing physics. It permits simulation, visualisation, and modelling of situations which are normally avoided either because of the difficulty of physical study or the complexity of the mathematical tools required.

Standard texts on Computational Physics such as Koonin and Meredith (1990) teach computation by having students develop or edit procedural code fragments to model a particular physical problem or system. This approach requires the student to learn and understand many details of a procedural programming language such as Basic, Pascal, Fortran or C. Although learning procedural programming is very useful, it can detract from the desired goal of teaching computation. A second approach, taken by, e.g., Hubbard and West (1992), is to develop custom "black-box" applications for illustrating specific physical concepts. Another approach, taken by e.g., Feagin (1994), involves using an integrated computational environment such as Mathematica. (Similar approaches are certainly possible with other high-level computer algebra systems such as Maple, see e.g., Greene (1993)).

References:

• Feagin, J., Quantum Methods with Mathematica, TELOS, Springer-Verlag, Santa Clara (1994)
• Greene, R. L., On Integrating Computers into the Physics Curriculum in Mathematical Computation with Maple V: Ideas and Applications (ed. Lee, T.), Birkhäuser, Boston (1993)
• Hubbard, J. H. and West, B. H., MacMath, Springer-Verlag, New York (1992)
• Koonin, S. E. and Meredith D. C. Computational Physics, Addison-Wesley, Redwood City (1990)

DESIGN PRINCIPLES and TEACHING/LEARNING AIMS:

This course uses computer algebra, to help students explore a wide variety of phenomena taken from a range of disciplines. This gives them a deeper understanding of these topics and helps elucidate a large number of computational techniques, both numerical and symbolic. Visualization is a key to the understanding of many of the topics presented. Where possible, interconnections between methods from different disciplines is highlighted.

The students are required to do visualization and interpretation. Experimentation is encouraged through asking a number of "What If" questions. The student solutions to the exam illustrates how the students do visualization, interpretation, and experimentation.

USE:

This computational physics course for third year science and engineering students consists of a suite of computational "experiments", implemented using interactive Mathematica Notebooks. The course is a "hands-on" laboratory style course consisting of 9 x 3 hour laboratory sessions with continuous assessment.

The project uses our Department's third year computing laboratory.

ASSESSMENT:

After completing the course, students are given two weeks to work on a "take-home" examination to see how well they can apply the computational methods they have learnt during the course to new problems.

Assessment is continuous and the final exam is worth 40% of the total mark. Students submit their solutions to each assignment in the form of annotated Mathematica Notebooks.

STUDENT SUPPORT:

Since Notebooks include text, graphics, and sound, it is easy for students to both show (graphically, numerically, visually, ...) how a solution was obtained. Moreover, when grading their solutions, the instructor further anotates the Notebooks (including computational demonstrations and graphics) to amplify points that the student has not yet appreciated or understood.

Mathematica includes interactive on-line documentation. Students can lookup any term or phrase used in a Notebook and this very quickly enables them to go much further than would otherwise be possible. The use of hyperlinks, palettes, and buttons increases the usablity of this powerful software tool. Experience has shown that science and engineering students very quickly adapt to this environment and make use it for a wide range of their other coursework -- and they take these skills with them when they progress onto postgraduate research.

EFFECTIVENESS:

Follow-up of students undertaking this course (given since 1992), has demonstrated the relevance of their computational training evidenced by the number of them applying such methods to their Honours and PhD projects.

At the end of the course students have:

• a capability for model building and solving which is unconstrained by traditional mathematical and physical limitations;
• a better understanding of the computational methods than would be obtained in a traditional "procedural" computational course.
• a basic understanding of Mathematica.

ENABLERS TO DEVELOPING INNOVATION:

This course has a significant positive effect on student learning because:

• they are learning a tool widely used by physical scientists;
• Mathematica is interactive and it encourages student experimentation.
  (This course is NOT intended to teach Mathematica so it has been constructed so as to make the learning curve gentle and, at the same time, foster experimentation.)

COST/BENEFITS:

The university has a site license for Mathematica and student copies are available for ~$100.

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