in Upper-Level Undergraduate Physics
Department of Physics, Lawrence University, Box 599, Appleton, WI 54911-5626
Voice: 920-832-6721; FAX: 920-832-6962; Email: david.m.cook@lawrence.edu
Text of Talk Delivered at the Summer Meeting of the American Association of Physics Teachers
Rochester, NY
23 July 2001
For more than a decade, use of graphical, symbolic, and numeric computational tools throughout the Lawrence undergraduate physics curriculum has steadily increased. As a component of a project supported by NSF CCLI-EMD grant DUE-9952285 and aimed at generating a flexible publication to help others follow Lawrence's lead, a dozen faculty members from around the country will meet at Lawrence for a week in early July, 2001, to experience the Lawrence approach hands-on, assess its exportability, and brainstorm about ways in which that publication might be further improved as a resource for supporting current and anticipated efforts of many departments to embed computation in their programs. This paper will describe the Lawrence approach and summarize discussions held in the workshop. Details will also be posted on the project web site, www.lawrence.edu/dept/physics/ccli.
Many of you probably know that, for a dozen years or more, we at Lawrence University have been developing the computational dimensions of our upper-level curriculum. We have built a computational laboratory that makes a wide spectrum of hardware and software available to students and, concurrently, we have developed numerous documents introducing computational tools and describing prototypical applications. We have also developed an approach to introducing students to these resources and drafted several hundred pages of instructional materials to support that approach. Many of you also know that the NSF-CCLI grant referenced in the abstract supports a substantial writing project whose main objective is the creation of an adaptable publication that I, the NSF, and Brooks-Cole (the publisher) all hope will be useful at other places seeking to increase the computational components of their curricula. In addition, to address both dissemination and assessment, the grant supports the holding at Lawrence of several faculty workshops, the first of which was held just two weeks ago. In this talk, I want primarily to describe that workshop. In the course of doing so, however, I will at the same time be telling you about the nature of the broader project and particularly about the structure of the publication that provided the text for the workshop.
Within the computational arena, the Lawrence curriculum, the text I am assembling, and the workshop just ended are all based on the conviction that our curricula must familiarize students
and that, at the same time, we must familiarize students with several types of symbolic and numerical analyses, including solving ordinary and partial differential equations, evaluating integrals, finding roots, performing data analyses, fitting curves to experimental data, preparing technical reports, ....
To these ends, I believe that students must be introduced early to each tool in a way that helps them learn how to control the tool itself, and that use of computational resources must permeate the curriculum. In the broadest of terms, we should---I argue---be structuring our curricula so that, ultimately, students will recognize when a computational approach may have merit and will have the personal confidence to pursue that approach on their own initiative.
| Su Eve | Orientation to UNIX, LaTeX, Compile C/FORTRAN Programs, Print Files, ... |
| Mo AM | Continue Sunday Eve |
| Mo PM | Orientation to IDL or MATLAB |
| Tu AM | Orientation to MAPLE |
| Tu PM | Catch-up |
| We AM | ODEs with MAPLE |
| We PM | ODEs with IDL or MATLAB |
| Th AM | Integration with MAPLE |
| Th PM | Integration with IDL or MATLAB |
| Fr AM | Root Finding |
| Fr PM | Use of Numerical Recipes |
| Sa AM | General Discussion |
We began on Sunday evening with an hour and a half session in which participants worked through portions of the tutorial that I use to introduce our students to the features of the operating system, including setting passwords, migrating in tree-structured directories, copying and renaming files, using the text editor, directing output to the printer, and compiling and running FORTRAN and C programs. At the beginning of the day on Monday, I took about an hour to describe the general character of programs like IDL and MATLAB for processing arrays and generating graphical displays. Then, for the rest of Monday, the participants finished off what of the Sunday evening exercise hadn't been completed and worked their way through much of the current draft of either the IDL chapter or the MATLAB chapter in the evolving manuscript. Tuesday was structured similarly, though it began with my describing the structure of a computer algebra system, specifically MAPLE, and continued for the rest of the day with participants working through much of the MAPLE chapter and---for at least a portion of the afternoon---catching their collective breaths. Once this background had been developed, we turned to computational strategies. On each of the following days, I spent an hour at the beginning talking about the focus of the day, both from a symbolic and from a numerical perspective. Then, using MAPLE and either IDL or MATLAB, participants worked through the pseudotutorial portions of chapters on ODEs on Wednesday, integration on Thursday, root finding on Friday morning, and uses of numerical recipes on Friday afternoon. In each case, after working through the introductory tutorial, participants addressed one or more exercises of the sort that might be assigned as homework problems for students.
To make sure participants could work in the CPL as much as they wanted, we issued to each a temporary Lawrence ID card giving them 24/7 access to the facility while they were on campus. While I wasn't personally there many evenings, I understand that the laboratory was busy during those times as participants explored topics or exercises more fully than they had time for in the more formal sessions.
On Saturday morning at the conclusion of the workshop, we spent an hour reviewing the week and talking about what happens next. Several of the participants are planning to test portions of the evolving text in their local environments during the coming year. Here are some of the comments made on the workshop itself:
Beyond the workshop, I would like to comment for a moment or two about the broader structure of the book in preparation. To accommodate the fact that we don't all use the same spectrum of hardware and software, I have envisioned a process that assembles a version of the text appropriate to each particular site by combining generic discussions of symbolic and numerical approaches to various types of problem with platform and program specific components that offer guidance in the use of the specific tools that happen to be available at the site. In short, I intend that the specific software and hardware treated in any particular incarnation of the book will be microscopically "tailor-able" to the spectrum of resources available at the instructor's site. Indeed, it is that feature that made it relatively easy for me to give workshop participants the option of using IDL or MATLAB, C or FORTRAN. Ultimately, {\em Mathematica\/} will join MAPLE and MACSYMA as possible choices. Guidance on the use of LSODE, Numerical Recipes (in FORTRAN or C), and LaTeX are already options.
The next few transparencies, which are similar to those that some of you may have seen in San Diego, show the structure of the book at various levels of magnification. Here, with the broadest brush, is my present list of planned chapters:
The structure of Chapter 8 on evaluating integrals exemplifies the structure of all of the chapters on various computational techniques (specifically, solving ODEs, evaluating integrals, finding roots). Presumably, before approaching any particular section in this chapter, the student would have studied the relevant sections in earlier chapters. Tentatively, the sections in Chapter 8 are titled
Finally, we take one step further down in the overall structure to show the present list of sample problems for Chapter 8, specifically
Even among sites that use the same spectrum of hardware and software, however, some aspects of local environments are still unique to individual sites. Rules of citizenship, practices and policies regarding accounts and passwords, the features and elementary resources of the operating system, the structuring of public directories, backup schedules, after-hours access, licensing restrictions in force on proprietary software, and numerous other aspects are subject to considerable local variation. This book makes no attempt to constrain local options in these matters. Throughout the book, individual users are directed to a publication called the Local Guide for site-specific particulars. A suggested template for that guide, specifically the one used at Lawrence, will be included in the supplementary materials available to each user, but it will require editing to reflect local practices.
The publisher---Brooks-Cole---was identified a year or more ago, and I have been working with their editorial and production departments to develop and test the method by which the desired flexibility can be achieved. The approach has already passed its feasibility test, and Brooks-Cole's editors claim that they will be able to produce the desired customization economically for orders of as few as ten copies. Further, once the structure has been fully worked out and debugged, there is no reason at all why other authors might not contribute components, so---over time---the product will expand to accommodate a wider and wider spectrum of hardware and software and maybe even to include broad topics not originally in the plan.
I want to make three more quick observations:
I will post the dates on that site as soon as they have been determined. Further, application for participation will be via a web-based form that will also be available at that site.