The Lawrence Approach

Text of Talk Delivered as Part of a Panel Discussion at

the March Meeting of the American Physical Socie

Montreal, Quebec, CANADA

25 March 2004

Session W38 (2:30--5:36 PM Room 520E, Palais dex Congres)

Department of Physics

Lawrence University

Box 599

Appleton, WI 54911-5626

Email: `
david.m.cook@lawrence.edu`

Department website: `
http://www.lawrence.edu/dept/physics`

Project website: `
http://www.lawrence.edu/dept/physics/ccli`

Most efforts using computers in physics curricula
focus on introductory courses or individual upper-level courses.
In contrast, since the mid 1980s, the Lawrence Department of Physics
has been striving to embed the use of
general purpose graphical, symbolic, and numeric computational tools
throughout our curriculum. Developed with support from the (US)
National Science Foundation, the Keck Foundation,
and Lawrence University, our approach involves
introducing freshman to tools for data acquisition and analysis,
offering sophomores a course that introduces them to
symbolic, numerical, and visualization tools, incorporating
computational approaches alongside traditional approaches to problems in
many intermediate and upper level courses, and making computational
resources available so that students come to see them as tools to be
used routinely *on their own initiative*
whenever their use seems appropriate.
A text titled *Computation and Problem Solving in Uncergraduate
Physics* and reflecting the developments at Lawrence is now complete,
at least in a first edition, but---because of microscopic customizability
that permits the text to be adapted to each end user's spectrum of
hardware and software, it
has not yet found a commercial publisher. Details about the Lawrence
curricular approach and information about how to acquire
copies of the text from the author can be found from links
at `
http://www.lawrence.edu/dept/physics/ccli`.

Since the mid 1980s, we in the
Department of Physics at Lawrence University
have been developing the computational dimensions of our upper-level
curriculum. Rather than create a major in computational physics,
we have focused on incorporating computation into a fairly
traditional physics major. To that end, we have built a
Computational Physics Laboratory---the CPL---that makes a
wide spectrum of hardware and software available to students,
and we have developed a curriculum that, first, introduces sophomores
to these resources and, second,
encourages them to continue to use the CPL in their subsequent studies.
Further, with support from a recent NSF CCLI-EMD grant, I have
completed a flexible and customizable text titled
*Computation and Problem Solving in Undergraduate
Physics---CPSUP*. This afternoon, I want to

- lay out the underlying convictions that have guided our curricular development,
- describe the Lawrence curricular components,
- describe the course we now require of all sophomore physics majors,
- say a little bit about a junior/senior course in computational physics to be introduced next fall, and
- describe---briefly---the structure of
*CPSUP*.

The primary tasks of an undergraduate
program for physics *majors* are to awaken in our
students a full realization of the beauty, breadth, and power of
our discipline and to help them develop not only a secure
understanding of
fundamental concepts but also the skills to use a variety of tools in
applying those concepts. Among the tools, we at Lawrence would
firmly include *computational* resources of
several sorts.

- We believe that our curricula must familiarize students
- with the functions and capabilities of at least one operating system,
- with the use of at least one good text editor,
- with a spreadsheet like Excel,
- with resources like IDL and MATLAB for numerical processing of numbers and arrays,
- with resources like MAPLE and MATHEMATICA for symbolic manipulation of expressions,
- with resources like Kaleidagraph, IDL, and MATLAB for graphical visualization of complex data,
- with C or FORTRAN programming sufficient to permit comfortable use of subroutine packages like Numerical Recipes, and
- with resources like LaTeX and
`tgif`for preparing technical reports and manuscripts;

- we believe that our curricula must familiarize our students with several types of symbolic and numerical analyses, including solving algebraic equations, solving ordinary and partial differential equations, evaluating integrals, finding roots, performing data analyses, fitting curves to experimental data, and manipulating images; and
- we believe that our students must learn to use a sophisticated, universally recognized, system for preparing and publishing documents that are festooned with equations and figures.

We also believe

- that our curricula must familiarize our students with the assessment of accuracy in finite-precision arithmetic;
- that students must be introduced to computational tools long before they are ready for a rigorous course in computational physics;
- that use of computational resources must permeate the curriculum; and
- that the
*initial*encounter with computational tools cannot be effectively accomplished as an aside but must instead be*the*focus of attention.

The best way to describe the Lawrence approach is to track the computational experience of an entering freshman physics major. Each year, full-time students at Lawrence take three courses in each of three ten-week terms. Class periods are 70 minutes long, and a one-term course translates officially into 3-1/3 semester hours. The typical program of a physics major is shown in OHD1. The minimum major is satisfied by the courses marked with an asterisk---ten in physics and four in mathematics. Courses in bold type direct students explicitly to the computer and, in most cases, include instruction in one or more of our computational resources. Of the twenty electives, three must be in physics, seven to ten will be chosen to satisfy various general education requirements, and ten to seven are completely free, though most of our (typically) ten graduates each year will take courses in physics, mathematics, and computer science beyond the minimum required for the major.

Available physics electives are shown in
OHD2.
Again, entries in bold type make explicit use of computational resources.
In many other courses, students use our resources regularly on their
own initiative. Majors *must* elect
three courses from the top group of eleven, and most take three or
four more from the entire spectrum. Tutorials and independent studies
sometimes
extend over more than one term and can culminate in honors in
independent study at graduation.

The computational experiences of Lawrence physics majors are summarized in OHD3. Prospective physics majors at Lawrence first encounter computational approaches in the introductory course. In particular, students use LoggerPro, Excel, and Kaleidagraph. Exercises assigned in the laboratory routinely involve automated data acquisition, statistical analysis, and curve fitting; exercises assigned in lectures occasionally send students to the laboratory computers for graphing theoretical results or pursuing numerical solutions to problems in dynamics.

Beyond the freshman year, majors---of course---continue to use Excel
and Kaleidagraph. They also have 24/7 access to our Computational
Physics Laboratory, which is equipped with nine Silicon Graphics
UNIX workstations, monochrome and color printers, and software in
all the categories I have enumerated.
Fall-term sophomores are introduced explicitly to Electronics Workbench
in our electronics course;
winter-term sophomores are required to take the course
*Computational Mechanics*, to which I will return in a moment; and
spring-term sophomores see additional uses in the course
*Electricity and Magnetism*.

With *Computational Mechanics*as a uniform background,
subsequent theoretical and experimental courses alike offer students
many opportunities to continue honing
their computational skills and, depending on the instructor, some
of these courses will direct students explicitly to the CPL for an
occasional exercise. One upper-level course---*Computational
Physics*, to which I will return---is heavily dependent on the CPL.
Most senior capstone projects exploit the resources of the CPL, at least
for visualization of data and/or preparation of reports.
Some projects, including those enumerated on this overhead, have
made extensive use of these facilities.

Two courses, one a required sophomore course and the other an elective
junior/senior course, are now included among our offerings.
In the winter of 2003 (just a year ago), we replaced an
*elective* course titled * Computational Tools in
Physics* and taken by only a few sophomore majors with
a new---and required---sophomore course
constructed by merging some of the topics covered in
*Computational Tools* with some of the topics covered in an
existing intermediate-level course in classical mechanics.
The new course is called *Computational Mechanics*.

Beginning with last year's sophomores,
*Computational Mechanics* became the
starting point in our nurturing of our students' abilities to take
full advantage of the resources of the CPL.
The atalog description of this course is shown in
OHD4,
The topics addressed
each week in this course are shown in
OHD5,
The course begins with a tutorial
exercise to acquaint students with the SGI workstations and the UNIX
operating system while also reviewing and embellishing introductory studies
of translational and rotational kinematics and dynamics,
impulse, momentum, work, kinetic energy, and common forces.
Students spend week 2 entirely in
the CPL becoming acquainted with the general capabilities of IDL, especially
for graphical visualization of scalar functions of one, two, and three
variables, and
with TGIF for generating drawings. In weeks 3 and 4, we return to
mechanics to set up and solve standard problems in one-dimensional
motion via standard analytic techniques, and to extend the definition of
potential energy and conservative forces to three dimensions.
Then, in weeks 5 and 6, after a pause for evaluation,
students encounter the elements of LaTeX and spend several days on
the standard analytic approaches to the central force problem.
The remainder
of our ten-week term is spent mostly in computationally related
activities, including an orientation to MAPLE, a discussion of
numerical algorithms for solving ODEs and evaluating integrals, and
experience using routines built into IDL for solving ODEs and
evaluating integrals. Examples include many of the problems
already discussed analytically but also introduce
non-linear and chaotic systems. Sample integrals are
found in the evaluation of potential energies, moments and products of
inertia, and electric and magnetic fields and potentials.

*Computational Mechanics* does not, of course, cover all of the
mechanics in its predecessor. In particular, Lagrangian mechanics and
rigid body dynamics were moved to our elective course *Advanced
Mechanics*. These topics thus remain available to junior and senior majors
but are not any longer encountered by *all* majors. We believe,
however, that this loss is more than compensated by the acquaintance
*all* of our majors now have with computational approaches and by
their and our ability to exploit computational approaches at
many points in our intermediate and advanced curriculum.

The second computational course, to be taught for the first time next
fall, is called *Computational Physics* and is a junior/senior
elective. Its catalog description is shown in
OHD6,
Some years ago, I harbored the illusion that finite-difference
and finite-element approaches to *partial*
differential equations could be incorporated into other
courses in our curriculum.
That effort faltered, first because it was difficult to find adequate
time in those courses and second because only
those students who had elected *Computational Tools*
had the necessary background. Now, with all majors *required*
to take
*Computational Mechanics*, the second of those impediments has
evaporated. I have created---better, I am in the process of
creating---a new course that will fill this significant gap in the
computational topics to which our majors are introduced.
At the moment, however, I can say little more than what is in the
course description. With support from a grant from the W. M. Keck
Foundation, I will spend a very large part of my summer finalizing the
details of the first offering of this course and drafting the text
materials.

The NSF grant mentioned at the beginning
provided support for expanding
the extensive library of instructional materials
developed at Lawrence into a flexible publication as a
resource for other institutions. To address the challenge posed by
the wide variety of hardware and software in use,
*CPSUP*
can be assembled in several different versions by selection
from a wide assortment of components, some of
which---the generic components---will be included in all
versions and others of which---those specific to particular software
packages---will be included only if the potential user requests them.
Thus, the specific software and hardware
treated in any particular version will be microscopically
``tailor-able'' to the spectrum of resources available
at the instructor's site.

The table of contents for the first edition of
*CPSUP* includes the chapters and appendices
listed in OHD7.
Chapter 1 stands alone; chapters 2 and 3 introduce
the general features of two common array processors; chapters 4, 5, and 6
introduce the general features of three different computer algebra
systems; chapters 7 and 8 introduce a programming
language and the numerical recipes library; chapters 9, 10, 11,
and 12 address
several important categories of computational processing; and the
appendices introduce a publishing system
and a program for producing drawings. Any particular version would
include at least one of chapters 2 and 3 and one of chapters 4, 5, and
6, and chapters 9, 11, and 12, though chapters 9, 11, and 12 would be
assembled with only those components that illustrate the programs included in
the selections from chapters 2--6. Chapters 7, 8, and 10 and
the appendices would be
included only if desired by the end user. Chapters flagged
with an asterisk are included in the version used at
Lawrence.

Chapters 2--6 and 10, which focus on individual application
programs, adopt a tutorial, self-study style and lead the reader through
an exploration of the main features of the corresponding programs.
They lean in some measure on vendor-supplied documentation and
on-line help to encourage and guide self-study.
Each of Chapters 9, 11, and 12 begins with a section that
sets six to eight representative physical
problems, the successful
addressing of which benefits from exploitation of the computational technique
with which the chapter deals. Subsequent sections
describe how one might use a *symbolic* tool
in application to some of the problems set in the first section,
describe appropriate numerical
algorithms generically, and then illustrate how those algorithms can be
invoked from a variety of application programs. Each chapter concludes
with numerous exercises. While the objective is
for students to become fluent in the use of a spectrum of
computational tools---and the chapters are organized by program or
by computational technique, the focus throughout
is on physical contexts.

Detailed information about *CPSUP*, including tables of
contents for each chapter and information about how to obtain
examination copies is contained in links at the URL

Even among sites that use the same spectrum of hardware and software,
however,
many aspects of local environments---some of them shown in
OHD8---are
still unique to individual
sites. *CPSUP* does not
constrain local options in these matters. Throughout the
book, individual users are directed to a
local guide for site-specific particulars.
A template for that guide, specifically the one used at
Lawrence, is included in the supplementary materials available
to each user, but it will require editing to reflect local practices.

The desired flexibility to tailor the book to a variety of circumstances would be unattainable without LaTeX, which, in particular, can decide in response to conditional statements controlled by Boolean flags which files should be included in any particular processing run. Further, additional topics can be added easily, and, in anticipation of the course I will be offering next fall, I am currently drafting a chapter on partial differential equations. Chapters on data analysis, curve fitting, Fourier analysis, and image processing are contemplated. Indeed, the flexibility of design means that, in time, other authors may be moved to contribute components, so the book may expand to accommodate a wider and wider spectrum of hardware and software and to include topics not originally incorporated.