Computers in Physics

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Wolfgang Christian and Denis Donnelly. Citation: .... Optics, and CUPS; see CIP 11: 1, 1997, p. 49) are used in ..... E. F. Redish, J. M. Saul, and R. N. Steinberg, Am. 1. Phys. ... George A. Antonelli and Wolfgang Christian, Comput. Phys. 10,243 ...
Computers in Physics Developing A Computer‐Rich Physics Curriculum at a Liberal‐Arts College Wolfgang Christian and Denis Donnelly Citation: Computers in Physics 11, 436 (1997); doi: 10.1063/1.4822586 View online: View Table of Contents: Published by the AIP Publishing Articles you may be interested in Maxwell to Einstein — A Liberal-Arts Physics Course Phys. Teach. 43, 418 (2005); 10.1119/1.2060635 Space colonization as a resource in the liberal‐arts curriculum: The case of economics AIP Conf. Proc. 148, 50 (1986); 10.1063/1.36024 Comparison of Physics to Psychology Majors at a Small Liberal-Arts College Am. J. Phys. 38, 269 (1970); 10.1119/1.1976303 Physics Curriculum for a Liberal Arts College Am. J. Phys. 34, 820 (1966); 10.1119/1.1973506 Physics in the Liberal Arts College Am. J. Phys. 6, 315 (1938); 10.1119/1.1991376

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Wolfgang Christian Wolfgang


Denis Donnelly [email protected]


he oft-quoted assertion that the advancement of physics is now equally dependent on experiment, theory, and computation has had little impact on undergraduate pedagogy.l The paddle-shaped scholar's pallet-now a notepadupon which a student transcribes a lecture, supplemented by 19th-century experiments in mechanics, optics, electricity, and magnetism, is still the principal method used to introduce the vast majority of students to physics in the undergraduate curriculum. This is not to say that computers have not found widespread use in the curriculum. Many programs have been improved using microcomputer-based laboratories (MBLs) for data acquisition and analysis, and there is evidence of cognitive gains as a result ofthis approach.2,3 Some professors have computerized their lectures to provide broad accessibility, but it is not clear that they have proceeded beyond electronic versions of annotated class notes. What has not happened is a systemic revision of the curriculum that takes into account the importance of computation in our profession. If the computer has changed professional practice and offers advantages over the technologies of previous generations, what are the advantages and how can they be incorporated into an education that has its roots in the seven original liberal arts: logic, grammar, geometry, arithmetic, rhetoric, music, and astronomy? Thinking about these questions has led to a decade-long revision of the Davidson College physics curriculum. This process has forced us to learn new skills and think about what our students and we do for a living, and how the computer fits into the big picture. The lessons that this process has have taught us are summarized briefly in "What Works (For Us)" (this page). Wolfgang Christian is a professor ofphysics and the director of the Scientific Computation Center at Davidson College, Davidson, NC 28036. He is one of erp's department editors for Book Reviews. E-mail: [email protected]

What Works (For Us) • Teach phy ics; do not hack. Special effects ound, an imation, or fancy layouts should be included only if they serve a purpose. • Start training students as freshmen. • tart with application package that are ea y to use and have wide applicabil ity (for examp le, Excel or Quattro). • Word processing (with graphic ' for drawing , equations and data) is more impOitant than you think. • The les ' oph i ticated the tudent, the more ophi ticat d th u r interface. • Oraphicaluser interfaces (OU ls) and protected operating systems are essential. • It i impo 'ible to revise the entire physics curriculum in one year. Focll your energy both in tenns of funding and curricular development. • Faculty offices must have access to the same tools that the students have in the computer labs and classrooms. • Make the technology ea y to u e in th lecture hall. • Do not underestimate the time required for adm ini tration. • Do not skimp on the initial hardware-it is not your primary co 't' Curricular development, training, faeilitie: and y tem administration are major long-t nTI co t . • The 'three- to four-year lifetime" quoted in the literature for hardware and oftware is too short. If the paradigm shift was worth doing the software and curricular material wi ll hang arollnd for years.

Building intuition Since students have different skills and career goals, physics instruction at an undergraduate liberal-arts college must be flexible. Some students write well; other students have good graphic-design skills; and other students have mathematical ability. Most students in an introductory phys~cs c~ass will not major in physics, and many will not major III SCIence. Computational physics, however, has broad appeal, since it is an effective way to develop problem-solving skills and to become computer-literate. It combines the respectability of

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physics with the appeal of current technology and can provide the foundation for computer use throughout the curriculum. Students perceive that they are not well educated without a good understanding of a computer's power and its limitations and are attracted to courses with a strong computer component. Learning to design a Hypertext Markup Language (HTML) document that communicates an idea can be part of the educational process; so can downloading information via the World Wide Web, FTP-inghomework, getting help from Computer Services, and e-mailing other students or the instructor. Although computers supplement lectures in almost all our physics courses, formal training in the use of computers begins in earnest in the calculus and non-calculus introductory sequence. Commercial computer applications (such as Quattro, Netscape Navigator, and Word) together with selected simulations (such as Electric Field Hockey, Logal Optics, and CUPS; see CIP 11: 1, 1997, p. 49) are used in almost all laboratories. Some students need considerable oneon-one instruction during their first laboratory encounter with a computer, whereas other students are ready to work independently. Davidson's introductory laboratories are ideal for this diverse population, since our labs are small (16 students maximum), long (3 h), and taught by the faculty member teaching the regular lecture (not a graduate student). Each laboratory bench is equipped with a Pentium-class networked computer and a digital data-acquisition system. Class syllabi, homework, and handouts have been rewritten in HTML and can be viewed on any networked campus computer. Many laboratories currently require students to complete a pre-laboratory before beginning an experiment. These prelabs usually require that students perform some analytical exercise related to the weekly experiment. The intent of the pre-lab is to help students to make the connection between the real world they are about to measure and the theory presented in lecture. Completion ofthe laboratories requires basic computer literacy, including a working knowledge ofthe Internet, browsers, spreadsheets, image analysis, and selected simulations. Experience has shown that former students continue to drop by the Physics Department to use the computer tools even after they have declared majors in other fields of study. Furthermore, the same commercial applications used in physics are used throughout the college so that students feel that the laboratory builds and adds to the knowledge base that they will need in their English, history, math, and sociology courses. Davidson College does not require that students purchase computers; however, 75% of entering students have computers in their dorm rooms, and the college maintains numerous computer clusters throughout the campus, including a 24-h-accessible cluster in the basement ofthe freshman dormitory. Many colleges and universities throughout the United States have similarly high numbers of computers. Access is no longer a significant barrier to the use of computer technology in teaching. Use of a wide variety of commercial, robust, state-of-theart tools builds a sense of confidence in the technology. It also builds intuition. Students who have been unable to execute a laboratory analysis on a spreadsheet because B3 has been

interpreted as a string rather than as a cell-and who have had internal representations explained to them by a sympathetic faculty member rather than being told to add a plus sign to the formula to make it work-are better prepared to understand data types when they encounter a high-level programming language. They have been there before. Students who have worked with a broad range of programs, albeit at an introductory level, have an appreciation for what is required and are ready to begin exploring computation in a systematic manner early in their undergraduate careers. At Davidson, we have decided that training in computational physics is most effective at the freshman and sophomore levels, and we have introduced new courses to provide this instruction. Math Methods, Py 201, covers traditional topics such as vector operators and linear algebra using a symbolic-algebra package, Mathematica. Class time is devoted to Mathematica syntax, and the program is then used as a lecture aid and to distribute class notes and examples. Students are encouraged to use it to check analytical solutions to integrals, solve ordinary differential equations using built-in numerical operators, sum large numbers of terms in a series to check for convergence, and make graphs and vector plots. Since Mathematica often returns odd results such as complex exponentials or large polynomials and students are unfamiliar with error and confluent hypergeometric functions, checking a homework solution is often nontrivial. Mathematica programming is not, however, a focus of the course, and few students master the intricacies of Mathematica's function-programming style. We believe, however, that a deeper understanding of computer strengths and limitations is important, and a second lower-division course, Py 200, that does emphasize programming using examples from throughout the sciences has been added to the curriculum. Students are then free to use-or not to use-computer tools in their upper-level courses.

Finding appropriate uses of the World Wide Web continues to challenge the education community.

Computational-physics course Computational Physics, Py 200, emphasizes simulation and modeling using a compiled language. We have chosen Pascal as our programming language, since it tends to reduce errors by enforcing strong type checking and program structure yet is rich enough in modem data structures to provide an easy transition to C and C++. We have adopted Borland Delphi as our programming environment and have developed a library of Delphi components, called Science Tools, that contains graphs, numerical methods, and input/output fields for floating-point numbers. Object-oriented programming is introduced from the beginning as a way to deal with the complexities of the Microsoft Windows operating system. Delphi allows students to build an application quickly while avoiding the syntactic side of the Windows API. Students begin an exercise by

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Figure 1. User inteiface for afinal project in the Computational Physics course constructed using Borland Delphi and Davidson College Science Tools components. designing and drawing a graphical user interface (OUr) containing buttons, menus, and graphs using an interface similar to a paint program. Clicking on any component that has been drawn in the our reveals properties such as window size, color, or caption in a separate inspector window. Doubleclicking on a control, such as a button, creates a small method (or procedure) that will respond to the user's mouse action at run time. In order to obtain a functioning Windows program, the student adds the appropriate code between the "begin" and "end" statements provided by Delphi and clicks the compile button. An example of a student program is shown in Fig. 1. Students are generally pleased at the ease with which they can create programs that have the same look and feel as the commercial programs that they have run in other classes. Teaching students using a rapid-application-development tool such as Delphi requires a change in pedagogy. Students are uninterested in watching an instructor mouse his or her way through a program. Even simple actions can produce multiple effects in separate windows that can be incomprehensible without an active-learner approach that requires student participation. A computer lab with one student per computer, a network, and high-resolution video projection are essential equipment for teaching such a computational-physics course. During the first few weeks of class, students sit at their computers and build user interfaces for simple programs, such as solving the quadratic equation or converting between Cartesian and polar coordinates, by closely following the instructor. The amount of traditional material covered (that is, numerical algorithms and syntax) is reduced, since the class is periodically stopped as the instructor walks about the room to ensure that everyone is caught up . Peer instruction through student-student consultation is encouraged. Problemsolving strategies (for example, how to anticipate and avoid taking the square root ofa negative number) are solicited from the class. Class often ends with an incomplete or "buggy" program that must be improved for the next period. Class notes are posted on the World Wide Web, and e-mail is used extensively to communicate hints and schedule changes.

After approximately one month of instruction, the building of user interfaces becomes a routine exercise, and prebuilt project shells can be downloaded at the beginning of the class. Class time is now spent discussing algorithms such as Euler, Verlet, and RK4 and adding them to existing code so that their effect on the solution can be observed. The aim at this point is to build an understanding of the interaction between the mathematics, physics, Pascal code, and the end user. Interesting student solutions to previous biweekly assignments are posted on the class Web page and used as discussion examples. The ideal assignment clarifies a student's understanding of the underlying physics as well as the algorithms. For example, the relaxation method for the solution of Poisson's equation is easily explained even to non-science students: "The value of the temperature at a point on a grid is approximately equal to the average of the temperature at the four nearest neighbors." Students quickly grasp the underlying idea of a matrix and a boundary condition as well as the problems inherent with the granularity of the grid. A contourplot component is already available in Science Tools for students to display and visualize the resulting isothermals. Questions about how to determine when we have arrived at a solution lead to a discussion of computation of error. This problem-solving approach is not ad hoc; it is used to build intuition and interest and to enable students to explore real scientific problems early in the undergraduate program. A similar approach was pioneered by the M.U.P.P.E.T. team at the University of Maryland and can, in fact, lead to undergraduate research as defined by Dwight Neuenschwander. 4 ,5 Many computational-physics students are concurrently enrolled in a second-semester introductory-physics course in which they study and measure equipotential lines on carbon paper painted with silver conductors. Other students are, or will be, enrolled in mathematics courses that cover linear algebra or numerical analysis. Their experience with programming has set the stage for the formal training that is offered in other courses, while their formal training in other courses often sets the stage for interesting computational projects. In order to complete the computational-physics course, students are required to choose and program a final project. Abstracts for the intended project are due after midterm, and

What is WebPhysics? WcbPhysic is a collaborative effort that wa e. tabl i hed in 1995 to promote the design, distribution tc ting, and sharing of Web-based curricular material. WcbPhy ic ha ince grown to even cro s-linked ite . It i a flexible, low-budget outlet for malI-volume, high-quality, HTML-ba cd curricular material. The project regularly offer curricu lum-development work hops at winter and . ummer meetings of the American Association of Physic Teacher. Information about the WebPhy ic project may be obtained frOI11 http://webphy ic

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Figure 2. Ryan Conaster displays his student poster. fonnal instruction ends two weeks before the end of tenn. Students are, however, required to sign up for a minimum of two faculty-student project consultations. Projects typically reflect the student's interests and chosen field of study. This past year students programmed natural selection of predator/prey, forest-fire spread using a percolation model, a threelevel laser system, investment portfolio management, fractal growth, and the ubiquitous N-body gravitational system. Students are more likely to be overly ambitious than timid in their choice of topic. These projects are, after all, a means of self-expression, and students feel empowered by this unexpected freedom in an introductory class. As a final incentive to do good work, on the last day of class, final projects are presented as poster papers in a department-wide student research symposium. Each computational-physics student is assigned a computer in the introductory laboratory and is required to prepare a poster with the usual title, abstract, theory, and sample output as shown in Fig. 2. Physics majors in upper-division laboratory courses and independent-study students also present their favorite experiment, often with a demonstration, on surrounding lab benches. This fonnat gives freshmen an excellent opportunity to meet upper-level students and learn about the physics major. Refreshments, campuswide announcements, and a friendly invitation to a student's roommate or friend ensure a good turnout. Everyone likes to look good in public, and students respond by producing very professional work. Anecdotal evidence suggests that this approach has helped to attract physics majors who would have been tempted by other fields of study.

on the Web to encourage interaction. Physics students are given an account on the department's server upon declaration of their major. Besides providing free laser printing and a large amount of disk space, the departmental account can be used to publish a personal home page. An evening Society of Physics Students meeting to design and build home pages is always a popular event. Students quickly learn that publishing on the Internet requires careful attention to detail. Presentations must be rethought to make effective use of hyperlinks. Graphics and layout become important, and clear writing is essential. Students are encouraged to learn electronic-publishing skills from each other, and, since students are often more knowledgeable than faculty, an interesting dynamic results from the reversal of traditional professor/student roles. The current junior laboratory instructor, Dr. Robert Cline, requires that laboratory reports be presented orally and posted to the home pages as shown in Fig. 3. A recent reviewer of a Davidson student winner for the 1996 Computers in Physics software awards said, "Submitting reports by way of the Web allows students unprecedented ability to include photos, color graphs, extensive hyperlinked footnotes, and animations. This new fonn of electronic delivery of scientific data will be very important, and this student entry is an excellent example of what is to come."6

A Study of the Hyperfine Structure of Rubidium conducted by


Abstract : The splitting ofenergy levels in the ntbidium atom is a result of the refalivislic and magnetic interactions related to angular momenta in the olOm. / ls a result of these interactions, the 5p energy level is split into the 5Plb and the 5pl/1 sublevels. This is /mown as the fine stmcture afthe atolll. Further splitting afthe 5s and the 5p'l7 /mown as the hyperfine stmcture. 'l1 also results. The splitting ofthese levels can be visualized using an oscilloscope. Both the absorption and emission spectra can be generated using a Lamb Dip apparatlls equipped with a diode laser. Upon the investigation ofthis splitting. the /i"equency difference between each level in the energy level diagram con be calculated along with the widths ofthe Doppler broadened peaks shown on the spectra. Click here to continue.

Advanced work Visualization may be the best beginning to building physical intuition, but writing is the best ending. Laboratories, independent-study projects, and student theses are always written with the aid of a word processor and are often posted

Figure 3. First page of ajunior lab report posted on the World Wide Web from a student's home page.

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Students wishing to continue training in computational physics often enroll in independent study/research courses. Many of these students develop exceptionally strong skills and have published their programs. The physics-Web-server pages on which students describe their research projects have gotten many "hits." Research groups-usually graduate students-download files and send e-mail to the authors, thereby providing the undergraduate students with a sense of belonging to a larger community. Search engines such as Lycos or Yahoo are democratic; keywords such as "Paul Trap" are as likely to tum up a Davidson honors thesis as a research paper at a majoruniversity.7,8 And, of course, it is the quality of the work and not the credentials of the author that matter. Adding new courses at the introductory level required us to change the physics graduation requirement. Davidson College academic regulations allow a department to specify up to 10 courses for the fulfillment of the major. An additional 12 courses are required by the college to fulfill distribution requirements in the fine arts, language, social sciences, and humanities. Since many more physics majors are continuing their studies in engineering, medicine, imaging, business, or computer science than in physics graduate school, it made little sense to demand that all students complete the traditional second semester of mechanics, electricity and magnetism, and quantum mechanics. These courses are no longer required to fulfill the major. They are offered, however, and students wishing to 'Pursue a traditional graduate-school track in physics invariably take them as electives. Students with different career goals are free to choose other courses. Our hope is that the computer-rich curriculum we have provided has given these students a better awareness of how physics fits into our technological society and how physicists actually work.

World Wide Web Finding appropriate uses of the World Wide Web continues to challenge the education community. Many Internet sites, including the Davidson WebPhysics site (see "What Is WebPhysics?" on p. 438), distribute media-rich curricular material. 9- 11 The Web provides a new channel for old information: homework assignments, test schedules, syllabi, and so forth. Good sites provide indexing and content that is unavailable through other technologies. The worst sites are merely transcriptions of a textbook or of faculty notes. In fairness to the World Wide Web, it has until recently required heroic effort to move beyond text and images. But that has changed. Recent browsers from Netscape and Microsoft support interactive Web pages through the use ofJava and J avaScript. High-speed networks are becoming available throughout many campuses, including dormitories, and most college students can now access the Web from home. The World Wide Web now offers

Visualization may be the best beginning to buildingphysical intuition, but writing is the best ending.

• -



Collision Examples Using Animator Be lrllre the SlIffII/ation hasfinisMd Wading before you begIn

Click on the problem nwnber to initialize the simulation at the top of the pasc. Then answer the question after you have nut the simulatIon. Yau may start and stop the simulations using the buuons on the bottom of the animation Click and drag inside the animation to read the coordinates • Pro i m I What is the ratio of the two masses? •



The red and the black balls have the same mass. Does the collision shown obey the laws of classical dynamics? • I'rol-Icm' Is Ibis coUlsion elastic? Is momentum conserved if the red and the black baIJs have the same mass.

Figure 4. Java animator applet currently being testedfor use in Web-based curricular material. an opportunity to develop and publish interactive curricular material that does not tie up class time, is available around the clock, and fosters collaborative exploratory learning experiences across college boundaries. This use of the Web constitutes a new pedagogical tool. A good example of an interactive technology that brings added benefit is the set of small scriptable Java applets-we call them Physlets-being developed at Davidson College and shown in Fig. 4. These platform-independent programs are flexible and well suited for instructional purposes such as the presentation of problems. They can be embedded directly into HTML documents and can interact with the user by employing a scripting language such as JavaScript. For example, the 75-kbyte Animator Physlet we have written is used to move a shape inside the applet's bounding box along a predefined path, [x(t), yet)]. Adding this Physlet to an HTML page is no different from adding an image. Creating a 10pixel-diameter ball that follows a parabolic trajectory requires the following script: Animator.addShape(1 0,"-1 0+6*t","-5+8*t-4.9t*t").

Although animation can certainly be accomplished using more sophisticated programs such as Interactive Physics or possibly even QuickTime movies, two or three lines of script connected to another problem can add additional shapes to the applet or change the trajectory into a sinusoidal oscillation. A VCR-like set of control buttons allows students to start, stop, and step the animation. The mouse can be used to read scaled coordinates. Presenting visual rather than textual representation of information necessary to do a problem changes the problemsolving strategy. It also allows for different types of questions. What is the acceleration of the red ball? Are the laws of

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classical dynamics observed in the collision between the red and the blue balls? Which planet in the animation does not obey Kepler's laws? In problems such as these, the student must observe the motion and make appropriate measurements to obtain a solution. Physlet-based problems-along with video-based problems-are now being distributed as part of a Web-based physics homework system at North Carolina State University. We believe that video and animation can significantly influence students' visualization of some types of physics and that mastery of these types of problems could significantly improve their understanding of physics concepts. It is now possible to author whole courses and distribute them on the Web. A good example is another WebPhysics project, Cockpit Physics, at the United States Air Force Academy. 12 (Cockpit Physics material is mirrored on the Indiana University/Purdue University Indianapolis WebPhysics server.) This project was conceived as a way to motivate USAF Academy cadets to become more interested in basic physics. It seeks to develop and deliver an entire course using Web technology. It is a complete set of interactive lessons with server-side logic for the tracking, evaluation, and recording of student responses. At present, a set of32 introductory physics lessons have been developed and are being delivered as HTML multimedia documents to cadets. The course has a substantial hands-on component, including standard table-top laboratory exercises. The delivery of the material, however, is entirely HTML-based. The material guides students along a branching path, which allows them to explore different facets of the day's subject at their own pace. The lessons include simple illustrations of the assigned reading and interactive screens in which the students may vary parameters in an equation under study to observe the resulting effects. The student may even be directed through an intricate lab in which the computer automatically collects the data. The instructor, who will be available to answer questions not covered in the computer lesson or to provide supplemental material, closely monitors this interaction. Effective teaching in a Web-based classroom requires techniques and skills ofthe instructor similar to the computational-physics course described earlier. Proper class management and use of real-time feedback about student progress is crucial to the success of such a learning environment. It is difficult to predict the evolutionary or possibly even revolutionary changes that computers and the delivery of high-quality interactive instructional resources will have on the curriculum during the next decade. Our experience, however, is that the technology is unlikely to eliminate or even reduce the need for faculty involvement in the learning process. Even if all the resources for a course were presented online and on demand by the finest teachers and even if natural-language evaluation of student understanding were possible, students would need the kind of guidance and interaction that is best organized around an academic community. Peer instruction, student poster sessions, and student authoring are unlikely to occur without active faculty involvement. We have found that providing students with a computerrich environment and the training to utilize this environment early in the undergraduate curriculum encourages these ac-

tivities. The flow of information throughout the campus is expanded, and the types of activities that the students can perform are enhanced. The challenge in effective use of computers was and will be to create content that addresses their misconceptions and to mentor students in order to trigger a lifelong interest in learning.


Technology is unlikely to eliminate or even reduce the need for faculty involvement in the learning process.

The author would like to thank the Physics Education Group at North Carolina State University and in particular Aaron Titus for many helpful suggestions and for testing the Java applets. It is also a pleasure to thank Laurence S. Cain for commenting on this manuscript and for providing departmental support for the development of the Computational Physics course. This work has been funded, in part, by sabbatical support from the Department of Energy through the Oak Ridge Institute for Science Education and by the Triangle Universities Nuclear Laboratory at Duke University.

References 1. The assertion that computation is co-equal with theory and experiment can be found on p. 2 of Monte Carlo Methods in Condensed Matter Physics, edited by Kurt Binder (Springer-Verlag, Berlin, 1992). 2. R. K. Thornton and D. R. Sokoloff, Am. 1. Phys. 58, 856-870 (1990). 3. E. F. Redish, J. M. Saul, and R. N. Steinberg, Am. 1. Phys. 65, 45 (1997). 4. E. F. Redish and J. M. Wilson, Am. J. Phys. 61, 222 (1993). 5. D. E. Neuenschwander, Newsletter of the Forum on Education of the American Physical Society, Spring 1996. 6. D. Donnelly, Comput. Phys. 10,532-541 (1996). 7. Susan Fischer and Wolfgang Christian, Comput. Phys. 10,123 (1996). 8. George A. Antonelli and Wolfgang Christian, Comput. Phys. 10,243 (1996). 9. W. Christian, E. T. Patterson, and G. Novak, "WebPhysics: Delivering Curricular Material Using the World Wide Web," in Proceedings of the International Conference on Physics in Undergraduate Education (ICUPE), College Park, Maryland, 31 July-3 August 1996, edited by E. F. Redish and 1. Rigden (American Institute of Physics, Woodbury, NY, 1997). 10. G. D. Bothun and S. D. Kevan, Comput. Phys. 10, 318-324 (1996). 11. A. B. Fraser, Syllabus 10 (4),18-20 (1996). 12. E. T. Patterson and G. Novak, "World Wide Web Technology As a New Teaching and Learning Environment," to be published in Int. 1. of Modem Physics C.

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