MathSoft: Cambridge, MA, 1996; free via ftp from www.mathsoft.com.

The movement to provide computer-based applications in chemistry has come to focus on three main areas: software aimed at specific applications (drawing, simulation, data analysis, etc.), multimedia applications designed to assist in the presentation of conceptual information, and packages to be used in conjunction with a particular textbook at a specific point in the chemistry curriculum. The result is a situation where no single software package devoted to problem solving can be used across a large segment of the curriculum. Adoption of World Wide Web (WWW) technology by a manufacturer of mathematical software, however, has produced software that provides an attractive means of providing a problem-solving resource to students in courses from freshman through senior level.

MathBrowser, a freeware web-enabled derivative of the MathCad mathematical software (MathSoft Inc., Cambridge, MA), is designed to reconcile the problem of how to distribute mathematically rich information over the WWW and to maintain interactivity for the end user. MathSoft Inc. has done this by adding support for hypertext transfer protocol (HTTP) commands (to request and receive documents over the Web), version 1.0 of the hypertext markup language (HTML), and image filters for GIF and JPEG formats (for display of web pages) to a nearly complete version of MathCad 5.0. The result is a robust rudimentary Web browser that can download, display, and then evaluate both HTML and MathCad files (through version 5.0). Rather than compete with Internet Explorer, Navigator, Mosaic, and other Web browsers, MathBrowser's primary function is to retrieve MathCad documents from a suitably configured Web server. Once retrieved, the MathCad documents serve as templates where users can modify values and observe how changes in variables change the final answer to a problem.

A partial list of the functions retained by MathBrowser includes solving simultaneous equations; contour surface and polar plots; integrals; derivatives; matrices; summation; support for Fourier and inverse Fourier transform; imaginary numbers; and dimensional analysis. MathBrowser does not support the Maple symbolic processor found in the commercial versions of MathCad or allow documents to be saved to any type of disk, so it cannot be used for authoring. This must be done with a licensed copy of MathCad 3.1­5.0. Though MathBrowser can handle almost any type of calculation desired, the software hides this from the user through its graphical interface where variables and equations are represented on the screen exactly as they would appear on a piece of paper.

As can be seen in Figure 1, no programming-like environment is used. Isolation from coding expressions is further enhanced for users of MathBrowser, since the template MathCad document has been authored off-line by someone else "more familiar" with MathCad.

MathBrowser requires a 386 or better CPU, Windows 3.1 or higher (with the Win32s libraries installed for Windows 3.1, included in Windows 95 and higher), 8 Meg RAM, TCP/IP network connection, VGA video output, and a mouse. A complete installation of MathBrowser requires 1.4 Meg disk space for the program and approximately 8 Meg for the Win32s libraries (if not already installed). At this time, MathBrowser is supported only on the PC platform. MathCad files for use by MathBrowser may be placed on any computer running WWW server software. The WWW server configuration file does need to be edited so that server software properly responds to requests for MathCad files. Current information on hardware/software requirements for MathBrowser and on how to configure most WWW server software to support MathCad documents may be found at the MathSoft Inc. MathBrowser home page (1).

As users of MathCad would expect, MathBrowser's calculation speed is excellent and changes made while in the automatic calculation mode are reflected as soon as the mouse is clicked away from the variable being edited. MathCad documents concerned with introductory-level chemistry problems show no appreciable calculation delays when running on a 486DX/33. (I did not have a system on which to test performance when only the minimum hardware specs were met.) Chemistry topics requiring more advanced calculations may experience some delay on a 486DX/33 system, but these are all but eliminated with increasing CPU power. For many older systems, performance appears to be more limited by the videocard and ISA than by the processor itself. File transfer times for MathCad documents over 10 Mbps local area networks are very reasonable, and use from home with a 14,400 bps modem-equipped 486DX/50MHz system has not been a problem under either Windows 3.1 or Windows 95. Running MathBrowser in the manual calculation mode will further speed up download and display, allowing the user to view the document before initiating calculation with a single keystroke. Printing speed is determined more by the attached printer than by MathBrowser-dot matrix printers obviously suffer in comparison to laser printers. One printing problem for beginning students is that a document authored in MathCad to accommodate page breaks for one printer may occasionally not retain those page breaks when viewed and printed under MathBrowser using a different printer. Users can overcome this problem by inserting their own page breaks into the document, which will force repagination before printing (the effect of page breaks can be checked using the "Print Preview" command). When viewing HTML documents, however, page breaks become less problematic than overall page layout, since MathBrowser only supports revision 1 of the HTML specification. This is most obvious in MathBrowser's inability to interpret tables in HTML. Rather than appearing in a tabular layout, table items are listed in a left-justified format with minimal spacing between them. Taken in the context of viewing HTML documents, this is an acceptable limitation; but when trying to provide a visually compact list of available MathCad files, the lack of table support proves to be a hindrance. Support of the HTTP protocol is solid, although MathBrowser does not support the double/single dot directory notation. Use of <a href="../../mcad/test.mcd"> syntax will result in no action on MathBrowser's part, whereas both <a href="/server/docs/mcad/test.mcd"> and <a href="http://www.xxx.edu/server/docs/mcad/test.mcd "> will cause a request for text.mcd to be issued. Over the last year I have been evaluating MathBrowser's ability in a student lab of twenty-four 486DX/33 computers. At no time has MathBrowser crashed or caused any conflicts with other software on the same computer, or had any type of negative impact on the Web server hosting the MathCad documents.

The inclusion of unit capabilities in MathBrowser is particularly important when trying to emphasize units in chemistry problems. MathBrowser supports any of MathCad's units and unit systems (SI, CGS, or US customary). Once units are associated with a particular variable, MathBrowser will evaluate them as it performs the numerical calculation(s) and display the appropriate result.

An example of this is provided in Figure 2. In order to determine the frequency for a particular wavelength, the wavelength variable is defined and the unit meter (m) is associated with it. The speed of light, c, has been defined previously with units of meters/second (m/s). When the result of the calculation is displayed, Hz units are automatically associated with the outcome based on analysis of the units involved.

Calculating the energy of a photon is shown in Figure 3. The frequency variable is defined and Hz are associated as the units. Planck's constant, h, would then be defined and have Js as the units (definition of h is shown in Fig. 2). When calculating the energy, MathBrowser will automatically report the result in J after canceling out s. If desired, h could be defined in terms of cal, kcal, Btu, or erg, the end result always having units of energy. Alternatively, if the units in the answer are changed, MathBrowser will automatically supply the proper conversion factor (Fig. 3). Improper use of units will cause the answer to be displayed with the units expressed in terms of all units present in the original variable definitions. If a mistake were made in the above example and wavelength (defined in m) had been inserted for frequency, the answer would be displayed with units of "m s J" instead of only the energy units used in the definition of Planck's constant: a clear indication of a mistake.

An instructor could identify the expected unit(s) in a template, and suggest that students check their results against this to help reinforce the utility of unit analysis in problem solving.

MathBrowser does include a "mole" unit, but cannot evaluate it because it has only a numerical definition. In cases where unit checking is not desired but unit identification is, MathBrowser supports a "dimensionless" form of any unit. Dimensionless units, essentially name tags, may be inserted and will be carried through the calculation, but no effort will be made to format the answer to the correct unit(s).

Chemistry problems require differing levels of mathematical proficiency at different times in the curriculum. For students well versed in mathematics, the manipulations required may not pose a challenge, and learning the chemistry can begin quickly. For students less comfortable with math, the chemistry is often obscured by the struggle to find the proper manipulation or by anxiety about whether the calculation was performed correctly. While written examples provided in the textbook or by the instructor help students to gain confidence in their problem-solving ability, the number of available examples depends on the course text and the instructor's determination. An interactive problem-solving system that allows students to insert data of their choosing into a properly constructed template provides an infinite number of examples for learning. Such a system could even be used by students to "check" the answers they calculated beforehand against what comes out from the template. Since MathBrowser allows only local editing of the template document and the content of the original template is never altered on the server, the student may reload it as many times as necessary.

MathBrowser is an excellent piece of software to consider for establishing a system whereby students can practice guided problem-solving and answer as many "what if" questions as desired. For two semesters I have used MathBrowser as a resource for my general chemistry courses and have found that, since students need not learn the syntax of MathCad in order to use documents viewed with MathBrowser, it is possible to train students with no previous Web browser experience in approximately 30 minutes. For students already familiar with the Web, this time can be reduced. The ability to reload the original document at any time is a tremendous help for putting at ease students worried about messing up the template or computer. Once they are satisfied that they can't disrupt anything, they will begin to quickly pick up the ease of inserting new values into the template and then looking at the new answer. If some type of independent work is expected, students may open the blank "scratchpad" window and try out their own ideas (they just can't save them) based on expressions copied from the displayed document, or insert original ones (Fig. 3). To save time for students, a page of expressions may be loaded and then copied and pasted into the scratchpad window for use. The graphical function bar to the left of the screen allows students to quickly modify existing equations or to create their own.

I hesitate comparing MathBrowser to the growing body of interactive chemistry tutorial software available for both the PC and Macintosh platforms because I do not see them as competing technologies. A qualitative survey of the available tutorials suggests that they are primarily oriented to the large general chemistry market and are less available for upper-level courses. Their attractive multimedia approach is arguably more useful for illustrating certain topics, but the real purpose for using MathBrowser, in my opinion, is to provide a readily accessible means of practicing problem-solving skills and providing summary information on topics with a strong math component. In this respect, tutorial software and MathBrowser are complementary technologies, not competing ones. MathBrowser has three advantages over tutorials. First, it is a permanently installed application resident on the hard disk in student computer labs and requires only that the network connection to the server be active. It does not require a CD-ROM drive or sound card to be fully utilized. Second, it can be used in a textbook-independent manner, making it immune to changes in course materials. Third, it is applicable across the entire chemistry curriculum and lets students quickly refer back to earlier documents to refresh their memories. For institutions where the upper-level courses have already incorporated or may soon incorporate a full version of MathCad, using MathBrowser in introductory courses provides a natural transition to the commercial product with no additional cost.

While MathBrowser may not have all the functionality of its commercial counterparts, it is an excellent free resource to begin exploring MathCad and the use of math-enabled documents over the web at any point in the curriculum. Both resident and commuter students can benefit from its availability, with the information supplied being limited only by the instructor. Already there is a body of literature with specific applications of MathCad in chemistry (2­15). As more MathCad-based chemistry-related resources become available in print and on the Internet, the application of MathBrowser to the curriculum will become easier as authoring in MathCad becomes less important for those interested in utilizing MathBrowser.

Literature Cited

1. http://www.mathsoft.com/browser/.

2. Zdravkovski, Z. J. Chem Educ. 1991, 68, A95.

3. Rioux, F. J. Chem. Educ. 1992, 69, A240.

4. Zdravkovski, A. J. Chem. Educ. 1992, 69, A242.

5. Alonso, V.; Camacho, L. J. Chem. Educ. 1993, 70, A312.

6. Brizuela, G. P.; Juan, A. J. Chem. Educ. 1993, 70, A256.

7. Turner, D. E. J. Chem. Educ. 1993, 70, A185.

8. Ramachandran, B. J. Chem. Educ. 1995, 72, 1082.

9. Young, S. H.; Madura, J. D.; Weizbicki, A. J. Chem. Educ. 1995, 72, 609.

10. Zielinski, T. J. J. Chem. Educ. 1995, 72, 631.

11. Holler, F. J. MathCad Applications for Analytical Chemistry; Saunders: Fort Worth, TX, 1994.

12. Noggle, J. H. Physical Chemistry Using MathCad; Pike Creek: Newark, DE, 1997.

13. Rioux, F. JCE Software 1994, 1D(2).

14. Rioux, F. JCE Software 1995, 3D(1).

15. Rioux, F. JCE Software 1997, 9C(1), in press.