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JCE SymMath has evolved from a collection of Mathcad documents that was initiated in 1996 under the auspices of the New Traditions project sponsored by NSF-DUE (1). Documents were shared with colleagues through the Web site (accessed Nov 2004). In 1998 the JCE feature column, Mathcad in the Chemistry Curriculum was created, providing a mechanism for peer review and publication of Mathcad documents in this Journal. The peer-reviewed documents became available through two sites: the Mathcad collection site and the JCE Online site. Succinct descriptions (summaries) of Mathcad documents were published in print in the Information, Textbooks, Media, Resources section of the Journal. This overlap of availability provided the widest dissemination route for furthering the goals of the New Traditions project.

Featured Documents
	Learning Molecular Geometry and Symmetry through Quantum Computations and Mathcad Exercises
	Using a Computer to Help Understand How Symmetry Principles Reduce Calculation
	An Introduction to Statistical Mechanics

In January 2003, through support from NSF’s National Science Digital Library project (2), the scope of the collection was increased to include documents created using the symbolic mathematics programs Mathematica, Maple, and MATLAB; in January 2004 the first set of Mathematica translations of Mathcad documents appeared in the renamed feature column, JCE SymMath (3). The joint dissemination of documents at the SymMath site and in the Journal continued throughout 2004. This was made possible through permission from the Journal.

Peer Review and Open Review

This column marks another transition for the SymMath collection. Now all peer-reviewed symbolic mathematics documents will be permanently integrated into the JCE DLib SymMath collection and will be available only through the Journal of Chemical Education (accessed Nov 2004). This peer-reviewed subset that will be available only through JCE DLib currently comprises approximately 40% of the entire SymMath collection. The balance of the collection, documents that fall under the open-review purview of the Journal, will remain available to everyone at the open-review Web site. These open-review documents are copyrighted by their authors and are available to any teacher for use in classes, but they may not be commercialized in any publication without the author’s permission. These changes in the SymMath, (previously Mathcad) collection prompt a discussion of copyright and fair use of both the open-review and the JCE peer-reviewed SymMath materials.

JCE Copyright Policy

The standard policy for any article published in print by JCE is that a subscriber may make one copy for each student in a class and distribute that copy to students in the teacher’s classroom. This same concept applies to distribution of SymMath documents. However, the notions of “distribute” and “classroom” are less clear in the digital world, where some methods of distributing to a class can mean distributing to everyone in the world who has access to the Web. Therefore clarification is needed.

To obtain the fully interactive SymMath document the teacher must have one of two types of JCE subscription: a personal subscription or an IP-number institutional subscription. A campus IP-number subscription provides students as well as faculty with access to any SymMath document—indeed anything at JCE Online—for their personal use and study. The sections that follow are intended to clarify what constitutes fair use of SymMath materials obtained from the Journal Web site or from the open-review Web site.

Fair Use Criteria

Several criteria must be met to satisfy the definition of fair use of copyrighted materials (4).

• The character of use must be educational and non-profit.
• It must be necessary to use the materials in their complete native form to meet the educational purpose of the materials.
• Use must be limited to the fraction of a copyrighted document that is needed to achieve the educational goal.
• The user must consider the effect on the market value of the materials used.

The Journal clearly enables use for educational purposes by granting teachers the right to provide one copy of an instructional document—the whole document—to each student in a class. (This statement appears on the first page of every SymMath document just below the title and author.)

The issue of market value is met by requiring that the faculty user and his/her students have access to the materials through subscription to the Journal in person or through a campus IP-number subscription. It also means, however, that it is illegal and unethical to make available to everyone on the Web either the materials themselves or a username and password that gives free access to the materials.

Course Web Sites

Sometimes it may be more convenient for teachers to distribute course materials through a course Web site. By the nature of the WWW, this aspect of fair use of teaching materials disseminated by the Journal is somewhat complicated. The copyright statement for SymMath documents clearly states that dissemination is permitted through a class intranet, where students must be registered in a course to have access, provided that permission has been obtained from the Journal. Such requests are routinely granted to institutional subscribers and will also be routinely granted to individual subscribers. A request can be as simple as sending an email to JCE that lists all documents to be used, the course number, and title in which they will be used, the names of the institution and department, and the name of the person requesting use. Given that the copyrighted portion of the SymMath collection consists of 40 extensive documents that span the chemistry curriculum and that each of these would require serious work by students spanning a week or so of effort, it is not unreasonable for a list of requested templates to extend to over 15 for a single course such as physical chemistry lecture and lab.

Derivative Works

Another question of fair use is the production of derivative works based on the published templates. It is sometimes necessary to customize a template or use parts of templates that have been rearranged to meet the needs of a specific course. It is important to remember that facts cannot be copyrighted; the mathematical functions for the solutions to the simple harmonic oscillator or the equations describing oscillating chemical reactions cannot be copyrighted. It is the full document and the style of presentation in which one finds these equations that is copyrighted and governed by fair use. Thus it is possible for more than one SymMath document to exist for the same topic, each focused on a different approach and each designed to meet the needs of a different cohort of students. Such derivative works should acknowledge the previously published documents in the usual bibliographic citation method used by all scientists. This is the normal mechanism for evolution of materials and recasting of ideas for different uses and different audiences. It is expected that these derivative works would be forwarded to the Journal for peer review and possible inclusion in the collection, thus becoming available for others to consider using in their classes. Derivative works can be a valuable resource for teachers and the educational community. It is through derivative works that the diversity of needs of faculty and students can be met and the quality of published materials enhanced.

New This Month

In this column, four documents are presented. Two, written for use with Mathcad, provide undergraduate and graduate physical chemistry students with an introduction to the mathematical formalism of symmetry operations. Each document focuses on a different aspect of the topic and yet each draws on similar concepts for implementation. The third document, a Mathematica notebook, is an introduction to statistical mechanics for undergraduate students but could be used by graduate students for review. The fourth document is a translation into the Mathematica notebook format of the Mathcad template, Visualizing Particle-in-a Box Wavefunctions by Edmund Tisko (5).

Learning Molecular Geometry and Symmetry Operations

In Learning Molecular Geometry and Symmetry through Hands-on Mathcad Exercises, Franklin Chen guides students through a series of exercises that permit them to study symmetry operations such as rotation and reflection through a mirror plane. The method is based on matrix operations that students review at the beginning of the template. This is followed by applying symmetry matrix operations to water, ammonia, methane, and benzene. The mathematics used is developed along with the symmetry concepts as applied to real molecules. The difficulty of the exercises in the document increases gradually as students gain experience. This document would be suitable for use with a junior-senior physical chemistry class. The ideas behind the exercises are fundamental, giving students entry to the more mathematical basis underpinning symmetry operations. I have used this template with my students successfully toward the end of the semester after they have had time to develop Mathcad skills in homework and laboratory assignments. This document would also be useful in any course where students use group theory.

Using Symmetry Principles to Reduce Calculations

Louis Kijewski provides a detailed analysis of how to obtain the normal vibrational modes of a three-oscillator system in Using a Computer to Help Understand How Symmetry Principles Reduce Calculations. First he sets up the six equations of motion and then uses symmetry matrices to simplify the calculations. This reduces the work needed to diagonalize the equations-of-motion matrix. The approach illustrates how more complicated problems can be solved when a computer does some of the algebra, calculus, and matrix multiplication required to determine the normal modes of vibration. In the document Kijewski presents the symmetry-adapted vectors and their equations, gives the equation for obtaining the number of irreducible representations in a reducible representation, and provides the proof of great orthogonality theorem for this problem. Projection operators generate the symmetry-adapted vectors. The document concludes with details for obtaining various modes of vibration and provides animations of each mode. This document would be very useful in a group theory course for advanced undergraduates and graduate students. Embedded exercises will help students master the required techniques. References to group theory resources are also provided.

An Introduction to Statistical Mechanics

In An Introduction to Statistical Mechanics, Michelle Francl provides students with the basic tools needed to analyze the gas phase HCl/DCl IR spectrum. This Mathematica notebook expands the traditional lecture material on IR vibrational/rotational spectroscopy to include an exploration of partition functions and their role in understanding IR spectra. This notebook is designed to be used in conjunction with class notes and an IR spectrum of gas phase HCl/DCl.  It would be easy for someone to modify this notebook to suit the needs of a particular physical chemistry course. Student tasks assigned in the notebook are interesting and clearly described. The Mathematica programming is at a basic level and thus suitable for the physical chemistry audience of undergraduate junior and senior chemistry majors. Plots of distribution over states give students visual emphasis to assist learning the fine structure concepts due to rotational energy contributions to an IR spectrum. For example, students are requested to prepare a bar graph of each of the first 11 rotational states of a vibrational transition, then study how the distribution changes with temperature. Imbedded questions guide student learning and provide for efficient completion of this instructional component of a class in harmonic oscillator spectroscopy.

Literature Cited

1. Landis, C. R.; Peace, G. E., Jr.; Scharberg, M. A.; Branz, S.; Spencer, J. N.; Ricci, R. W.; Zumdahl, S. A.; Shaw, D. J. Chem. Educ. 1998, 75, 741–744.
2. JCE Editorial Staff. J. Chem. Educ. 2004, 81, 17.
3. Zielinski, Theresa Julia. J. Chem. Educ. 2004, 81, 155–158.
4. For information about fair use see this general overview or these guidelines for educational use (accessed Nov 2004).
5. Tisko, Edmund L. J. Chem. Educ. 2003, 80, 581.

About the Feature Editor
	Theresa Julia Zielinski
JCE Citation
	Zielinski, T. J. J. Chem. Educ. 2005 82 172.
Keywords
	Computer-Based Learning; Mathematics / Mathematical Methods; Physical Chemistry