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JCE SymMath: Symbolic Mathematics in Chemistry
Theresa Julia Zielinski Monmouth University West Long Branch, NJ 07764-1898
Symbolic Mathematics Engines in Teaching Chemistry A Symposium Report1 Mark Ellison Department of Chemistry, Wittenberg University, P.O. Box 720, Springfield, OH 45501;
[email protected] A panel of educators, Michelle Francl, Manfred Minimair, Mihai Scarlete, and Theresa Zielinski, discussed the use of Symbolic Mathematics Engines (SMEs) in chemical education as part of the Division of Computers in Chemistry at the ACS National Meeting in Philadelphia. The panelists, experts in the use of SMEs (including Maple, Mathcad, and Mathematica), have experience in both undergraduate and graduate teaching of applied mathematics, computer science, computational chemistry, and experimental physical chemistry. Current Status of SME Usage Maple, Mathcad, and Mathematica, popular SME programs, are powerful tools for modeling chemical systems. The software, by handling the computational details, allows students to focus on exploring the fundamental properties of the mathematical models under study. Many physical chemistry textbooks include CD-ROMs containing SME documents. Additionally, documents can be obtained at the SymMath WWW site (http://bluehawk.monmouth.edu/ ~tzielins/mathcad/). These documents, contributed by many active chemists, include a subset that are published in JCE as part of the JCE Digital Library (http://www.jce.divched.org/ JCEDLib/SymMath/). More than 100 Mathcad documents illustrating a wide variety of topics in (primarily physical) chemistry are available at present. The collection is growing to include Mathematica and Maple documents. The panelists agreed that proficiency in using computer models to understand chemistry is one of the most important skills that students can learn. When students work through the exercises, they gain a deep understanding of the topic involved. Furthermore, when students write about their experience after completing an exercise, concept retention improves. Caveats Although use of SME documents provides important benefits, the panel noted several shortcomings. First, each software program has its own syntax, and unfamiliarity can frustrate students. Second, students resist expending the effort required to learn new software. These problems are best approached by starting easy, building student confidence, and then progressing to more complicated tasks. Finally, the panel acknowledged that students could fall in to the trap of thinking, “If the computer calculated it, it must be right.” Exer-
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cises must impart to the students a realization that the quality of the results depends on both the model of the physical system and the inner workings of the software package. Thus, the use of SME exercises becomes an opportunity to discuss the details of the computation with the students. A Lively Discussion One of the first questions from the audience involved use of class projects in which students obtain data from the literature and then model the chemical system. Michelle Francl responded that she does such an activity for the kinetics of oscillating reactions. The audience wanted to know how successfully the students’ models matched those found in the literature. Francl replied that the students did not always replicate the results found in the literature. In some instances, she had to contact the author to request necessary information not included in the paper. Mihai Scarlete noted that many concepts taught in physical chemistry, such as kinetics, atomic and molecular spectroscopy, and thermodynamics, have literature data available and could be used for such a project. The audience also noted that few students pursue a career in computational chemistry and wondered why much, if any, effort should be devoted to incorporating SME into the curriculum. The panel agreed that introducing undergraduate students to computer modeling of physical systems is extremely important. The best approach is to start slow, allowing the students to build confidence by tackling small systems before moving on to more complex systems. If a student demonstrates aptitude in this area, her/his abilities should be developed. Still, all students benefit from learning to use mathematical models and especially the limits of applicability of these models. Looking to the Future The panelists agreed that many more topics in chemistry are amenable to SMEs exploration. Manfred Minimair suggested that symbolic computational tools should be taught more widely in mathematics classes and that software developers should strive to make their tools easier to use. Mihai Scarlete concurred, proposing that software developers should move toward a single computational engine rather than maintaining the current competing products. Theresa Zielinski noted the progression of the use of computers in chemistry and hopes that within 10 years nearly every course will have SMEs integrated into classroom and laboratory activities. Fi-
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JCE SymMath: Symbolic Mathematics in Chemistry nally, Michelle Francl wants to see a textbook that has SMEs embedded into the framework. This author imagines an electronic textbook in which important concepts are not just spelled out in text and equations as when simply reading the book, but rather students proceed through the text by performing interactive modeling exercises that deepen their understanding.
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Note 1. This article is based on a panel discussion on symbolic calculation in chemical education in the “Symbolic Calculation in Chemistry” symposium, sponsored by the ACS Division of Computers on Chemistry, on August 26, 2004, at the 228th ACS National Meeting.
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