When judging the appropriateness of a symbolic mathematics document one should consider the difference between a learning object and a learning asset. Learning objects are self-contained lessons with well defined outcomes as specified in their goals and objectives. Learning objects are complete and fully developed treatments of a single topic. They can stand alone and be used by students to master a topic. Assets, on the other hand, cannot stand alone. Learning assets are small items such as video clips, animations, and applets that can be used to create learning objects by embedding them into fuller presentations created by an instructor.

The SymMath DLib collection consists of learning objects. Each symbolic mathematics document presents a fully developed presentation of a topic with clearly articulated goals and objectives that focus student learning. Students interactively manipulate mathematical segments, read explanations, complete exercises, interpret plots, create animations, and complete mastery learning projects. Any SymMath document that presents a complete topic be it small or large is appropriate for the collection. The essential feature of all SymMath objects is a structure that permits students to learn through interaction with the material via exercises and reflection leading to mastery. In this column we present four new documents for use by physical chemistry instructors. Each of the new documents is short or medium in length and will permit students to accomplish clearly delineated learning objectives.

Phase Diagrams

In Computing Liquid–Vapor Phase Diagrams for Non-Ideal Binary Mixtures, Franklin Chen introduces the mathematical models that are used to describe binary mixture vapor–liquid equilibria. This document focuses on the solubility parameter theory approach to calculate the activity coefficients of non-ideal mixtures. Students prepare standard boiling point binary phase diagrams for an ideal liquid pair (toluene and benzene) and for a non-ideal liquid pair (water and propanol). van Laar’s theory is used to calculate the activity coefficients for the non-ideal liquid pair. The document contains 18 exercises that help students to master the concepts. This document would be especially interesting to faculty who teach engineers or those who emphasize phase equilibria in their courses.

Simulating Circular Birefringence and Circular Dichroism

The Circular Birefringence and Circular Dichroism (CD) Simulation Mathcad document by Zachary Brown and Ronald Starkey provides a very useful introduction to polarized light concepts that most students find difficult to understand. Through this document students can interactively study the behavior of incident light with a chiral medium. The authors introduce left and right circularly polarized light and the concept that plane polarized light is composed of equal components of right and left polarized light. This concept permits extension to the generation of elliptically polarized light. This document is more didactic in its approach than most in the SymMath collection. Students are primarily asked to manipulate graphics and interpret the diagrams in order to gain insight into CD spectroscopy. There is a mastery exercise requesting students to develop animations for the processes discussed. There is also an exploration exercise that requires students to examine the literature for uses of CD spectroscopy in biochemistry research. This document would find use in physical chemistry and biophysical chemistry courses as well as other courses where students are introduced to CD spectroscopy.

Analyzing Damped Oscillating Data

In Data Analysis (Damped Oscillations) Using the Genfit Function by R. D. Poshusta, we have a little gem of a document for introducing non-linear curve fitting to students. The document shows students how to read data into a Mathcad template. The accompanying Mathcad document, sim_dmp.mcd, permits generation of sample damped oscillating data that students can use to practice non-linear curve fitting. Students need to learn that in order to use a non-linear curve fitting procedure they must know the function representing the data and be able to examine the data to determine initial guess values for the fitting parameters. Most students do not get sufficient practice with interpreting plots and extracting key data from the plot. This document provides that practice. The author thinks that this method is general enough to work for many mathematical models. Faculty and students can generate additional data sets for damped oscillations with sim_dmp.mcd. These additional data sets for damped oscillations can help students practice the concepts and provide faculty with an assessment strategy. “Fitting Two Parameter Equations to Gas Data” by Theresa Julia Zielinski (accessed Apr 2005) is another document that treats the same subject using a different approach.

The Uncertainty Principle

The Exploring the Uncertainty Principle document by Franklin Chen presents a range of exercises and instruction to help students heighten their understanding of the uncertainty principle. The document follows the treatment found in many physical chemistry texts and thus can be used by many instructors. The activities in the document center on the use of Gaussian functions and their representation by linear combinations of particle-in-a-box wave functions to help students to develop an understanding of the meaning of σ_x and σ_p. The document permits students to discover that a Gaussian function with smaller standard deviation requires more eigenfunctions in its expansion than a Gaussian with a larger standard deviation. The exercises in the document are not overly difficult and most students would be able to complete them as one homework assignment. If students work in groups to complete this document they will have even better mastery of the topic than if they did the work alone.