MILTON: A Mathematica Package and Interface Applet for Freshman and Sophomore Level Courses

Bill Waller

University of Houston-Downtown
One Main Street
Houston, Texas, 77002

Grant Number: DUE: 9552147

The purpose of this poster is demonstrate some of the features and uses of the software "system" called MILTON (an acronym loosely derived from "Mathematica Interactive Library Toolbar"). MILTON was developed by the presenters in support of the ILI grant entitled "A Laboratory Classroom to Support an Alternative Technology-Based Mathematics Curriculum." The purpose of this grant was to equip (or upgrade) two laboratory classrooms of PCs to support an alternative technology-based mathematics curriculum that any technical major could pursue through at least the first two years. A poster illustrating the overall nature and goals of the grant was presented at last year's session. For this poster, however, as the grant nears its completion, we have chosen to focus on one of the most promising aspects of the project: the success we have achieved in integrating the use of Mathematica into lower-division courses. We feel this success has been possible due to MILTON.

MILTON consists of two major parts: a Mathematica package of functions specially designed for use at the freshman and sophomore level, and a toolbar coded in Visual Basic that provides an alternative to the command-line Notebook interface for executing functions in the package. The function package consists of more than 30 so-called "high-level" functions. By "high-level" function we mean a function capable of processing both numerical and symbolic input, which might request or require user interaction during execution, and which may have complex output consisting of numerical, textual and graphical components. Many examples of such functions will be demonstrated. At present, students can utilize the same package for four courses: College Algebra, Applied Calculus, Precalculus, and Discrete Math, with more functions from the package introduced to the student as he or she progresses through these courses. This consistency sharply reduces the amount of time a student must devote to studying documentation, help diminishes the culture shock that accompanies each new semester, and furnishes a crucial unifying motif the student can use to mentally link topics from one course to the next. Each high-level function is centered around a particular skill, concept or result. Functions are also used to instantiate and manipulate models of abstract objects, such as certain types of sets. At the most basic level, skill functions serve to simplify or eliminate difficult computations; but these functions do not act as mere oracles that automatically perform certain types of computations or execute key algorithms. There is not be a one-to-one correspondence between problem types and skill functions. Function interfaces and outputs are organized to obligate conceptual understanding, and there are many instances when the output from one function is needed as input to other functions to successfully construct a solution to a problem.

To protect novice students from the underlying Mathematica syntax and to simplify the use of Mathematica package, we have developed a Visual Basic applet in the form of a toolbar of buttons and dialog boxes. Each of these buttons corresponds to a high-level function and has a distinct and intuitive icon that represents the function. By clicking on the button, a dialog box is opened that allows the user to input the various parameters that are necessary for that function to execute. The applet then constructs the correct command-line syntax for the function and pastes this into the Mathematica notebook where it is executed automatically.

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