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# Adaptive Learning Module for Mathematical Functions

The target audience of the ALMMF is working adults, undergraduate university students, and well-prepared high school students. Technical professionals, for example in applied science and engineering, could use the ALMMF as a refresher on the properties of elementary mathematical functions. Undergraduates could use it as a supplement to standard coursework, and high school students interested in mathematics could use it as an introduction to higher mathematics. Prerequisites for use of the ALMMF are the real and complex number systems, high school algebra, plane geometry, and introductory calculus.

An ALMMF user is expected to be self-motivated, that is, interested in a particular topic and willing to invest time to learn something about it. This is the same motivation that brings readers to the classical references, but the ALMMF concept aims to provide a richer learning experience by providing explanations, derivations, proof sketches, references, diagrams, color graphics, animations, examples, problems and typical applications, all within a dynamic, interactive and interconnected set of carefully designed Web pages.

The ALMMF is related to the DLMF Project1, a more general effort now in progress that will result in a Digital Library of Mathematical Functions. The DLMF will disseminate validated reference data for mathematical functions and associated topics from a free public Web site at NIST. Modeled after the Handbook of Mathematical Functions [1], published by the National Bureau of Standards in 1964 under the editorship of M. Abramowitz and I.A. Stegun, the DLMF is oriented to the needs of scientific professionals. It will provide definitions and notations for elementary and higher functions, and a generous selection of their mathematical properties that are of importance in scientific applications. A typical chapter is the one on Airy functions. Its contents include notation, differential equation, graphs and visualization, Maclaurin series, integral representations, relations to other functions, asymptotic expansions, modulus and phase, zeros, integrals, products, generalizations, methods of computation, references to published tables, approximations, and online access to software. The style is highly condensed, with a minimum of explanation. Topics associated with mathematical functions that will be covered in condensed style include algebraic and analytical methods, asymptotic approximations, numerical methods, computer algebra, and statistics. The project involves 12 or so NIST staff and approximately 50 outside experts as associate editors, authors and validators. Internal NIST funding has been augmented by a substantial 3-year grant from the National Science Foundation.

The ALMMF intersects the DLMF in the DLMF chapter on elementary functions. The author of this chapter, Dr. Steven Krantz, Washington University, St. Louis, will receive his contract from NIST in October 2000. The chapter should be complete in early 2001, except for revisions necessitated by editorial review and an independent validator's report. It will be incorporated into the DLMF Web site in preliminary form by the end of 2001, and in final form by the end of 2002. The ALMMF will provide a tutorial treatment of the material in this chapter, with references and active links to the DLMF Web site.

Next: Catalog of Resources Up: Interactive Resources For Elementary Previous: Introduction
Daniel W Lozier 2000-09-06