Short Course Description and Disclaimer ------------------------------------------------------------------------ This is a set of lecture notes for a short course on Approximation Theory that I offered to graduate students at Bowling Green State University, Bowling Green, Ohio, in the Summer of 1994 (and, in somewhat different form, in the Summer of 1989). The course was intended as a survey of elementary techniques in Approximation Theory for novices and non-experts. Experts in the field seeking new, original, or research topics should look elsewhere. This is strictly for beginners! There is enough material here for roughly 20 to 25 hour-and-a-half lectures; hardly a full semester course. On the other hand, it is probably sufficient background to facilitate further study. Disclaimer These are classroom notes, not original research; they are offered here primarily as labor-saving tools for students and their teachers. Much of this material has been culled from various articles, books, seminar notes, and classroom notes that I have accumulated over the years. Thus, portions may have been taken from copyrighted material. On the other hand, certain portions of these notes are original and are taken from my notes for an eventual book. In any case, it would be very uncool to publish, or otherwise use for profit, any or all of these notes. At the very least, I would have a conniption and never speak to you again. You are otherwise welcome to use these notes in any way you see fit: Give copies to friends and family, "cut and paste" to save time typing up your own versions, or whatever. If you use the notes in seminars or courses of your own, I would greatly appreciate hearing your reactions. The notes are written in Plain TeX, but make use of a few of the AMS-Fonts (Blackboard Bold plus a couple of special symbols); pretty but not essential. Comments on the files included here: The individual chapters are more or less independent -- you don't actually need them all just to read one or two. The file "680-setup.tex" is essential, it contains macros and definitions used in nearly every other file. ------------------------------------------------------------------------ Neal Carothers carother@math.bgsu.edu http://www.bgsu.edu/~carother/