This 32-page Primer (at bottom of page) is a workbook introduction to Geometric Algebra and some highlights of its applications in classical and relativistic mechanics. It is designed for use in an all day (6 hr.) workshop, so it is not a self-contained introduction. Rather, it requires a workshop leader who is fully conversant with GA to help participants unravel the intricacies of the workbook.Download this 32-page paper: Primer for Geometric Algebra (David Hestenes, July 2005).
I begin by organizing workshop participants into groups of three or four. After leading discussion on some portion of the workbook for 5 or 10 minutes, I engage the groups in a follow-up problem or activity (many of which are given in the workbook). I have them outline their findings on a Whiteboard for discussion with the whole class. The cycle is then repeated through the next portion of the workbook. I have used the Primer for several all day AAPT Workshops, where most of the time was spent on classical mechanics. Thus, the workbook contains plenty of material for a two-day workshop. The AAPT workshop was open to both high school physics teachers and college faculty, and reports are that it was appreciated by both groups.
My firm belief is that most of the material in the workbook should be accessible and intriguing to high school physics students when properly packaged, so teaching the workshops helps me learn how that packaging should be designed. It would be premature to recommend GA for a regular place in the high school curriculum. But, I believe the time will come! In the meantime, I recommend that serious students of Geometric Algebra study my book New Foundations for Classical Mechanics, which provides a thorough treatment of all the material in the Primer and much more. (Note, however, that the relativity portion of the Primer is included only in the Second Edition). The Primer may be helpful in extracting some of the most noteworthy portions of the book, but I have yet to hear a report on that. I have used the book successfully for many years as textbook for a graduate course in classical mechanics, but I am sure that, with judicious choices by a qualified instructor, it can be used for an undergraduate course. Unfortunately, there are few such instructors, so the serious student will have to design his or her own course of self study.
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