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5.0 out of 5 stars Fascinating!, 4 Jun 2013
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This review is from: New Foundations for Classical Mechanics (Fundamental Theories of Physics) (Paperback)
Hestenes had dedicated most of his career to developing Geometric algebra which, by some aberration, the maths community glossed over. They seemed to decide that Clifford's geometric algebra meant algebra rather than geometry. As a consequence the physicists have been left to fend for themselves and produced some beautiful routes to deeper intuitive understanding and easier practical means of working in multidimensional spaces. This book (I'm told) is the most accessible entry into the subject. I certainly find it very good as far as I've gone. Not least for the many excellent diagrams and exercises based on actual application of the ideas rather than bald examples of doing theoretical proofs, which so many algebra books use as a cop-out, leaving the student with working tools and no idea of where to apply them other than following like sheep. The very practical outlook of the book in using real geometrical insight and showing the profound benefit that the geometric product gives over mere exterior algebra in both solving and penetrating the exploitation of graded structures for separating out scalars and invariant features is masterly. The student aware of these insights is much better equipped to go on into differential geometry, complex analysis and eg. projective or conformal geometry or invariant theory. It's certainly helped me considerably in the latter topics.

The main disappointment about the book is however that geometric calculus, the development into differential geometry, is not covered in the same volume, though instead the many examples across a wide range of practical applications give the physicist many valuable insights into many areas of mechanics..
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