Differential geometry is the study of the curvature and calculus of curves and surfaces. "A New Approach to Differential Geometry using Clifford's Geometric Algebra" simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space.

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Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.

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Clifford algebras have become an indispensable tool for physicists at the cutting edge of theoretical investigations. Applications in physics range from special relativity and the rotating top at one end of the spectrum, to general relativity and Dirac's equation for the electron at the other. Clifford algebras have also become a virtual necessity in some areas of physics, and their usefulness is expanding in other areas, such as algebraic manipulations involving Dirac matrices in quantum thermodynamics; Kaluza- Klein theories and dimensional renormalization theories; and the formation of superstring theories. This book, aimed at beginning graduate students in physics and math, introduces readers to the techniques of Clifford algebras.