EAN: 9783030017552

COMPACT TEXTBOOKS IN MATHEMATICS GEOMETRIC MU...

This book enables the reader to discover elementary concepts of geometric algebra and its
applications with lucid and direct explanations. Why would one want to explore geometric
algebra? What if there existed a universal mathematical language that allowed one: to make
rotations in any dimension with simple formulas  to see spinors or the Pauli matrices and their
products  to solve problems of the special theory of relativity in three-dimensional Euclidean
space  to formulate quantum mechanics without the imaginary unit  to easily solve difficult
problems of electromagnetism  to treat the Kepler problem with the formulas for a harmonic
oscillator  to eliminate unintuitive matrices and tensors  to unite many branches of
mathematical physics? What if it were possible to use that same framework to generalize the
complex numbers or fractals to any dimension  to play with geometry on a computer  as well as
to make calculations in robotics  ray-tracing and brain science? In addition  what if such a
language provided a clear  geometric interpretation of mathematical objects  even for the
imaginary unit in quantum mechanics? Such a mathematical language exists and it is called
geometric algebra. High school students have the potential to explore it  and undergraduate
students can master it. The universality  the clear geometric interpretation  the power of
generalizations to any dimension  the new insights into known theories  and the possibility of
computer implementations make geometric algebra a thrilling field to unearth.

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