Geometric Multiplication of Vectors
An Introduction to Geometric Algebra in Physics
Authors: Josipović, Miroslav
 An excellent starting point for beginners in the field
 An advanced high school student can learn basic concepts from the book
 Gradual introduction of concepts with many figures and solved examples
 A fresh look at the problems of modern theoretical physics
 Comparison of standard mathematics to geometric algebra with examples
 Lots of guidelines for a further study
 The informal approach was preferred to adopt new concepts more easily
 There are given problems for selfsolving, some of which can be a challenge
 Many arguments are given why to learn and use geometric algebra
 Some important applications of geometric algebra were discussed
 The reader can use the original Mathematica software that follows the book as well as the free GAViewer application
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 About this Textbook

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 threedimensional 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, raytracing 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.
 About the authors

Miroslav Josipović is a Croatian physicist and musician with special interest in revising the language of mathematical physics and in creating new ways of teaching physics.
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Bibliographic Information
 Bibliographic Information

 Book Title
 Geometric Multiplication of Vectors
 Book Subtitle
 An Introduction to Geometric Algebra in Physics
 Authors

 Miroslav Josipović
 Series Title
 Compact Textbooks in Mathematics
 Copyright
 2019
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783030017569
 DOI
 10.1007/9783030017569
 Softcover ISBN
 9783030017552
 Series ISSN
 22964568
 Edition Number
 1
 Number of Pages
 XXV, 238
 Number of Illustrations
 90 illustrations in colour
 Topics