Geometric Multiplication of Vectors, 1st ed. 2019
An Introduction to Geometric Algebra in Physics

Compact Textbooks in Mathematics Series


Language: Anglais

Approximative price 40.08 €

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254 p. · 15.5x23.5 cm · Paperback

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.

Basic Concepts.- Euclidean 3D Geometric Algebra.- Applications.- Geometric Algebra and Matrices.- Appendix.- Solutions for Some Problems.- Problems.- Why Geometric Algebra?.- Formulae.- Literature.- References.
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.
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 self-solving, 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