Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Vince, John A. (1941-....)
Titre(s) : Imaginary mathematics for computer science [Texte électronique] / John Vince
Publication : Cham : Springer, copyright 2018
Description matérielle : 1 online resource (xvii, 301 pages) : color illustrations
Note(s) : Notes bibliogr.
The imaginary unit i = √-1 has been used by mathematicians for nearly five-hundred
years, during which time its physical meaning has been a constant challenge. Unfortunately,
René Descartes referred to it as "imaginary", and the use of the term "complex number"
compounded the unnecessary mystery associated with this amazing object. Today, i =
√-1 has found its way into virtually every branch of mathematics, and is widely employed
in physics and science, from solving problems in electrical engineering to quantum
field theory. John Vince describes the evolution of the imaginary unit from the roots
of quadratic and cubic equations, Hamilton's quaternions, Cayley's octonions, to Grassmann's
geometric algebra. In spite of the aura of mystery that surrounds the subject, John
Vince makes the subject accessible and very readable. The first two chapters cover
the imaginary unit and its integration with real numbers. Chapter 3 describes how
complex numbers work with matrices, and shows how to compute complex eigenvalues and
eigenvectors. Chapters 4 and 5 cover Hamilton's invention of quaternions, and Cayley's
development of octonions, respectively. Chapter 6 provides a brief introduction to
geometric algebra, which possesses many of the imaginary qualities of quaternions,
but works in space of any dimension. The second half of the book is devoted to applications
of complex numbers, quaternions and geometric algebra. John Vince explains how complex
numbers simplify trigonometric identities, wave combinations and phase differences
in circuit analysis, and how geometric algebra resolves geometric problems, and quaternions
rotate 3D vectors. There are two short chapters on the Riemann hypothesis and the
Mandelbrot set, both of which use complex numbers. The last chapter references the
role of complex numbers in quantum mechanics, and ends with Schrödinger's famous
wave equation. Filled with lots of clear examples and useful illustrations, this compact
book provides an excellent introduction to imaginary mathematics for computer science
La pagination de l'édition imprimée correspondante est de : XVII-301 p.
Sujet(s) : Informatique -- Mathématiques
Indice(s) Dewey :
004.015 1 (23e éd.) = Informatique - Principes mathématiques
Identifiants, prix et caractéristiques : ISBN 9783319946375. - ISBN 3319946374. - ISBN 9783319946382. - ISBN 3319946382. -
ISBN 9783319946368 (erroné). - ISBN 3319946366 (erroné). - ISBN 9783030068875. - ISBN
3030068870
Identifiant de la notice : ark:/12148/cb45779194f
Notice n° :
FRBNF45779194
(notice reprise d'un réservoir extérieur)
Table des matières : Introduction ; Complex Numbers ; Matrix Algebra ; Quaternions ; Octonions ;
Geometric Algebra ; Trigonometric Identities using Complex Numbers ; Combining Waves
using Complex Numbers ; Circuit Analysis using Complex Numbers ; Geometry Using
Geometric Algebra ; Rotating Vectors using Quaternions ; Complex Numbers and the
Riemann Hypothesis ; The Mandelbrot Set ; Conclusion ; Index.
