Imaginary Mathematics for Computer Science

Professor John Vince began working in computer graphics at Middlesex Polytechnic in 1968. His research activities centered on computer animation software and resulted in the PICASO and PRISM animation systems. Whilst at Middlesex, he designed the UK’s first MSc course in Computer Graphics and developed a popular program of short courses in computer animation for television designers. In 1986 he joined Rediffusion Simulation as a Research Consultant and worked on the development of real-time computer systems for commercial flight simulators. In 1992 he was appointed Chief Scientist of Thomson Training Simulation Ltd. In 1995 he was appointed Professor of Digital Media at the National Centre for Computer Animation at Bournemouth University and in 1999 he was made Head of Academic Group for Computer Animation. He was awarded a DSc by Brunel University in recognition of his work in computer graphics. He has written and edited over 40 books on computer graphics, computer animationand virtual reality, including the following Springer titles:• Mathematics for Computer Graphics (2014)• Calculus for Computer Graphics (2013)• Matrix Transforms for Computer Games and Animation (2012)• Expanding the Frontiers of Visual Analytics and Visualization (2012)• Quaternions for Computer Graphics (2011)• Rotation Transforms for Computer Graphics (2011)

“This interesting book is very easy to read and understand. While the topics are not new, they are explained in lucid terms for anyone who is interested in sophisticated mathematics. … The topics are very real, and I think the book would be of significant interest to many people, not just computer scientists. … you may never see another text with so many worked examples--and meaningful examples at that; they alone are worth the price of the book.” (James Van Speybroeck, Computing Reviews, June 04, 2019)“The book is quite different from typical books that introduce readers to complex variables. … This book can serve as a reference for students working in physics or computer science seeking an introduction to complex numbers; this is helped by the lengthy chapter summaries.” (M. Bona, Choice, Vol. 56 (10), June, 2019)

• 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.