Foundation Mathematics for Computer Science

John Vince describes a range of mathematical topics to provide a foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author's visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications.

Each chapter includes full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will consolidate comprehension of abstract mathematical concepts.

Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions. During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barycentric coordinates, transfinite sets and prime numbers. Whether you intend to pursue a career in programming, scientific visualisation, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

“Computer graphics/animation specialist Vince … presents a detailed list of facts from the areas of mathematics that students may need before taking a course in computer science. … the best use of the book is as a reference source. In that regard, the book may help readers because it includes relevant facts from all the mentioned fields in one place. Summing Up: Recommended. Only comprehensive mathematics collections serving lower- and upper-division undergraduates and general readers.” (M. Bona, Choice, Vol. 53 (9), May, 2016)

“It is an amazing achievement that so many concepts are explained in one well-written book. This will give a great start as well as a solid foundation to anyone aspiring to a career in computer science, whether it be programming, big data, visualization, or another area. I highly recommend it to final-year high school students or first-year undergraduate students.” (Naga Narayanaswamy, Computing Reviews, November, 2015)

Prof 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 animation and virtualreality, 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)