# Foundation Mathematics for Computer Science

## A Visual Approach

Textbook

1. Front Matter
Pages i-xix
2. John Vince
Pages 1-4
3. John Vince
Pages 5-33
4. John Vince
Pages 35-53
5. John Vince
Pages 55-78
6. John Vince
Pages 79-88
7. John Vince
Pages 89-99
8. John Vince
Pages 101-118
9. John Vince
Pages 119-131
10. John Vince
Pages 133-145
11. John Vince
Pages 147-164
12. John Vince
Pages 165-186
13. John Vince
Pages 187-224
14. John Vince
Pages 225-258
15. John Vince
Pages 259-287
16. John Vince
Pages 289-350
17. John Vince
Pages 351-393
18. Back Matter
Pages 395-407

### Introduction

In this second edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the original book and written new chapters on combinatorics, probability, modular arithmetic and complex numbers. These subjects complement the existing chapters on number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers.

John Vince describes a range of mathematical topics to provide a solid 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.

This second edition includes new, 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 help consolidate the understanding of abstract mathematical concepts.

Whether you intend to pursue a career in programming, scientific visualisation, artificial intelligence, 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.

### Keywords

Foundation Mathematics Modular Arithmetic Combinatorics Computer Games Computer Graphics Function Graphs

#### Authors and affiliations

1. 1.Bournemouth UniversityBreinton, HerefordUK

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 animation and 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)

### Bibliographic information

• Book Title Foundation Mathematics for Computer Science
• Book Subtitle A Visual Approach
• Authors John Vince
• DOI https://doi.org/10.1007/978-3-030-42078-9
• Copyright Information Springer Nature Switzerland AG 2020
• Publisher Name Springer, Cham
• eBook Packages Computer Science Computer Science (R0)
• Softcover ISBN 978-3-030-42077-2
• eBook ISBN 978-3-030-42078-9
• Edition Number 2
• Number of Pages XIX, 407
• Number of Illustrations 24 b/w illustrations, 254 illustrations in colour
• Topics
• Buy this book on publisher's site