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In this third edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the second edition, and added chapters on systems of counting, area and volume. These subjects complement the existing chapters on visual mathematics, numbers, algebra, logic, combinatorics, probability, modular arithmetic, trigonometry, coordinate systems, determinants, vectors, complex numbers, 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.
Computer science is a very large subject, and graduates pursue a wide variety of careers, including programming, systems design, cryptography, website design, real-time systems, computer animation, computer games, data visualisation, etc. Consequently, it is impossible to write a mathematics book that caters to all of these career paths. Nevertheless, I have attempted to describe a range of mathematical topics that I believe are relevant, and have helped me during my own career in Computer Science. The book’s subtitle ‘A Visual Approach’ reflects the importance I place on coloured illustrations and function graphs, of which there are over 210 and 90 tables. Many chapters contain a variety of worked examples.
1 Visual Mathematics
2 Numbers
3 Systems of Counting
4 Algebra
5 Logic
6 Combinatorics
7 Probability
8 Modular Arithmetic
9 Trigonometry
10 Coordinate Systems
11 Determinants
12 Vectors
13 Complex Numbers
14 Matrices
15 Geometric Matrix Transforms
16 Calculus: Derivatives
17 Calculus: Integration
18 Area
19 Volume
Appendix A. Limit of (sin θ )/θ
Appendix B. Integrating cosn θ