## Computer MathematicsComputing is an exact science and the systematic study of any aspect necessarily involves the use of mathematical models. Moreover, the rate at which the subject is evolving demands a facility for developing new mathematical systems to keep pace with new computing systems and this requires an appreciation of how mathematics works. An understanding of the underlying mathematical structure facilitates the construction of suitable computer programs to perform computations. Assuming no specific knowledge of mathematics, the authors describe all the basic concepts required and progress from sets (rather than numbers) through a variety of algebraic structures that permit the precise description, specification and subsequent analysis of many problems in computing. The material included provides the essential mathematical foundations for core topics of computer science and extends into the areas of language theory, abstract machine theory and computer geometry. Computer Mathematics will be of interest to undergraduate students of computer science and mathematics, post-graduate computing 'conversion' course students and computer professionals who need an introduction to the mathematics that underpins computer science theory. |

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### Contents

Relations | 29 |

Functions | 61 |

Basic concepts of arithmetic | 110 |

Matrices | 191 |

Graph theory | 215 |

Languages and grammars | 254 |

Finite automata | 298 |

Computer geometry | 339 |

The Greek alphabet | 382 |

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### Common terms and phrases

addition adjacency matrix algorithm alphabet applied arithmetic associated bijection binary operation binary relation Boolean algebra called circuit closure complement concepts consider construction coordinates corresponding curve defined Definition denote derived determine diagram digraph edge elements equation equivalence relation Example Exercises exist field finite set formal function geometric give given goto grammar graph G hence identity implies injective input integer inverse isomorphic labelled language lattice left-recursive linear machine mapping mathematical multiplication n-tuples non-empty non-terminals notation obtain order relation output parsing permutation productions Proof properties Proposition reader regular expressions regular grammar represent representation result rotation Section sentence sentential forms sequence shown in Figure Similarly specific strings structure subset substring surjective symbols symmetric theorem tion total order transformations traversal unique usual values vector space vertex vertices written zero zero divisors