Discrete Mathematics for New Technology
Institute of Physics Publishing (Verlag)
978-0-7503-0136-7 (ISBN)
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Discrete Mathematics for New Technology has been designed to cover the core mathematics requirement for undergraduate computer science students in the UK and the USA. This has been approached in a comprehensive way whilst maintaining an easy to follow progression from the basic mathematical concepts covered by the GCSE in the UK and by high-school algebra in the USA, to the more sophisticated mathematical concepts examined in the latter stages of the book. The rigorous treatment of theory is punctuated by frequent use of pertinent examples. This is then reinforced with exercises to allow the reader to achieve a "feel" for the subject at hand. Hints and solutions are provided for these brain-teasers at the end of the book. Although aimed primarily at computer science students, the structured development of the mathematics enables this text to be used by undergraduate mathematicians, scientists and others who require an understanding of discrete mathematics. The topics covered include: logic and the nature of mathematical proof, set theory, relations and functions, matrices and systems of linear equations, algebraic structures, Boolean algebras and a thorough treatise on graph theory. The authors have extensive experience of teaching undergraduate mathematics at colleges and universities in the British and American systems. They have developed and taught courses for a variety of non-specialists and have established reputations for presenting rigorous mathematical concepts in a manner which is accessible to this audience. Their current research interests lie in the fields of algebra, topology and mathematics education. Discrete Mathematics for New Technology is therefore a rare thing; a readable, friendly textbook designed for non-mathematicians, presenting material which is at the foundations of mathematics itself. It is essential reading.
Logic: Propositions and truth values. Logical connectives and truth tables. Tautologies and contradictions. Logical equivalence and logical implication. The algebra of propositions. More about conditionals. Arguments. Predicate logic. Arguments in predicate logic. Mathematical proof: The nature of proof. Axioms and axiom systems. Methods of proof. Mathematical induction. Sets: Sets and membership. Subsets. Operations on sets. Counting techniques. The algebra of sets. Families of sets. The cartesian product. Relations: Relations and their representations. Properties of relations. Intersections and unions of relations. Equivalence relations and partitions. Order relations. Hasse diagrams. Application: relational databases. Functions: Definitions and examples. Composite functions. Injections and surjections. Bijections and inverse functions. More on cardinality. Databases: functional dependence and normal forms. Matrix algebra: Introduction. Some special matrices. Operations on matrices. Elementary matrices. The inverse of a matrix. Systems of linear equations: Introduction. Matrix inverse method. Gauss-Jordan elimination. Gaussian elimination. Algebraic structures: Binary operations and their properties. Algebraic structures. More about groups. Some families of groups. Substructures. Morphisms. Group codes. Boolean algebra: Introduction. Properties of Boolean algebras. Boolean functions. Switching circuits. Logic networks. Minimization of Boolean expressions. Graph theory: Definitions and examples. Paths and circuits. Isomorphism of graphs. Trees. Planar graphs. Directed graphs. Applications of graph theory: Introduction. Rooted trees. Sorting. Searching strategies. Weighted graphs. The shortest path and travelling salesman problems. Networks and flows. References and further reading. Hints and solutions to selected exercises. Index.
| Erscheint lt. Verlag | 1.1.1992 |
|---|---|
| Zusatzinfo | 25 Illustrations, black and white |
| Verlagsort | London |
| Sprache | englisch |
| Maße | 156 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| ISBN-10 | 0-7503-0136-8 / 0750301368 |
| ISBN-13 | 978-0-7503-0136-7 / 9780750301367 |
| Zustand | Neuware |
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