Discrete Mathematics : for New Technology

ISBN-13: 9780750301350 / Angielski / Miękka / 1992 / 696 str.

R. Garnier; J. Taylor; Rowan Garnier

Opis

This textbook has been designed to cover the core mathematics requirements for undergraduate computer science students. The text follows a straightforward progression from the basic mathematical concepts covered by the GCSE to more sophisticated concepts which are illustrated with examples and exercises. Hints and solutions are provided for all brain-teasers listed in the book. Topics include logic and the nature of mathematical proof, set theory, relations and functions, matrices and systems of linear equations, algebraic structures, Boolean algebras and graph theory.

Recenzje

"There is now a wide agreement that mathematics for computer scientists is not calculus and numerical analysis but discrete mathematics. According to this idea this book is a lovely text for undergraduate students, useful also at freshman-sophomore level."
-Zentralblatt für Mathematik und ihre Grenzgebiete

"Discrete Mathematics for New Technology is a nice introduction to logic, sets, and algebraic structures."
-New Scientist

"The book has a number of noteworthy features which make it a text to be considered seriously by those who wish to teach a course in this area. The material is carefully written and clearly presented in a user-friendly way which makes it a pleasure to read. There is a wealth of well-judged examples, with frequent historical notes to provide background and cartoons to lighten the style."
-Times Higher Education Supplement

Spis treści

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.

O autorze

Rowan Garnier and John Taylor