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Discrete Mathematics Using a Computer

Autor John O'Donnell, Cordelia Hall, Rex Page
en Limba Engleză Paperback – 14 aug 2006
Computer science abounds with applications of discrete mathematics, yet s- dents of computer science often study discrete mathematics in the context of purely mathematical applications. They have to ?gure out for themselves how to apply the ideas of discrete mathematics to computing problems. It is not easy. Most students fail to experience broad success in this enterprise, which is not surprising, since many of the most important advances in science and engineeringhavebeen, precisely, applicationsofmathematicstospeci?cscience and engineering problems. Tobesure,mostdiscretemathtextbooksincorporatesomeaspectsapplying discrete math to computing, but it usually takes the form of asking students to write programs to compute the number of three-ball combinations there are in a set of ten balls or, at best, to implement a graph algorithm. Few texts ask students to use mathematical logic to analyze properties of digital circuits or computer programs or to apply the set theoretic model of functions to understand higher-order operations. A major aim of this text is to integrate, tightly, the study of discrete mathematics with the study of central problems of computer science.
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Specificații

ISBN-13: 9781846282416
ISBN-10: 1846282411
Pagini: 464
Ilustrații: XIX, 441 p. 68 illus.
Dimensiuni: 155 x 235 x 24 mm
Greutate: 0.65 kg
Ediția:2nd ed. 2006
Editura: SPRINGER LONDON
Colecția Springer
Locul publicării:London, United Kingdom

Public țintă

Lower undergraduate

Cuprins

Programming and Reasoning with Equations.- to Haskell.- Equational Reasoning.- Recursion.- Trees.- Logic.- Propositional Logic.- Predicate Logic.- Set Theory.- Set Theory.- Inductively Defined Sets.- Relations.- Functions.- Applications.- The AVL Tree Miracle.- Discrete Mathematics in Circuit Design.

Textul de pe ultima copertă

Discrete Mathematics Using a Computer offers a new, "hands-on" approach to teaching Discrete Mathematics. Using software that is freely available on Mac, PC and Unix platforms, the functional language Haskell allows students to experiment with mathematical notations and concepts -- a practical approach that provides students with instant feedback and allows lecturers to monitor progress easily.
This second edition of the successful textbook contains significant additional material on the applications of formal methods to practical programming problems. There are more examples of induction proofs on small programs, as well as a new chapter showing how a mathematical approach can be used to motivate AVL trees, an important and complex data structure.
Designed for 1st and 2nd year undergraduate students, the book is also well suited for self-study. No prior knowledge of functional programming is required; everything the student needs is either provided or can be picked up easily as they go along.
Key features include:
• Numerous exercises and examples
• A web page with software tools and additional practice problems, solutions, and explanations, as well as course slides
• Suggestions for further reading
Complete with an accompanying instructor's guide, available via the web, this volume is intended as the primary teaching text for Discrete Mathematics courses, but will also provide useful reading for Conversion Masters and Formal Methods courses.
Visit the book’s Web page at: http://www.dcs.gla.ac.uk/~jtod/discrete-mathematics/

Caracteristici

Takes an entirely original approach to the teaching Discrete Mathematics, aimed at making it easier for students to learn difficult concepts Uses a simple functional language, requiring no prior knowledge of Functional Programming All the material needed to use the book will be available for download via ftp Includes an Instructors Guide, available via the Worldwide Web