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Discrete Mathematics Using a Computer

  • Textbook
  • © 2006

Overview

Authors:
  1. John O’Donnell

    1. Computing Science Department, University of Glasgow, Glasgow, UK

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  2. Cordelia Hall

    1. Computing Science Department, University of Glasgow, Glasgow, UK

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  3. Rex Page

    1. School of Computer Science, University of Oklahoma, Norman, USA

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  • 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

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xix
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  2. Programming and Reasoning with Equations

    1. Front Matter

      Pages 1-1
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    2. Introduction to Haskell

      Pages 3-35

    3. Equational Reasoning

      Pages 37-46

    4. Recursion

      Pages 47-60

    5. Introduction

      Pages 61-81

    6. Trees

      Pages 83-106

  3. Logic

    1. Front Matter

      Pages 107-107
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    2. Propositional Logic

      Pages 109-162

    3. Predicate Logic

      Pages 163-185

  4. Set Theory

    1. Front Matter

      Pages 187-187
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    2. Set Theory

      Pages 189-206

    3. Inductively Defined Sets

      Pages 207-222

    4. Relations

      Pages 223-265

    5. Functions

      Pages 267-309

  5. Applications

    1. Front Matter

      Pages 311-311
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    2. The AVL Tree Miracle

      Pages 313-353

    3. Discrete Mathematics in Circuit Design

      Pages 355-375

  6. Back Matter

    Pages 377-441
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Keywords

About this book

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.

Authors and Affiliations

  • Computing Science Department, University of Glasgow, Glasgow, UK

    John O’Donnell, Cordelia Hall

  • School of Computer Science, University of Oklahoma, Norman, USA

    Rex Page

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