離散數(shù)學

前言

This updated edition is intended for a one- or two-term introductory course in discrete mathematics, based on my experience in teaching this course over many years and requests from users of previous editions. Formal mathematics prerequisites are minimal; calculus is not required. There are no computer science prerequisites. The book includes examples, exercises, figures, tables, sections on problem-solving, sections containing problem-solving tips, section reviews, notes, chapter reviews, self-tests, and computer exercises to help the reader master introductory discrete mathematics. In addition, an Instructor's Guide and website are available.In the early 1980s there were few textbooks appropriate for an introductory course in discrete mathematics. However, there was a need for a course that extended students' mathematical maturity and ability to deal with abstraction, which also included useful topics such as combinatorics, algorithms, and graphs. The original edition of thishook （1984） addressed this need and significantly influenced the development of discrete mathematics courses. Subsequently, discrete mathematics courses were endorsed by many groups for several different audiences, including mathematics and computer science majors. A panel of the Mathematical Association of America （MAA） endorsed a year-long course in discrete mathematics. The Educational Activities Board of the Institute of Electrical and Electronics Engineers （IEEE） recommended a freshman discrete mathematics course. The Association for Computing Machinery （ACM） and IEEE accreditation guidelines mandated a discrete mathematics course. This edition, like its predecessors, includes topics such as algorithms, combinatorics, sets, functions, and mathematical induction endorsed by these groups. It also addresses understanding and constructing proofs and, generally, expanding mathematical maturity.

內(nèi)容概要

本書從算法分析和問題求解的角度，全面系統(tǒng)地介紹了離散數(shù)學的基礎(chǔ)概念及相關(guān)知識，并在其前一版的基礎(chǔ)上進行了修改與擴展。書中通過大量實例，深入淺出地講解了數(shù)理邏輯、組合算法、圖論、布爾代數(shù)、網(wǎng)絡(luò)模型、形式語言與自動機理論等與計算機科學密切相關(guān)的前沿課題，既著重于各部分內(nèi)容之間的緊密聯(lián)系，又深入探討了相關(guān)的概念、理論、算法和實際應(yīng)用。本書內(nèi)容敘述嚴謹、推演詳盡，各章配有相當數(shù)量的習題與書后的提示和答案，為讀者迅速掌握相關(guān)知識提供了有效的幫助。    本書既可作為計算機科學及計算數(shù)學等專業(yè)的本科生和研究生教材，也可作為工程技術(shù)人員和相關(guān)人員的參考書。

作者簡介

作者：(美國)Richard Johnosonbaugh

書籍目錄

Preface 1 Sets and Logic  　1.1 Sets  　1.2 Propositions  　1.3 Conditional Propositions and Logical Equivalence  　1.4 Arguments and Rules of Inference  　1.5 Quantifiers  　1.6 Nested Quantifiers  　Problem-Solving Corner: Quantifiers  　Notes  　Chapter Review  　Chapter Self-Test  　Computer Exercises  2 Proofs  　2.1 Mathematical Systems, Direct Proofs, and Counterexamples  　2.2 More Methods of Proof 　　Problem-Solving Corner: Proving Some Properties of Real Numbers  　2.3 Resolution Proofst  　2.4 Mathematical Induction 　　Problem-Solving Corner: Mathematical Induction  　2.5 Strong Form of Induction and the Well-Ordering Property  　Notes  　Chapter Review  　Chapter Self-Test  　Computer Exercises  3 Functions, Sequences, and Relations  　3.1 Functions 　　Problem-Solving Corner: Functions  　3.2 Sequences and Strings  　3.3 Relations  　3.4 Equivalence Relations  　　Problem-Solving Corner: Equivalence Relations  　3.5 Matrices of Relations  　3.6 Relational Databasest  　Notes  　Chapter Review  　Chapter Self-Test  　Computer Exercises  4 Algorithms  　4.1 Introduction  　4.2 Examples of Algorithms  　4.3 Analysis of Algorithms  　　Problem-Solving Corner: Design and Analysis of an Algorithm  　4.4 Recursive Algorithms  　Notes  　Chapter Review  　Chapter Self-Test  　Computer Exercises  5 Introduction to Number Theory  　5.1 Divisors  　5.2 Representations of Integers and Integer Algorithms  　5.3 The Euclidean Algorithm  　Problem-Solving Corner: Making Postage  　5.4 The RSA Public-Key Cryptosystem  　Notes  　Chapter Review  　Chapter Self-Test  　Computer Exercises  6 Counting Methods and the Pigeonhole Principle  　6.1 Basic Principles  265　Problem-Solving Corner: Counting  ……7 Recurence Relations8 Graph Theory9 Trees10 Network Models11 Boolean Algebras and Combinatorial Circuits12 Automata, Grammars, and languages13 Computational GeometryA MatricesB Algebra ReviewC PesudocodeReferencesHints and Solutions to Selected ExercisesIndex

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