离散数学及其在计算机科学中的应用-(英文版)

本书特色

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本书专为计算机科学专业的学生而设计,不仅提供学生必需的离散数学知识,而且能够启发后续专业课程的学习兴趣。本书主要内容涵盖计数、密码学与数论、逻辑与证明、归纳法、递归、概率以及图论,推导严谨、代码清晰、练习丰富。本书不仅适合作为高校计算机相关专业离散数学课程的教材,也适合从事计算机行业的技术人员参考。

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目录

Contents CHAPTER1 Counting 311.1 Basic Counting 31The Sum Principle 31Abstraction 33Summing Consecutive Integers 33The Product Principle 34Two-Element Subsets 36Important Concepts, Formulas, and Theorems 37Problems 381.2 Counting Lists, Permutations, and Subsets 40Using the Sum and Product Principles 40Lists and Functions 42The Bijection Principle 44k-Element Permutations of a Set 45Counting Subsets of a Set 46Important Concepts, Formulas, and Theorems 48Problems 501.3 Binomial Coeffiients 52Pascal’s Triangle 52A Proof Using the Sum Principle 54The Binomial Theorem 56Labeling and Trinomial Coefficient 58Important Concepts, Formulas, and Theorems 59Problems 601.4 Relations 62What Is a Relation? 62Functions as Relations 63Properties of Relations 63Equivalence Relations 66Partial and Total Orders 69Important Concepts, Formulas, and Theorems 71Problems 721.5 Using Equivalence Relationsin Counting 73The Symmetry Principle Equivalence Relations 75The Quotient Principle 76Equivalence Class Counting 76Multisets 78The Bookcase Arrangement Problem 80The Number of k-Element Multisets of an n-Element Set 81Usingthe Quotient Principle to Explain a Quotient 82Important Concepts, Formulas, and Theorems 83Problems 84CHAPTER2 Cryptography and Number Theory 892.1 Cryptography and Modular Arithmetic 89Introduction to Cryptography 89Private-Key Cryptography 90Public-Key Cryptosystems 93Arithmetic Modulo n 95Cryptography Using Addition mod n 98Cryptography Using Multiplication mod n 99Important Concepts, Formulas, and Theorems 101Problems 1022.2 Inverses and Greatest Common Divisors 105Solutions to Equations and Inverses mod n 105Inverses mod n 106Converting Modular Equations to Normal Equations 109Greatest Common Divisors 110Euclid’s Division Theorem 111Euclid’s GCD Algorithm 114Extended GCD Algorithm 115Computing Inverses 118Important Concepts, Formulas, and Theorems 119Problems 1202.3 The RSA Cryptosystem 123Exponentiation mod n 123The Rules of Exponents 123Fermat’s Little Theorem 126The RSA Cryptosystem 127The Chinese Remainder Theorem 131Important Concepts, Formulas, and Theorems 132Problems 1342.4 Details of the RSA Cryptosystem 136Practical Aspects of Exponentiation mod n 136How Long Does It Take to Use the RSA Algorithm? 139How Hard Is Factoring? 140Finding Large Primes 140Important Concepts, Formulas, and Theorems 143Problems 144CHAPTER3 Reflectionon Logic and Proof 1473.1 Equivalence and Implication 147Equivalence of Statements 147Truth Tables 150DeMorgan’s Laws 153Implication 155If and Only If 156Important Concepts, Formulas, and Theorems 159Problems 1613.2 Variables and Quantifier 163Variables and Universes 163Quantifier 164Standard Notation for Quantificatio 166Statements about Variables 168Rewriting Statements to Encompass Larger Universes 168Proving Quantifie Statements Trueor False 169Negation of Quantifie Statements 170Implicit Quantificatio 173Proof of Quantifie Statements 174Important Concepts, Formulas, and Theorems 175Problems 1773.3 Inference 179Direct Inference (Modus Ponens) and Proofs 179Rules of Inference for Direct Proofs 181Contrapositive Ruleof Inference 183Proof by Contradiction 185Important Concepts, Formulas, and Theorems 188Problems 189CHAPTER4 Induction, Recursion, and Recurrences 1914.1 Mathematical Induction 191Smallest Counterexamples 191The Principle of Mathematical Induction 195Strong Induction 199Induction in General 201A Recursive Viewof Induction 203Structural Induction 206Important Concepts, Formulas, and Theorems 208Problems 2104.2 Recursion, Recurrences, and Induction 213Recursion 213Examples of First-Order Linear Recurrences 215Iteratinga Recurrence 217Geometric Series 218First-Order Linear Recurrences 221Important Concepts,

封面

离散数学及其在计算机科学中的应用-(英文版)

书名:离散数学及其在计算机科学中的应用-(英文版)

作者:克利福德.斯坦

页数:508

定价:¥99.0

出版社:机械工业出版社

出版日期:2017-10-01

ISBN:9787111580973

PDF电子书大小:83MB 高清扫描完整版

百度云下载:http://www.chendianrong.com/pdf

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