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出版社：機械工業出版社 ISBN：9787111645306 商品編碼：66408535645 品牌：鳳凰新華（PHOENIX 出版時間：1900-01-01 審圖號：9787111645306 代碼：139 作者：肯尼思·H.
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內容介紹
本書是經典的離散數學教材，被quanqiu數百所大學廣為采用。書中全面而繫統地介紹了離散數學的理論和方法，主要包括：邏輯和證明，集合、函數、序列、求和與矩陣，算法，數論和密碼學，歸納與遞歸，計數，離散概率，關繫，圖，樹，布爾代數，計算模型。全書取材廣泛，除包括定義、定理的嚴格陳述外，還配備大量的例題、圖表、應用實例和練習。D8版做了與時俱進的更新，成為更加實用的教學工具。本書可作為高等院校數學、計算機科學和計算機工程等專業的教材，也可作為科技領域從業人員的參考書。
目錄
1 The Foundations: Logic and Proofs....................................1 1.1 Propositional Logic............................................................1 1.2 Applications of Propositional Logic.............................................17 1.3 Propositional Equivalences....................................................26 1.4 Predicates and Quantifiers.....................................................40 1.5 Nested Quantifiers............................................................60 1.6 Rules of Inference.............................................................73 1.7 Introduction to Proofs.........................................................84 1.8 Proof Methods and Strategy....................................................96 End-of-Chapter Material.....................................................115 2 Basic Structures: Sets, Functions, Sequences, Sums, and atrices....................................121 2.1 Sets........................................................................121 2.2 Set Operations...............................................................133 2.3 Functions...................................................................1471 The Foundations: Logic and Proofs....................................1
1.1 Propositional Logic............................................................1
1.2 Applications of Propositional Logic.............................................17
1.3 Propositional Equivalences....................................................26
1.4 Predicates and Quantifiers.....................................................40
1.5 Nested Quantifiers............................................................60
1.6 Rules of Inference.............................................................73
1.7 Introduction to Proofs.........................................................84
1.8 Proof Methods and Strategy....................................................96
End-of-Chapter Material.....................................................115
2 Basic Structures: Sets, Functions, Sequences, Sums, and atrices....................................121
2.1 Sets........................................................................121
2.2 Set Operations...............................................................133
2.3 Functions...................................................................147
2.4 Sequences and Summations...................................................165
2.5 Cardinality of Sets...........................................................179
2.6 Matrices....................................................................188
End-of-Chapter Material.....................................................195
3 Algorithms.........................................................201
3.1 Algorithms..................................................................201
3.2 The Growth of Functions.....................................................216
3.3 Complexity of Algorithms....................................................231
End-of-Chapter Materia.....................................................244
4 Number Theory and Cryptography..................................251
4.1 Divisibility and Modular Arithmetic...........................................251
4.2 Integer Representations and Algorithms........................................260
4.3 Primes and Greatest Common Divisors........................................271
4.4 Solving Congruences.........................................................290
4.5 Applications of Congruences.................................................303
4.6 Cryptography...............................................................310
End-of-Chapter Materia.....................................................324
5 Induction and Recursion............................................331
5.1 Mathematical Induction......................................................331
5.2 Strong Induction and Well-Ordering...........................................354
5.3 Recursive Definitions and Structural Induction..................................365
5.4 Recursive Algorithms........................................................381
5.5 Program Correctness.........................................................393
End-of-Chapter Materia.....................................................398
6 Counting...........................................................405
6.1 The Basics of Counting.......................................................405
6.2 The Pigeonhole Principle.....................................................420
6.3 Permutations and Combinations...............................................428
6.4 BiDmial Coeficients and Identities...........................................437
6.5 Generalized Permutations and Combinations...................................445
6.6 Generating Permutations and Combinations....................................457
End-of-Chapter Materia.....................................................461
7 Discrete Probability.................................................469
7.1 An Introduction to Discrete Probability........................................469
7.2 Probability Theory...................................... 顯示全部信息
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