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出版社:機械工業出版社 ISBN:9787111645306 商品編碼:66958392878 品牌:文軒 出版時間:2020-01-01 代碼:139 作者:肯尼思·H.羅森(KennethH.Rose
" 作 者:(美)肯尼思·H.羅森(Kenneth H.Rosen) 著 定 價:139 出 版 社:機械工業出版社 出版日期:2020年01月01日 頁 數:942 裝 幀:平裝 ISBN:9787111645306 ●1 The Foundations:Logic and Proofs1 1.1 Propositional Logic1 1.2 Applications of Propositional Logic17 1.3 Propositional Equivalences26 1.4 Predicates and Quantifiers40 1.5 Nested Quantifiers60 1.6 Rules of Inference73 1.7 Introduction to Proofs84 1.8 Proof Methods and Strategy96 End-of-Chapter Material115 2 Basic Structures:Sets,Functions,Sequences,Sums,and atrices121 2.1 Sets121 2.2 Set Operations133 2.3 Functions147 2.4 Sequences and Summations165 2.5 Cardinality of Sets179 2.6 Matrices188 End-of-Chapter Material195 3 Algorithms201 3.1 Algorithms201 3.2 The Growth of Functions216 3.3 Complexity of Algorithms231 End-of-Chapter Materia244 4 Number Theory and Cryptography251 4.1 Divisibility and Modular Arithmetic251 4.2 Integer Representations and Algorithms260 4.3 Primes and Greatest Common Divisors271 4.4 Solving Congruences290 4.5 Applications of Congruences303 4.6 Cryptography310 End-of-Chapter Materia324 5 Induction and Recursion331 5.1 Mathematical Induction331 5.2 Strong Induction and Well-Ordering354 5.3 Recursive Definitions and Structural Induction365 5.4 Recursive Algorithms381 5.5 Program Correctness393 End-of-Chapter Materia398 6 Counting405 6.1 The Basics of Counting405 6.2 The Pigeonhole Principle420 6.3 Permutations and Combinations428 6.4 Binomial Coeficients and Identities437 6.5 Generalized Permutations and Combinations445 6.6 Generating Permutations and Combinations457 End-of-Chapter Materia461 7 Discrete Probability469 7.1 An Introduction to Discrete Probability469 7.2 Probability Theory477 …… 8 Advanced Counting Techniques 9 Relations 10 Graphs 11 Trees 12 Boolean Algebra 13 Modeling Computation Appendices Suggested Readings B-1 Answers to Odd-Numbered Exercises S-1 Index of Biographies I-1 Index I-2 本書是經典的離散數學教材,被全球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。第8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。 ![](https://img10.360buyimg.com/imgzone/jfs/t1/147514/7/5440/73116/5f34a3beE3ba58783/f5b2391383f5625c.jpg)
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