| 作者 |
| 丛书名 |
| 出版社 |
| 原 Mcgraw-Hill |
| ISBN |
| 简要 |
| 简介 |
| 内容简介书籍数学书籍 本书是作者在多年教授离散数学所获得的经验基础上写出的，其目的是为学生提供准确而可读的教材，使离散数学的概念和技术得以清晰地介绍和演示。向爱怀疑的学生们展示离散数学的实用性。为计算机科学专业的学生提供一切必需的数学基础。使数学专业的学生理解数学概念的重要性以及这些概念为什么对应用而言是重要的。为教师（指导者）设计一个灵活而全面的教学工具。 本教材的内容包括了逻辑、代数、图论、组合数学和计算理论的基础知识，讲解生动而直观，可作为1至2个学期离散数学入门课的教材，适用于包括数学专业、计算机科学专业、工程专业在内的许多专业的学生。 |
| 目录 |
| CONTENTS Preface ix The Companion Web Site xix To the Student xxi 1 The Foundations: Logic, Sets, and Functions 1 1.1 Logic 1.2 Propositional Equivalences 14 1.3 Predicates and Quantifiers 21 1.4 Sets 38 1.5 Set Operations 46 1.6 Functions 56 1.7 Sequences and Summations 69 1.8 The Growth of Functions 80 Key Terms and Results 92 Review Questions 94 Supplementary Exercises 95 Computer Projects 97 Computations and Explorations 97 Writing Projects 97 2 The Fundamentals: Algorithms, the Integers, and Matrices 99 2.1 Algorithms 99 2.2 Complexity of Algorithms 105 2.3 The Integers and Division 112 2.4 Integers and Algorithms 127 ~.5 Applications of Number Theory 137 2.6 Matrices 150 Key Terms and Results 161 Review Questions 162 Supplementary Exercises 163 Computer Projects 164 Computations and Explorations 165 Writing Projects 165 3 Mathematical Reasoning 167 3.1 Methods of Proof 167 3.2 Mathematical Induction 186 3.3 Recursive Definitions 202 3.4 Recursive Algorithms 214 3.5 Program Correctness 219 Key Terms and Results 225 Review Questions 226 Supplementary Exercises 227 Computer Projects 229 Computations and Explorations 230 Writing Projects 230 4 Counting 232 4.1 The Basics of Counting 4.2 The Pigeonhole Principle 244 4.3 Permutations and Combinations 250 4.4 Discrete Probability 260 4.5 Probability Theory 267 4.6 Generalized Permutations and Combinations 286 4.7 Generating Permutations and Combinations 296 Key Terms and Concepts 301 Review Questions 302 Supplementary Exercises 303 Computer Projects 306 Computations and Explorations 306 Writing Projects 307 5 Advanced Counting Techniques 308 5.1 Recurrence Relations 308 5.2 Solving Recurrence Relations 319 5.3 Divide-and-Conquer Relations 332 5.4 Generating Functions 338 5.5 Inclusion-Exclusion 354 5.6 Applications of Inclusion-Exclusion 360 Key Terms and Results 368 Review Questions 369 Supplementary Exercises 369 Computer Projects 371 Computations and Explorations 372 Writing Projects 372 6 Relations 374 6.1 Relations and Their Properties 374 6.2 n-ary Relations and Their Applications 384 6.3 Representing Relations 390 6.4 Closures of Relations 396 6.5 Equivalence Relations 408 6.6 Partial Orderings 415 Key Terms and Results 430 Review Questions 431 Supplementary Exercises 432 Computer Projects 436 Computations and Explorations 436 Writing Projects 436 7 Graphs 438 7.1 Introduction to Graphs 438 7.2 Graph Terminology 445 7.3 Representing Graphs and Graph Isomorphism 456 7.4 Connectivity 467 7.5 Euler and Hamilton Paths 475 7.6 Shortest Path Problems 490 7.7 Planar Graphs 501 7.8 Graph Coloring 510 Key Terms and Results 519 Review Questions 521 Supplementary Exercises 522 Computer Projects 525 Computations and Explorations 526 Writing Projects 527 8 Trees 528 8.1 Introduction to Trees 528 8.2 Applications of Trees 541 8.3 Tree Traversal 547 8.4 Trees and Sorting 562 8.5 Spanning Trees 570 8.6 Minimum Spanning Trees 580 Key Terms and Results 587 Review Questions 588 Supplementary Exercises 588 Computer Projects 591 Computations and Explorations 591 Writing Projects 592 9 Boolean Algebra 593 9.1 Boolean Functions 593 9.2 Representing Boolean Functions 600 9.3 Logic Gates 604 9.4 Minimization of Circuits 611 Key Terms and Results 625 Review Questions 625 Supplementary Exercises 626 Computer Projects 627 Computations and Explorations 628 Writing Projects 628 10 Modeling Computation 629 10.1 Languages and Grammars 629 10.2 Finite-State Machines with Output 640 10.3 Finite-State Machines with No Output 647 10.4 Language Recognition 656 10.5 Turing Machines 666 Key Terms and Results 674 Review Questions 675 Supplementary Exercises 675 Computer Projects, 677 Computations and Explorations 678 Writing Projects 678 Appendixes A- I A. I Exponential and Logarithmic Functions A-1 A.2 Pseudocode A-5 Suggested Readings B-1 Index of Biographies I- I Index 1-3 LISTOFSYMBOLS L-1 |