離散數學教科書課程大綱離散數學乃是電腦的數學基礎，主要探討的對象是『資料』與『程式』，主要內容如下。
以資料為導向的主題、可分為『邏輯資料』、『數字資料』、『字串資料』等三類。
以程式為導向的主題、可分為『迴圈式』、『遞迴式』、『推理式』等三類。
教科書大綱Table of Contents Preface To the Student The Companion Web Site 1 The Foundations: Logic, Sets, and Functions 1.1 Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Sets 1.5 Set Operations 1.6 Functions 1.7 Sequences and Summations 1.8 The Growth Functions 2 The Fundamentals: Algorithms, the Integers, and Matrices 2.1 Algorithms 2.2 Complexity of Algorithms 2.3 The Integers and Division 2.4 Integers and Algorithms 2.5 Applications of Number Theory 2.6 Matrices 3 Mathematical Reasoning 3.1 Methods of Proof 3.2 Mathematical Induction 3.3 Recursive Definitions 3.4 Recursive Algorithms 3.5 Program Correctness 4 Counting 4.1 The Basics of Counting 4.2 The Pigeonhole Principle 4.3 Permutations and Combinations 4.4 Discrete Probability 4.5 Probability Theory 4.6 Generalized Permutations and Combinations 4.7 Generating Permutations and Combinations 5 Advanced Counting Techniques 5.1 Recurrence Relations 5.2 Solving Recurrence Relations 5.3 Divide-and-Conquer Relations 5.4 Generating Functions 5.5 Inclusion-Exclusion 5.6 Applications of Inclusion-Exclusion 6 Relations 6.1 Relations and Their Properties 6.2 n-ary Relations and Their Applications 6.3 Representing Relations 6.4 Closures of Relations 6.5 Equivalence Relations 6.6 Partial Orderings 7 Graphs 7.1 Introduction to Graphs 7.2 Graph Terminology 7.3 Representing Graphs and Graph Isomorphism 7.4 Connectivity 7.5 Euler and Hamilton Paths 7.6 Shortest Path Problems 7.7 Planar Graphs 7.8 Graph Coloring 8 Trees 8.1 Introduction to Trees 8.2 Applications of Trees 8.3 Tree Traversal 8.4 Trees and Sorting 8.5 Spanning Trees 8.6 Minimum Spanning Trees 9 Boolean Algebra 9.1 Boolean Functions 9.2 Representing Boolean Functions 9.3 Logic Gates 9.4 Minimization of Circuits 10 Modeling Computation 10.1 Languages and Grammars 10.2 Finite-State Machines with Output 10.3 Finite-State Machines with No Output 10.4 Language Recognition 10.5 Turing Machines Appendixes A.1 Exponential and Logarithmic Functions A.2 Pseudocode Suggested Readings Solutions to Odd-Numbered Exercises Index of Biographies Index 參考書基礎離散數學 , 黃中彥著, 新文京出版社 - http://www.books.com.tw/exep/prod/booksfile.php?item=0010270242第一章 集 合 第二章 命題代數與基本論證方法 第三章 關 係 第四章 偏序、格與布林代數 第五章 基本組合理論 第六章 遞迴關係 第七章 代數結構 第八章 圖與樹入門 附 錄 題 解 線上資源 |
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作者：陳鍾誠 E-mail:ccc@kmit.edu.tw。  本著作係採用創用 CC 「姓名標示─相同方式分享 2.5 台灣版」授權條款釋出。 大學課程網 | 手機入口網 |
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