离散数学暨组合数学

书籍目录

preface1 Truth Tables,Logic,and Proofs  1.1 Statements and Connectives  1.2 Conditional Statements  1.3 Equivalent Statements  1.4 Axiomatic Systems:Arguments and Proofs  1.5 Completeness in Propositional Logic  1.6 Karnaugh Maps  1.7 Circuit Diagrams2 Set Theory  2.1 Introduction to Sets  2.2 Set Operations  2.3 Venn Diagrams  2.4 Boolean Algebras  2.5 Relations  2.6 Partially Ordered Sets  2.7 Equivalence Relations3 Logic,Integers,and Proofs  3.1 Predicate Calculus  3.2 Basic Concepts of Proofs and the Structure of Integers  3.3 Mathematical Induction  3.4 Divisibility  3.5 Prime Integers  3.6 Congruence Relations4 Functions and Matrices  4.1 Functions  4.2 Special Functions  4.3 Matrices  4.4 Cardinality  4.5 Cardinals Continued5 Algorithms and Recursion  5.1 The “for” Procedure and Algorithms for Matrices  5.2 Recursive Functions and Algorithms  5.3 Complexity of Algorithms  5.4 Sorting Algorithms  5.5 Prefix and Suffix Notation  5.6 Binary and Hexadecimal Numbers  5.7 Signed Numbers  5.8 Matrices Continued6 Graphs,Directed Graphs,and Trees  6.1 Graphs  6.2 Directed Graphs  6.3 Trees  6.4 Instant Insanity  6.5 Euler Paths and Cycles  6.6 Incidence and Adjacency Matrices  6.7 Hypercubes and Gray Code7 Number Theory  7.1 Sieve of Eratosthenes  7.2 Fermat's Factorization Method  7.3 The Division and Euclidean Algorithms  7.4 Continued Fractions  7.5 Convergents8 Counting and Probability  8.1 Basic Counting Principles  8.2 Inclusion-Exclusion Introduced  8.3 Permutations and Combinations  8.4 Generating Permutations and Combinations  8.5 Probability Introduced  8.6 Generalized Permutations and Combinations  8.7 Permutations and Combinations with Repeition  8.8 Pigeonhole Principle  8.9 Probability Revisited  8.10 Bayes' Theorem  8.11 Markov Chains9 Algebraic Structures10 Number Theory Revisited11 Recursion Revisited12 Counting Continued13 Generating Functions14 Graphs Revisited15 Trees16 Networks17 Theory of Computation18 Theory of Codes19 Enumeration of Colors20 Rings,Integral Domains,and Fields21 Group and Semigroup Characters22 Applications of Number TheoryBibliographyHints and Solutions to Selected ExercisesIndex

作者简介

本书结构严谨、简洁易懂、逻辑性强，其内容涵盖了离散数学各种基础主题，每个主题的概念都与计算机工程和数学的实际应用相结合。本书不仅介绍了很多的基本概念，而且还讨论了一些扩展主题，如逻辑、集合、图、树、迭代、代数、计算理论和组合数学，并有大量实例，以帮助学生巩固所学知识。  

    全书讨论严谨，实例、习题多，是一本有关计算机基础数学理论的很好教材。

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