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內容簡介: |
本书内容分为数理逻辑、集合论、代数结构、图论等四个主要部分,包含命题逻辑、一阶谓词逻辑、集合、二元关系、函数、代数结构、特殊代数系统、图、特殊图及图的应用、树等10个章节。本书以应用型人才培养为目标,突出离散数学作为计算机及相关本科的专业基础课这一定位,本书可作为计算机科学与技术、软件工程、智能科学与技术、物联网工程、网络工程等专业离散数学课程的教材。
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關於作者: |
黄玮,男,1978年生人,副教授,在读博士,现任教于福州理工学院,具有知名企业的从业经历,曾获\微软金牌讲师”等头衔,长期从事软件工程、虚拟现实研发与教学工作,主持和完成过各类省级、市级科研项目5项,获软件著作权14项,发表科研论文9篇。
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目錄:
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目 录 第 1 章 命题逻辑 ····································································································.1 1.1 命题与联结词 ·····························································································.1 1.2 命题公式及其赋值 ······················································································.5 1.3 等值式 ·······································································································.8 1.4 析取范式与合取范式 ·················································································.10 1.4.1 范式的基本概念 ··············································································.10 1.4.2 主范式及其表示 ··············································································.12 1.4.3 主范式的求解 ··················································································.13 1.4.4 主范式的数量 ··················································································.15 1.5 联结词的完备集 ························································································.16 1.5.1 真值函数 ·························································································.16 1.5.2 联结词完备集 ··················································································.17 1.6 命题逻辑的推理理论 ·················································································.18 1.6.1 推理的基本概念 ··············································································.18 1.6.2 推理定律和推理规则 ·······································································.19 1.6.3 命题逻辑的推理方法 ·······································································.19 1.7 命题逻辑的应用 ························································································.23 1.7.1 命题公式在计算机中的表示 ·····························································.23 1.7.2 程序优化 ·························································································.24 1.7.3 资源分配 ·························································································.24 1.7.4 计算机硬件电路设计 ·······································································.25 1.8 命题逻辑实验 ····························································································.25 习题 1 ···············································································································.27 第 2 章 一阶逻辑 ···································································································.30 2.1 一阶逻辑的基本概念 ·················································································.30 2.2 一阶逻辑公式及其解释 ··············································································.33 2.2.1 一阶逻辑公式的符号 ·······································································.33 2.2.2 一阶逻辑公式的结构 ·······································································.34 2.2.3 量词的辖域 ·····················································································.34 2.2.4 公式的解释 ·····················································································.35 2.3 一阶逻辑等值式及演算 ··············································································.37 2.4 一阶逻辑前束范式 ·····················································································.38 2.5 一阶逻辑的推理理论 ·················································································.39 2.6 一阶逻辑实验 ····························································································.43 习题 2 ···············································································································.43 第 3 章 集合论 ·······································································································.47 3.1 集合的基本概念 ························································································.47 3.2 集合的基本运算 ························································································.50 3.3 有限集的计数 ····························································································.54 3.4 集合论实验 ·······························································································.55 习题 3 ····················
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