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| 內容簡介： |
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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： |
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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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