計算機數學基礎, 6/e
Christoph Meinel，Martin Mundhenk 季松 程峰 等譯
- 出版商: 清華大學
- 出版日期: 2022-01-01
- 定價: $414
- 售價: 8.5 折 $352
- 語言: 簡體中文
- 裝訂: 平裝
- ISBN: 7302579660
- ISBN-13: 9787302579663
-
相關分類:
Computer-Science
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商品描述
本書是作者之一梅內爾教授（(Christoph Meinel）在德國特裡爾大學任教為電腦科學專業及經濟信息學專業第一學期的學生設計的課程。該課程的主要目的是為學生提供專業的數學知識和技能，以便他們可以獲得電腦科學及其相關專業所必需的數學基礎。
目錄大綱
目錄
第 1章緒論 .......................................................................................................1
第一部分數學基礎知識
第 2章命題 .......................................................................................................7
2.1定義和舉例 .............................................................................................7
2.2命題聯結詞 .............................................................................................8
2.3重言式和矛盾式 .................................................................................... 13
2.4命題形式化 ........................................................................................... 17
2.5命題的量化 ........................................................................................... 18
第 3章集合和集合運算..................................................................................... 21
3.1集合 ..................................................................................................... 21
3.2集合相等 .............................................................................................. 23
3.3補集 ..................................................................................................... 25
3.4空集 ..................................................................................................... 26
3.5子集和超集 ........................................................................................... 27
3.6冪集和集合族 ....................................................................................... 28
3.7集合的交集、並集和補集 ....................................................................... 30
3.8笛卡兒積 .............................................................................................. 34
3.9集合運算的其他基本規律 ....................................................................... 37
第 4章數學證明............................................................................................... 39
第 5章關系 ..................................................................................................... 43
5.1定義和舉例 ........................................................................................... 43
5.2關系運算 .............................................................................................. 47
5.3關系的重要性質 .................................................................................... 50
5.4等價關系與劃分 .................................................................................... 52
電腦數學基礎 (第 6版)
5.5等價關系的運算 .................................................................................... 57
5.6偏序關系 .............................................................................................. 61
第 6章映射與函數 ........................................................................................... 65
6.1定義及第一個例子 ................................................................................. 65
6.2滿射、單射和雙射 ................................................................................. 69
6.3序列和集合族 ....................................................................................... 74
6.4集合的基數 ........................................................................................... 77
6.5參考資料 .............................................................................................. 80
第二部分技術支持
第 7章數學證明方法 ........................................................................................ 85
7.1直接證明法 ........................................................................................... 85
7.2換質位法證明 ....................................................................................... 87
7.3反證法 ................................................................................................. 88
7.4等價證明 .............................................................................................. 89
7.5原子命題證明 ....................................................................................... 90
7.6個案分析證明 ....................................................................................... 92
7.7帶量詞的命題證明 ................................................................................. 93
7.8組合證明 .............................................................................................. 96
第 8章完全歸納法 ......................................................................................... 100
8.1完全歸納法的思路 ............................................................................... 101
8.2歸納證明舉例 ..................................................................................... 101
8.3歸納證明的結構 .................................................................................. 104
8.4廣義完全歸納法 .................................................................................. 106
8.5歸納定義 ............................................................................................ 107
第 9章組合計數............................................................................................. 116
9.1基本計數原則 ..................................................................................... 116
9.2排列和二項式系數 ............................................................................... 121
9.3計算二項式系數 .................................................................................. 125
第 10章離散概率論 ....................................................................................... 133
10.1隨機試驗和概率 ................................................................................ 133
10.2條件概率 .......................................................................................... 141
10.3隨機變量 .......................................................................................... 143
目錄
10.4二項分佈和幾何分佈 .......................................................................... 149
10.5參考資料 .......................................................................................... 153
第三部分數學結構
第 11章布爾代數........................................................................................... 157
11.1布爾函數及其表達形式 ...................................................................... 157
11.2布爾代數的定義 ................................................................................ 163
11.3布爾代數示例 .................................................................................... 164
11.4布爾代數的性質 ................................................................................ 170
11.5布爾代數中的偏序 ............................................................................. 174
11.6布爾代數的原子 ................................................................................ 176
11.7布爾表達式的規範形式 ...................................................................... 180
11.8最小化布爾表達式 ............................................................................. 182
11.9同構基本定理 .................................................................................... 184
11.10電路代數 ......................................................................................... 188
第 12章圖和樹 .............................................................................................. 193
12.1基本概念 .......................................................................................... 194
12.2圖中的通路和迴路 ............................................................................. 199
12.3圖和矩陣 .......................................................................................... 203
12.4圖同構 .............................................................................................. 210
12.5樹 .................................................................................................... 212
第 13章命題邏輯........................................................................................... 218
13.1布爾代數和命題邏輯 .......................................................................... 218
13.2範式 ................................................................................................. 223
13.3可滿足性等價公式 ............................................................................. 225
13.4不可滿足的子句集合 .......................................................................... 229
13.5霍恩子句的可滿足性 .......................................................................... 232
13.6歸結原理 .......................................................................................... 235
13.7 2KNF中的子句集 ............................................................................. 242
第 14章模算術 .............................................................................................. 245
14.1因數關系 .......................................................................................... 246
14.2模的加法和乘法 ................................................................................ 249
14.3模運算 .............................................................................................. 253
電腦數學基礎 (第 6版)
14.4最大公因數和歐幾里得算法 ................................................................ 257
14.5費馬小定理 ....................................................................................... 261
14.6使用費馬小定理的加密 ...................................................................... 265
14.7 RSA加密算法 .................................................................................. 270
14.8參考資料 .......................................................................................... 272
