普林斯顿数学指南.第三卷
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ISBN：9787030395283
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简介
《普林斯顿数学指南（第三卷）》是由Fields 奖得主T. Gowers 主编、133 位著名数学家共同参与撰写的大型文集. 《普林斯顿数学指南（第三卷）》由288 篇长篇论文和短篇条目构成, 目的是对20 世纪最后一二十年纯粹数学的发展给出一个概览, 以帮助青年数学家学习和研究其最活跃的部分, 这些论文和条目都可以独立阅读. 原书有八个部分, 除第Ⅰ部分是一个简短的引论、第Ⅷ部分是《普林斯顿数学指南（第三卷）》的“终曲”以外, 《普林斯顿数学指南（第三卷）》分为三大板块, 核心是第Ⅳ部分“数学的各个分支”, 共26 篇长文, 介绍了20 世纪最后一二十年纯粹数学研究中最重要的成果和最活跃的领域, 第Ⅲ部分“数学概念”和第Ⅴ部分“定理与问题”都是为它服务的短条目. 第二个板块是数学的历史, 由第Ⅱ部分“现代数学的起源”(共7 篇长文)和第Ⅵ部分“数学家传记”(96 位数学家的短篇传记)组成. 第三个板块是数学的应用, 即第Ⅶ部分“数学的影响”(14 篇长文章). 作为《普林斯顿数学指南（第三卷）》“终曲”的第Ⅷ部分“结束语：一些看法”则是对青年数学家的建议等7 篇文章.
中译本分为三卷, 第一卷包括第Ⅰ~Ⅲ部分, 第二卷即第Ⅳ部分, 第三卷包括第Ⅴ~Ⅷ部分.
目录
译者序序撰稿人第Ⅴ
部分定理与问题.......................................................... 1
Ⅴ.1ABC猜想............................................................. 1
Ⅴ.2阿蒂亚–辛格指标定理.................................................2
Ⅴ.3巴拿赫–塔尔斯基悖论.................................................6
Ⅴ.4Birch-Swinnerton-Dyer猜想........................................... 8
Ⅴ.5卡尔松定理........................................................... 9
Ⅴ.6中心极限定理........................................................ 11
Ⅴ.7有限单群的分类..................................................... 12
Ⅴ.8狄利克雷素数定理................................................... 14
Ⅴ.9遍历定理.............................................................14
Ⅴ.10费马大定理......................................................... 19
Ⅴ.11不动点定理......................................................... 21
Ⅴ.12四色定理........................................................... 27
Ⅴ.13代数的基本定理.................................................... 31
Ⅴ.14算术的基本定理.................................................... 32
Ⅴ.15哥德尔定理......................................................... 33
Ⅴ.16Gromov多项式增长性定理......................................... 37
Ⅴ.17希尔伯特零点定理.................................................. 38
Ⅴ.18连续统假设的独立性............................................... 38
Ⅴ.19不等式.............................................................. 39
Ⅴ.20停机问题的不可解性............................................... 44
Ⅴ.21五次方程的不可解性............................................... 48
Ⅴ.22刘维尔定理和罗特定理............................................. 50
Ⅴ.23Mostow强刚性定理.................................................52
Ⅴ.24P 对NP 问题...................................................... 56
Ⅴ.25庞加莱猜想......................................................... 56
Ⅴ.26素数定理与黎曼假设............................................... 57
Ⅴ.27加法数论的问题与结果............................................. 58
Ⅴ.28从二次互反性到类域理论........................................... 63
Ⅴ.29曲线上的有理点与莫德尔猜想...................................... 68
Ⅴ.30奇异性的消解.......................................................71
Ⅴ.31黎曼–罗赫定理......................................................72
Ⅴ.32Robertson-Seymour定理............................................ 74
Ⅴ.33三体问题........................................................... 76
Ⅴ.34单值化定理......................................................... 80
Ⅴ.35韦伊猜想........................................................... 81
第Ⅵ
部分数学家传记......................................................... 87
Ⅵ.1毕达哥拉斯.......................................................... 87
Ⅵ.2欧几里得.............................................................88
Ⅵ.3阿基米德.............................................................90
Ⅵ.4阿波罗尼乌斯........................................................ 91
Ⅵ.5阿尔花拉子米..................................................... 93
Ⅵ.6斐波那契.............................................................94
Ⅵ.7卡尔达诺.............................................................94
Ⅵ.8庞贝里............................................................... 95
Ⅵ.9维特................................................................. 95
Ⅵ.10斯特凡.............................................................. 97
Ⅵ.11笛卡儿.............................................................. 97
Ⅵ.12费马............................................................... 100
Ⅵ.13帕斯卡.............................................................102
Ⅵ.14牛顿............................................................... 103
Ⅵ.15莱布尼兹.......................................................... 105
Ⅵ.16泰勒............................................................... 108
Ⅵ.17哥德巴赫.......................................................... 109
Ⅵ.18伯努利家族........................................................ 109
Ⅵ.19欧拉............................................................... 112
Ⅵ.20达朗贝尔.......................................................... 116
Ⅵ.21华林............................................................... 118
Ⅵ.22拉格朗日.......................................................... 119
Ⅵ.23拉普拉斯.......................................................... 122
Ⅵ.24勒让德.............................................................124
Ⅵ.25傅里叶.............................................................126
Ⅵ.26高斯............................................................... 128
Ⅵ.27泊松............................................................... 129
Ⅵ.28波尔扎诺.......................................................... 131
Ⅵ.29柯西............................................................... 132
Ⅵ.30莫比乌斯.......................................................... 133
Ⅵ.31罗巴切夫斯基......................................................134
Ⅵ.32格林............................................................... 136
Ⅵ.33阿贝尔.............................................................137
Ⅵ.34鲍耶伊.............................................................139
Ⅵ.35雅可比.............................................................140
Ⅵ.36狄利克雷.......................................................... 142
Ⅵ.37哈密顿.............................................................144
Ⅵ.38德摩根.......................................................... 145
Ⅵ.39刘维尔.............................................................145
Ⅵ.40库默尔.............................................................147
Ⅵ.41伽罗瓦.............................................................148
Ⅵ.42西尔维斯特........................................................ 150
Ⅵ.43布尔............................................................... 152
Ⅵ.44魏尔斯特拉斯......................................................154
Ⅵ.45切比雪夫.......................................................... 155
Ⅵ.46凯莱............................................................... 156
Ⅵ.47厄尔米特.......................................................... 158
Ⅵ.48克罗内克.......................................................... 159
Ⅵ.49黎曼............................................................... 161
Ⅵ.50戴德金.............................................................163
Ⅵ.51马蒂厄.............................................................165
Ⅵ.52约当............................................................... 165
Ⅵ.53李................................................................. 166
Ⅵ.54康托............................................................... 168
Ⅵ.55克利福德.......................................................... 171
Ⅵ.56弗雷格.............................................................172
Ⅵ.57克莱因.............................................................174
Ⅵ.58弗罗贝尼乌斯......................................................176
Ⅵ.59柯瓦列夫斯卡娅................................................... 177
Ⅵ.60伯恩塞德.......................................................... 179
Ⅵ.61庞加莱.............................................................180
Ⅵ.62佩亚诺.............................................................182
Ⅵ.63希尔伯特.......................................................... 183
Ⅵ.64闵可夫斯基........................................................ 186
Ⅵ.65阿达玛.............................................................187
Ⅵ.66弗雷德霍姆........................................................ 189
Ⅵ.67德拉瓦莱布散............................................... 189
.. .
Ⅵ.68豪斯道夫.......................................................... 191
Ⅵ.69嘉当............................................................... 192
Ⅵ.70博雷尔.............................................................194
Ⅵ.71罗素............................................................... 194
Ⅵ.72勒贝格.............................................................196
Ⅵ.73哈代............................................................... 197
Ⅵ.74里斯............................................................... 200
Ⅵ.75布劳威尔.......................................................... 201
Ⅵ.76艾米诺特........................................................ 203
.
Ⅵ.77谢尔品斯基........................................................ 205
Ⅵ.78伯克霍夫.......................................................... 206
Ⅵ.79李特尔伍德........................................................ 208
Ⅵ.80外尔............................................................... 211
Ⅵ.81斯科伦.............................................................213
Ⅵ.82拉马努金.......................................................... 214
Ⅵ.83柯朗............................................................... 216
Ⅵ.84巴拿赫.............................................................218
Ⅵ.85维纳............................................................... 221
Ⅵ.86阿廷............................................................... 223
Ⅵ.87塔尔斯基.......................................................... 225
Ⅵ.88科尔莫戈罗夫......................................................226
Ⅵ.89丘奇............................................................... 229
Ⅵ.90霍奇............................................................... 230
Ⅵ.91冯诺依曼........................................................ 231
.
Ⅵ.92哥德尔.............................................................234
Ⅵ.93韦伊............................................................... 235
Ⅵ.94图灵............................................................... 237
Ⅵ.95鲁宾逊.............................................................239
Ⅵ.96布尔巴基.......................................................... 241
第Ⅶ
部分数学的影响........................................................ 245
Ⅶ.1数学与化学......................................................... 245
Ⅶ.2数理生物学......................................................... 260
Ⅶ.3小波及其应用.......................................................276
Ⅶ.4网络中的流通的数学............................................... 298
Ⅶ.5算法设计的数学.................................................... 311
Ⅶ.6信息的可靠传输.................................................... 322
Ⅶ.7数学与密码......................................................... 335
Ⅶ.8数学和经济学的思考............................................... 349
Ⅶ.9货币的数学......................................................... 370
Ⅶ.10数理统计学........................................................ 381
Ⅶ.11数学与医学统计................................................... 389
Ⅶ.12数学的分析与哲学的分析..........................................399
Ⅶ.13数学与音乐........................................................ 411
Ⅶ.14数学与艺术........................................................ 425
第Ⅷ
部分卷末的话：一些看法............................................... 446
Ⅷ.1解题的艺术......................................................... 446
Ⅷ.2您会问“数学是为了什么？”....................................... 464
Ⅷ.3数学的无处不在.................................................... 482
Ⅷ.4数的意识........................................................... 492
Ⅷ.5数学:一门实验科学................................................ 505
Ⅷ.6对青年数学家的建议............................................... 519
Ⅷ.7数学大事年表.......................................................534
显示全部信息
部分定理与问题.......................................................... 1
Ⅴ.1ABC猜想............................................................. 1
Ⅴ.2阿蒂亚–辛格指标定理.................................................2
Ⅴ.3巴拿赫–塔尔斯基悖论.................................................6
Ⅴ.4Birch-Swinnerton-Dyer猜想........................................... 8
Ⅴ.5卡尔松定理........................................................... 9
Ⅴ.6中心极限定理........................................................ 11
Ⅴ.7有限单群的分类..................................................... 12
Ⅴ.8狄利克雷素数定理................................................... 14
Ⅴ.9遍历定理.............................................................14
Ⅴ.10费马大定理......................................................... 19
Ⅴ.11不动点定理......................................................... 21
Ⅴ.12四色定理........................................................... 27
Ⅴ.13代数的基本定理.................................................... 31
Ⅴ.14算术的基本定理.................................................... 32
Ⅴ.15哥德尔定理......................................................... 33
Ⅴ.16Gromov多项式增长性定理......................................... 37
Ⅴ.17希尔伯特零点定理.................................................. 38
Ⅴ.18连续统假设的独立性............................................... 38
Ⅴ.19不等式.............................................................. 39
Ⅴ.20停机问题的不可解性............................................... 44
Ⅴ.21五次方程的不可解性............................................... 48
Ⅴ.22刘维尔定理和罗特定理............................................. 50
Ⅴ.23Mostow强刚性定理.................................................52
Ⅴ.24P 对NP 问题...................................................... 56
Ⅴ.25庞加莱猜想......................................................... 56
Ⅴ.26素数定理与黎曼假设............................................... 57
Ⅴ.27加法数论的问题与结果............................................. 58
Ⅴ.28从二次互反性到类域理论........................................... 63
Ⅴ.29曲线上的有理点与莫德尔猜想...................................... 68
Ⅴ.30奇异性的消解.......................................................71
Ⅴ.31黎曼–罗赫定理......................................................72
Ⅴ.32Robertson-Seymour定理............................................ 74
Ⅴ.33三体问题........................................................... 76
Ⅴ.34单值化定理......................................................... 80
Ⅴ.35韦伊猜想........................................................... 81
第Ⅵ
部分数学家传记......................................................... 87
Ⅵ.1毕达哥拉斯.......................................................... 87
Ⅵ.2欧几里得.............................................................88
Ⅵ.3阿基米德.............................................................90
Ⅵ.4阿波罗尼乌斯........................................................ 91
Ⅵ.5阿尔花拉子米..................................................... 93
Ⅵ.6斐波那契.............................................................94
Ⅵ.7卡尔达诺.............................................................94
Ⅵ.8庞贝里............................................................... 95
Ⅵ.9维特................................................................. 95
Ⅵ.10斯特凡.............................................................. 97
Ⅵ.11笛卡儿.............................................................. 97
Ⅵ.12费马............................................................... 100
Ⅵ.13帕斯卡.............................................................102
Ⅵ.14牛顿............................................................... 103
Ⅵ.15莱布尼兹.......................................................... 105
Ⅵ.16泰勒............................................................... 108
Ⅵ.17哥德巴赫.......................................................... 109
Ⅵ.18伯努利家族........................................................ 109
Ⅵ.19欧拉............................................................... 112
Ⅵ.20达朗贝尔.......................................................... 116
Ⅵ.21华林............................................................... 118
Ⅵ.22拉格朗日.......................................................... 119
Ⅵ.23拉普拉斯.......................................................... 122
Ⅵ.24勒让德.............................................................124
Ⅵ.25傅里叶.............................................................126
Ⅵ.26高斯............................................................... 128
Ⅵ.27泊松............................................................... 129
Ⅵ.28波尔扎诺.......................................................... 131
Ⅵ.29柯西............................................................... 132
Ⅵ.30莫比乌斯.......................................................... 133
Ⅵ.31罗巴切夫斯基......................................................134
Ⅵ.32格林............................................................... 136
Ⅵ.33阿贝尔.............................................................137
Ⅵ.34鲍耶伊.............................................................139
Ⅵ.35雅可比.............................................................140
Ⅵ.36狄利克雷.......................................................... 142
Ⅵ.37哈密顿.............................................................144
Ⅵ.38德摩根.......................................................... 145
Ⅵ.39刘维尔.............................................................145
Ⅵ.40库默尔.............................................................147
Ⅵ.41伽罗瓦.............................................................148
Ⅵ.42西尔维斯特........................................................ 150
Ⅵ.43布尔............................................................... 152
Ⅵ.44魏尔斯特拉斯......................................................154
Ⅵ.45切比雪夫.......................................................... 155
Ⅵ.46凯莱............................................................... 156
Ⅵ.47厄尔米特.......................................................... 158
Ⅵ.48克罗内克.......................................................... 159
Ⅵ.49黎曼............................................................... 161
Ⅵ.50戴德金.............................................................163
Ⅵ.51马蒂厄.............................................................165
Ⅵ.52约当............................................................... 165
Ⅵ.53李................................................................. 166
Ⅵ.54康托............................................................... 168
Ⅵ.55克利福德.......................................................... 171
Ⅵ.56弗雷格.............................................................172
Ⅵ.57克莱因.............................................................174
Ⅵ.58弗罗贝尼乌斯......................................................176
Ⅵ.59柯瓦列夫斯卡娅................................................... 177
Ⅵ.60伯恩塞德.......................................................... 179
Ⅵ.61庞加莱.............................................................180
Ⅵ.62佩亚诺.............................................................182
Ⅵ.63希尔伯特.......................................................... 183
Ⅵ.64闵可夫斯基........................................................ 186
Ⅵ.65阿达玛.............................................................187
Ⅵ.66弗雷德霍姆........................................................ 189
Ⅵ.67德拉瓦莱布散............................................... 189
.. .
Ⅵ.68豪斯道夫.......................................................... 191
Ⅵ.69嘉当............................................................... 192
Ⅵ.70博雷尔.............................................................194
Ⅵ.71罗素............................................................... 194
Ⅵ.72勒贝格.............................................................196
Ⅵ.73哈代............................................................... 197
Ⅵ.74里斯............................................................... 200
Ⅵ.75布劳威尔.......................................................... 201
Ⅵ.76艾米诺特........................................................ 203
.
Ⅵ.77谢尔品斯基........................................................ 205
Ⅵ.78伯克霍夫.......................................................... 206
Ⅵ.79李特尔伍德........................................................ 208
Ⅵ.80外尔............................................................... 211
Ⅵ.81斯科伦.............................................................213
Ⅵ.82拉马努金.......................................................... 214
Ⅵ.83柯朗............................................................... 216
Ⅵ.84巴拿赫.............................................................218
Ⅵ.85维纳............................................................... 221
Ⅵ.86阿廷............................................................... 223
Ⅵ.87塔尔斯基.......................................................... 225
Ⅵ.88科尔莫戈罗夫......................................................226
Ⅵ.89丘奇............................................................... 229
Ⅵ.90霍奇............................................................... 230
Ⅵ.91冯诺依曼........................................................ 231
.
Ⅵ.92哥德尔.............................................................234
Ⅵ.93韦伊............................................................... 235
Ⅵ.94图灵............................................................... 237
Ⅵ.95鲁宾逊.............................................................239
Ⅵ.96布尔巴基.......................................................... 241
第Ⅶ
部分数学的影响........................................................ 245
Ⅶ.1数学与化学......................................................... 245
Ⅶ.2数理生物学......................................................... 260
Ⅶ.3小波及其应用.......................................................276
Ⅶ.4网络中的流通的数学............................................... 298
Ⅶ.5算法设计的数学.................................................... 311
Ⅶ.6信息的可靠传输.................................................... 322
Ⅶ.7数学与密码......................................................... 335
Ⅶ.8数学和经济学的思考............................................... 349
Ⅶ.9货币的数学......................................................... 370
Ⅶ.10数理统计学........................................................ 381
Ⅶ.11数学与医学统计................................................... 389
Ⅶ.12数学的分析与哲学的分析..........................................399
Ⅶ.13数学与音乐........................................................ 411
Ⅶ.14数学与艺术........................................................ 425
第Ⅷ
部分卷末的话：一些看法............................................... 446
Ⅷ.1解题的艺术......................................................... 446
Ⅷ.2您会问“数学是为了什么？”....................................... 464
Ⅷ.3数学的无处不在.................................................... 482
Ⅷ.4数的意识........................................................... 492
Ⅷ.5数学:一门实验科学................................................ 505
Ⅷ.6对青年数学家的建议............................................... 519
Ⅷ.7数学大事年表.......................................................534
显示全部信息
普林斯顿数学指南.第三卷
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