Sets for Mathematics 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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Lawvere, F. W./ Rosebrugh, Robert 作者

Cambridge Univ Pr

译者

2003-1 出版日期

276 页数

$ 75.71 价格

Pap

丛书系列

9780521010603 图书编码

Sets for Mathematics 在线电子书图书标签: 范畴论数理逻辑集合论物理数学基础思维哲学 nemlophics

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Sets for Mathematics 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. For the first time in a text, this book uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure of the axiom of choice. An appendix provides an explicit introduction to necessary concepts from logic, and an extensive glossary provides a window to the mathematical landscape.

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