Conceptual Mathematics: A First Introduction to Categories

Conceptual Mathematics: A First Introduction to Categories pdf epub mobi txt 电子书 下载 2025

出版者:Cambridge University Press
作者:F. William Lawvere
出品人:
页数:408
译者:
出版时间:2009-8-31
价格:USD 65.00
装帧:Paperback
isbn号码:9780521719162
丛书系列:
图书标签:
  • 范畴论
  • 数学
  • Category
  • 数学-范畴论
  • Mathematics
  • 入门
  • 计算机
  • 范畴
  • 数学
  • 范畴论
  • 抽象代数
  • 逻辑学
  • 数学基础
  • 结构主义
  • 数学哲学
  • 现代数学
  • 教育
  • 入门
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具体描述

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics, Second Edition, introduces the concept of ’category’ for the learning, development, and use of mathematics, to both beginning students and general readers, and to practicing mathematical scientists. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories.

作者简介

F. William Lawvere, State University of New York, Buffalo

F. William Lawvere is a Professor Emeritus of Mathematics at the State University of New York. He has previously held positions at Reed College, the University of Chicago and the City University of New York, as well as visiting Professorships at other institutions worldwide. At the 1970 International Congress of Mathematicians in Nice, Prof. Lawvere delivered an invited lecture in which he introduced an algebraic version of topos theory which united several previously 'unrelated' areas in geometry and in set theory; over a dozen books, several dozen international meetings, and hundreds of research papers have since appeared, continuing to develop the consequences of that unification.

Stephen H. Schanuel, State University of New York, Buffalo

Stephen H. Schanuel is a Professor of Mathematics at the State University of New York at Buffalo. He has previously held positions at Johns Hopkins University, Institute for Advanced Study and Cornell University, as well as lecturing at institutions in Denmark, Switzerland, Germany, Italy, Colombia, Canada, Ireland, and Australia. Best known for Schanuel's Lemma in homological algebra (and related work with Bass on the beginning of algebraic K–theory), and for Schanuel's Conjecture on algebraic independence and the exponential function, his research thus wanders from algebra to number theory to analysis to geometry and topology.

目录信息

Foreword
Note to the reader
Preview
Part I. The Category of Sets:
1. Sets, maps, composition
Part II. The Algebra of Composition:
2. Isomorphisms
Part III. Categories of Structured Sets:
3. Examples of categories
Part IV. Elementary Universal Mapping Properties:
4. Universal mapping properties
Part V. Higher Universal Mapping Properties:
5. Map objects
6. The contravariant parts functor
7. The components functor
Appendix 1. Geometry of figures and algebra of functions
Appendix 2. Adjoint functors
Appendix 3. The emergence of category theory within mathematics
Appendix 4. Annotated bibliography.
· · · · · · (收起)

读后感

评分

范畴论入门,据说是高中生就能看明白,我看到第三部分不小心就迷糊了,要多看几遍,练习要一道一道的来才行,否则就看着看着觉得自己还是懂的,然后就不懂了。 总体不简单,略陡峭,里面还有一些范畴在物理上应用的介绍。

评分

范畴论入门,据说是高中生就能看明白,我看到第三部分不小心就迷糊了,要多看几遍,练习要一道一道的来才行,否则就看着看着觉得自己还是懂的,然后就不懂了。 总体不简单,略陡峭,里面还有一些范畴在物理上应用的介绍。

评分

范畴论入门,据说是高中生就能看明白,我看到第三部分不小心就迷糊了,要多看几遍,练习要一道一道的来才行,否则就看着看着觉得自己还是懂的,然后就不懂了。 总体不简单,略陡峭,里面还有一些范畴在物理上应用的介绍。

评分

范畴论入门,据说是高中生就能看明白,我看到第三部分不小心就迷糊了,要多看几遍,练习要一道一道的来才行,否则就看着看着觉得自己还是懂的,然后就不懂了。 总体不简单,略陡峭,里面还有一些范畴在物理上应用的介绍。

评分

范畴论入门,据说是高中生就能看明白,我看到第三部分不小心就迷糊了,要多看几遍,练习要一道一道的来才行,否则就看着看着觉得自己还是懂的,然后就不懂了。 总体不简单,略陡峭,里面还有一些范畴在物理上应用的介绍。

用户评价

评分

Not really a fan... will definitely come back though.

评分

满分!就喜欢这种深入浅出讲数学的。

评分

全书叙述以学生与老师对话的形式展开,是范畴论入门的初等教材

评分

满分!就喜欢这种深入浅出讲数学的。

评分

Not really a fan... will definitely come back though.

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