图书标签: 范畴论 数学 category-theory Math Category 代数 category_theory 范畴
发表于2024-12-23
Category Theory for the Sciences pdf epub mobi txt 电子书 下载 2024
Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs -- categories in disguise. After explaining the "big three" concepts of category theory -- categories, functors, and natural transformations -- the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with selected solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
David I. Spivak is a Research Scientist in the Department of Mathematics at MIT.
約是目前唯一的面向科學界又不走科普風的範疇論書籍,內含物理、化學、生物等領域範例,能有效幫助讀者了解範疇論的可能應用場景。只是進度有些緩慢,前面幾章一直「賣關子」(Spivak的書都有此特點),且整體偏重數據庫應用(與作者研究興趣有關),以至於把書名改為「data science」也不為過。不建議作為正式教材學習,更適合有一定基礎後閱讀開闊視野(可與Fong & Spivak 2018結合)。
评分范畴理论在数学中的历史。尽管有其他学科也关注范畴,但本书都没有细谈。因此我也就没有细看了……
评分introductory examples of applying category theory in science
评分introductory examples of applying category theory in science
评分范畴理论在数学中的历史。尽管有其他学科也关注范畴,但本书都没有细谈。因此我也就没有细看了……
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Category Theory for the Sciences pdf epub mobi txt 电子书 下载 2024