数学要素
Elements of Mathematics
John C. Stillwell · 初版 2016 年
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Elements of Mathematics 带领读者展开一场引人入胜的探索之旅，它始于初等数学，但正如 John Stillwell 所指出的，这门学科并不像人们想象的那样基础或浅显。如今初等数学中包含的主题并非自古就如此归类，只有在经历重大数学进展与发现之后，某些主题才得以成为“初等”内容。Stillwell 从独特的 21 世纪视角审视初等数学，不仅描绘了该学科的美感与广度，还指出了它的局限性。从高斯
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看起来和 John Stillwell 的经典之作《数学的要素：从欧几里得到哥德尔》很像 - https://press.princeton.edu/books/hardcover/9780691171685/el... 这本书给算术、计算、代数、几何、微积分、组合学、概率论、数理逻辑各安排了一章……
Seems similar to John Stillwell's classic Elements of Mathematics: From Euclid to Gödel - https://press.princeton.edu/books/hardcover/9780691171685/el... It has one chapter each for Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, Logic.…
你可能会觉得我在其他评论里提到的这两本书挺有用的：Ian Stewart 的《现代数学概念》（Concepts of Modern Mathematics）- https://store.doverpublications.com/products/9780486284248；John Stillwell 的《数学的要素：从欧几里得到哥德尔》- https://press.princeton.edu/books/hardcover/9780691171685/el... 两本书都对现代数学的各个领域及其相互关系进行了非常精彩的梳理……
You might find the couple of books that i mention in my other comments here useful; Concepts of Modern Mathematics by Ian Stewart - https://store.doverpublications.com/products/9780486284248 Elements of Mathematics: From Euclid to Gödel by John Stillwell - https://press.princeton.edu/books/hardcover/9780691171685/el... Both of them give a nice tour of various domains within modern mathematics and their inter-relationships…
……Jeremy Kun 的数学书范围很广，如果你也对编程感兴趣的话就很合适。如果历史也是你的心头好，Edna Kramer 的《现代数学的本质与发展》（Nature and Growth of Modern Mathematics）是一本极好的书。John Stillwell 的《数学的要素》对各个学科做了广泛的综述，读起来有一种清爽干脆的数学味。John 和 Barbara Hubbard 合著的《向量微积分、线性代数和微分形式》则是一本极佳的入门……
…Mathematics by Jeremy Kun is wide ranging and appropriate if there is also interest in programming. Nature and Growth of Modern Mathematics by Edna Kramer is a wonderful book if history is a passion as well. Elements of Mathematics by John Stillwell is a broad overview of subjects. It has a crisp mathematical feel to it. Vector Calculus, Linear Algebra, and Differential Forms by John & Barbara Hubbard is a beautiful introduction…
……物有所值。2) Aleksandrov、Kolmogorov 等人合著的《数学：它的内容、方法和意义》（Mathematics: Its Content, Methods and Meaning）——基础数学领域绝对神级的全景概览。Dover 出版的，所以超级便宜。3) John Stillwell 的《数学的要素：从欧几里得到哥德尔》——写得就像是对伟大的菲利克斯·克莱因《高观点下的初等数学》一书的某种现代升级。选题尤其出彩，考虑到……
…worth the money. 2) Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov et al. - Absolutely brilliant overview of Basic Mathematics. Published by Dover and hence very affordable. 3) Elements of Mathematics: From Euclid to Gödel by John Stillwell - Written as sort of an update to the great Felix Klein's Elementary Mathematics from an Advanced Standpoint books. The Topics are particularly well chosen given…
修定的 Stewart 版本基本上没变，只是 Stewart 加了一篇序言，以及一个 37 页的章节“最新进展”。John Stillwell 也有一本很不错的通识书《数学的要素：从欧几里得到哥德尔》（Elements of Mathematics From Euclid to Gödel）。
The revised Stuart edition nothing is changed except Stewart has added a preface, and a 37 page chapter "Recent Developments". John Stillwell also has a good survey book "Elements of Mathematics From Euclid to Gödel"
……直觉和情境来解决数学问题。Pask - 《伟大的原理》（Magnificent Principia），带你领略牛顿的《原理》，既包含了牛顿原本的几何语言，也涵盖了现代向量微积分版本。Stillwell - 《数学的要素》，探讨了数学史上源自 8 个学科的一些重要经典问题：算术、计算、代数、几何、微积分、组合学、概率论、数理逻辑。太赞了！Yandell……
…intuitions and scenarios to solve mathematical problems. Pask - Magnificent Principia. Tour of newtons principia that includes both newtons geometric language and modern vector calculus version. Stillwell - Elements of Mathematics. Discusses some important classical problems in the history of mathematics taken from 8 subjects: arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, logic. Wow! Yandell…