向量微积分、线性代数与微分形式
Vector calculus, linear algebra, and differential forms
Hubbard, John H.、John H. Hubbard、Barbara Burke Hubbard · 初版 1999 年
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为什么值得读
- 从基础出发将向量微积分与代数等领域统合发展
- 保持严格数学证明并强调第一性原理推导
- 打破狭隘学科界限建立不同数学分支的深层联系
Hacker News 上怎么说
正在加载完整评论……
……视角太狭窄的话，就会错失不同领域之间那些美妙的联系，而正是这些联系能改变我们思考问题的角度。大概两年前我也遇到过类似的情况。去读读 Hubbard 和 Hubbard 写的《Vector Calculus, Linear Algebra, and Differential Forms》吧，你绝对不会失望的。没准，它既有（足够的）严谨性，又有大量基于第一性原理的数学推导。不仅如此，作者还找到了一种绝妙的方式，将极其丰富的……
…too narrow focus one looses these lovely connections between different fields that allow to change the perspective on how we think about problems. I was in a similar situation some 2 years ago. Try "Vector Calculus, Linear Algebra, and Differential Forms" by Hubbard and Hubbard. You will not be disappointed. Yes, you get (enough) rigor and a lot of first principles mathematics. Nonetheless, the authors have found a lovely way to integrate a wealth of…
……Halmos 写的《Finite-Dimensional Vector Spaces》，但这本难度更大。可惜的是 Axler 的最新版加了些容易让人分心的插图和线框，破坏了它原本的一些 TeX 极简优雅感。你也可以用 Hubbard & Hubbard 的《Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach》一举替换掉这两本书。另一条路线是参加一个主攻逻辑和抽象代数的 bootcamp。我还没见过面向初学者开这种课的，但我认为……
…Finite-Dimensional Vector Spaces by Halmos. But it's harder. Sadly the latest edition of Axler has distracting pictures and boxes that have done away with some of it's TeX elegance. You can also replace both books by Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, by Hubbard & Hubbard. An alternative route is to do a bootcamp where logic and abstract algebra is the area of focus. I've never seen such a course offered to beginners, but I think…
对我来说最好的一本书就是 Hubbard 和 Hubbard 写的《Vector Calculus, Linear Algebra, and Differential Forms》。这是（据我所知）唯一一本能带你从零基础一路走到把书名里这些学科融会贯通的书。而且这种融会贯通真的能引向……
The best book for me was "Vector Calculus, Linear Algebra, and Differential Forms" by Hubbard and Hubbard. It is the only book (I know of) that brings you from absolute basics to an integrated development of the subjects from its title. And that integrated developments actually leads…
……以及 Tu 的《Differential Forms in Algebraic Topology》，Springer，1982年版。重点看 1.1-1.3。* 同样很有用的还有：H. M. Schey 的《Div, Grad Curl and All That》，Norton，2005年版。* 还有：Hubbard 和 Hubbard 的《Vector Calculus, Linear Algebra and Differential Forms》，Prentice Hall 1999年版。* 以及：T. Needham 的《Visual Complex Analysis》，牛津大学出版社，1997年版。
…and Tu, Differential Forms in Algebraic Topology , Springer, 1982. See especially 1.1-1.3. * Also useful: H. M. Schey, Div, Grad Curl and All That , Norton, 2005. * Also useful: Hubbard and Hubbard, Vector Calculus, Linear Algebra and Differential Forms, Prentice Hall 1999. * Also useful: T. Needham, Visual Complex Analysis , Oxford University Press, 1997.
……但要不是读了它，我觉得自己现在绝不可能对它们这么投入。我也听说过关于《Measurement》的很多好评，不过自己还没读过。我读过的另一本极棒的数学书是《Vector Calculus, Linear Algebra, and Differential Forms》，虽然要是让一个14岁的人去硬啃，估计会挺受打击的。补一句：另外回想起来，我记得自己十几岁的时候焦虑得不行，因为感觉有太多……
…but don't think I'd be nearly involved with them as I am now had I not read it. I've also heard great things about Measurement but haven't read it myself. Another great math book that I have read is Vector Calculus, Linear Algebra, and Differential Forms, though trying to get through that at 14 would probably be a bit disheartening. Edited to add: Also, looking back I remember how stressed I was as a teenager because it seemed like there was so much…
我觉得 Barbara Burke Hubbard 和 John H. Hubbard 写的《Vector Calculus, Linear Algebra, and Differential Forms》就是一个很好的例子。https://www.amazon.com/Vector-Calculus-Linear-Algebra-Differ...
Vector Calculus, Linear Algebra, and Differential Forms by Barbara Burke Hubbard and John H. Hubbard is a good example I think. https://www.amazon.com/Vector-Calculus-Linear-Algebra-Differ...