对于任何想进一步了解这一点的人，我强烈推荐 Harold Edwards 的《Advanced Calculus: A Differential Forms Approach》和 Loring Tu 的《An Introduction to Manifolds》。前者读起来几乎像小说，是数学阐述的真正享受。它也有点……
For anyone wanting to learn more about this, I highly recommend Advanced Calculus: A Differential Forms Approach by Harold Edwards and An Introduction to Manifolds by Loring Tu. The former reads almost like a novel and is a real treat of mathematical exposition. It's also a little…
……为后面部分打下的基础层。金字塔是个错误的比喻。在我看来，学习数学应该像创作一幅画。我所知道的最好的例子之一是 Harold Edwards 的《Advanced Calculus: A Differential Forms Approach》。前三章以启发式的方式介绍材料。接下来的三章绕回这些材料，彻底证明所介绍的一切……
…foundational layers for the later portions. A pyramid is the wrong metaphor. In my opinion, learning mathematics should be like creating a painting. One of the best examples of this I know of is the book Advanced Calculus: A Differential Forms Approach by Harold Edwards. The first three chapters introduce the material heuristically. The next three chapters circle back on the material, thoroughly proving everything introduced…
……等等）会有助于提供所需的背景知识。《Conceptual Mathematics》这本书据称是面向高中生的。也许可以试一试，看看会怎样。如果他们懂微积分，那么 Harold Edwards 的《Advanced Calculus: A Differential Forms Approach》是一颗宝石。前三章应该可读，因为它们对该主题进行了启发式的讨论。
…etc.) would help provide the needed background. The book Conceptual Mathematics is claimed to be aimed at high school students. Maybe give it a whirl and see what happens. If they know calculus, then Advanced Calculus: A Differential Forms Approach by Harold Edwards is a gem. The first three chapters should be readable, as they give heuristic discussions of the topic.
你可能会喜欢《Conceptual Mathematics: A First Introduction to Categories》、《Creative Mathematics》、《Advanced Calculus: A Differential Forms Approach》和《Geomtrical Vectors》这些书。https://www.amazon.com/dp/052171916X/ https://www.amazon.com/dp/0883857502/ https://www.amazon.com/dp/0817637079/ https://www.amazon.com/dp/0226890481/
You may like the books Conceptual Mathematics: A First Introduction to Categories, Creative Mathematics, Advanced Calculus: A Differential Forms Approach, and Geomtrical Vectors. https://www.amazon.com/dp/052171916X/ https://www.amazon.com/dp/0883857502/ https://www.amazon.com/dp/0817637079/ https://www.amazon.com/dp/0226890481/
……1-流形，所以 dx 确实有那个含义，但你需要理解微分形式是什么才能明白这一点。不过不一定需要光滑流形的完整一般性。Harold Edwards 的《Advanced Calculus: A Differential Forms Approach》和《Advanced Calculus: A Geometric View》为欧几里得流形讲授微分形式。
…1-manifold, so dx does have that meaning, but you need to understand what a differential form is to know that. One doesn't necessarily need the full generality of smooth manifolds though. Harold Edwards' Advanced Calculus: A Differential Forms Approach and Advanced Calculus: A Geometric View teach differential forms for Euclidean manifolds.
……电影。书中，仿生人是纯粹理性的存在，而电影则给他们裹上了一层浪漫主义的光环。18. 《How we learn》（Benedict Carey）——数十年的学习研究浓缩于一本书 19. 《Advanced Calculus: A Differential Forms Approach》（Harold M. Edwards）——我读过的最好的数学书！对我来说，它从根本上打开了眼界。Edwards 真是一位有天赋的老师。20. 《Three men in a boat》（Jerome……
…films. In the book androids are purely rational beings, whereas the film wraps them in an aura of romanticism. 18. How we learn (Benedict Carey) - decades of learning research condensed in a book 19. Advanced Calculus: A Differential Forms Approach (Harold M. Edwards) - the best math book I've read so far! For me it was eye-opening in a fundamental way. Edwards is truly a gifted teacher. 20. Three men in a boat (Jerome…
对于任何想进一步了解这一点的人，我强烈推荐 Harold Edwards 的《Advanced Calculus: A Differential Forms Approach》和 Loring Tu 的《An Introduction to Manifolds》。前者读起来几乎像小说，是数学阐述的真正享受。它也有点……
For anyone wanting to learn more about this, I highly recommend Advanced Calculus: A Differential Forms Approach by Harold Edwards and An Introduction to Manifolds by Loring Tu. The former reads almost like a novel and is a real treat of mathematical exposition. It's also a little…
……为后面部分打下的基础层。金字塔是个错误的比喻。在我看来，学习数学应该像创作一幅画。我所知道的最好的例子之一是 Harold Edwards 的《Advanced Calculus: A Differential Forms Approach》。前三章以启发式的方式介绍材料。接下来的三章绕回这些材料，彻底证明所介绍的一切……
…foundational layers for the later portions. A pyramid is the wrong metaphor. In my opinion, learning mathematics should be like creating a painting. One of the best examples of this I know of is the book Advanced Calculus: A Differential Forms Approach by Harold Edwards. The first three chapters introduce the material heuristically. The next three chapters circle back on the material, thoroughly proving everything introduced…
……等等）会有助于提供所需的背景知识。《Conceptual Mathematics》这本书据称是面向高中生的。也许可以试一试，看看会怎样。如果他们懂微积分，那么 Harold Edwards 的《Advanced Calculus: A Differential Forms Approach》是一颗宝石。前三章应该可读，因为它们对该主题进行了启发式的讨论。
…etc.) would help provide the needed background. The book Conceptual Mathematics is claimed to be aimed at high school students. Maybe give it a whirl and see what happens. If they know calculus, then Advanced Calculus: A Differential Forms Approach by Harold Edwards is a gem. The first three chapters should be readable, as they give heuristic discussions of the topic.
你可能会喜欢《Conceptual Mathematics: A First Introduction to Categories》、《Creative Mathematics》、《Advanced Calculus: A Differential Forms Approach》和《Geomtrical Vectors》这些书。https://www.amazon.com/dp/052171916X/ https://www.amazon.com/dp/0883857502/ https://www.amazon.com/dp/0817637079/ https://www.amazon.com/dp/0226890481/
You may like the books Conceptual Mathematics: A First Introduction to Categories, Creative Mathematics, Advanced Calculus: A Differential Forms Approach, and Geomtrical Vectors. https://www.amazon.com/dp/052171916X/ https://www.amazon.com/dp/0883857502/ https://www.amazon.com/dp/0817637079/ https://www.amazon.com/dp/0226890481/
……1-流形，所以 dx 确实有那个含义，但你需要理解微分形式是什么才能明白这一点。不过不一定需要光滑流形的完整一般性。Harold Edwards 的《Advanced Calculus: A Differential Forms Approach》和《Advanced Calculus: A Geometric View》为欧几里得流形讲授微分形式。
…1-manifold, so dx does have that meaning, but you need to understand what a differential form is to know that. One doesn't necessarily need the full generality of smooth manifolds though. Harold Edwards' Advanced Calculus: A Differential Forms Approach and Advanced Calculus: A Geometric View teach differential forms for Euclidean manifolds.
……电影。书中，仿生人是纯粹理性的存在，而电影则给他们裹上了一层浪漫主义的光环。18. 《How we learn》（Benedict Carey）——数十年的学习研究浓缩于一本书 19. 《Advanced Calculus: A Differential Forms Approach》（Harold M. Edwards）——我读过的最好的数学书！对我来说，它从根本上打开了眼界。Edwards 真是一位有天赋的老师。20. 《Three men in a boat》（Jerome……
…films. In the book androids are purely rational beings, whereas the film wraps them in an aura of romanticism. 18. How we learn (Benedict Carey) - decades of learning research condensed in a book 19. Advanced Calculus: A Differential Forms Approach (Harold M. Edwards) - the best math book I've read so far! For me it was eye-opening in a fundamental way. Edwards is truly a gifted teacher. 20. Three men in a boat (Jerome…