Advanced calculus
by Harold M. Edwards · first published 1969
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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…
on “Differential Forms and Integration (2008) [pdf]” ↗…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…
on “The Most Common Errors in Undergraduate Mathematics (2009)” ↗…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.
on “Ask HN: Recommend a maths book for a teenager?” ↗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/
on “What Is Applied Category Theory? (2018)” ↗…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.
on “Notation as a Tool of Thought (1979)” ↗…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…
on “Ask HN: Books you read in 2018?” ↗Harold Edwards: Advanced Calculus: A Differential Forms Approach (https://www.maa.org/press/maa-reviews/advanced-calculus-a-di....) Tristan Needham: Visual Complex Analysis (https://www.maa.org/press/maa-reviews/visual-complex-analysi...)…
on “Ask HN: Math books you recommend just for the way they are written?” ↗