Visual Differential Geometry and Forms
by Tristan Needham · first published 2021
80% recommend20% neutral
Why HN recommends it
Visual, diagram-driven introduction to differential geometry and differential forms, built to develop spatial intuition. It requires little formal mathematics, suiting engineers and self-learners.
Summarised by Claude from recommending comments
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…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...) Tristan Needham: Visual Differential Geometry and Forms (https://press.princeton.edu/books/paperback/9780691203706/vi...)
on “Ask HN: Math books you recommend just for the way they are written?” ↗> I still don’t have much intuition for k-vectors and k-forms The references that you cite are great. Also Tristan Needham's book "Visual Differential Geometry and Forms", or the classic "Gravitation" where this visual language was fist exposed. Besides this continuous interpretation, you may also enjoy further insight via the discrete case, called "discrete exterior…
on “The Visualization of Differential Forms (2021)” ↗There also is the excellent book "Visual Differential Geometry and Forms" by Tristan Needham, which takes a similar visual intuitive explanation style. Also it features pictures of fruit pierced by lots of toothpicks.
on “A pictorial introduction to differential geometry (2017)” ↗…I find it tough going. Some books I liked for self study because they have answers: Introduction to Analysis, Mattock. Elementary Differential Geometry, Pressley. There is also recently Needham's Visual Differential Geometry and Forms, which is great. Edit: I should also mention Topology without Tears (free, online, very good) https://www.topologywithouttears.net/
on “So you want to study mathematics” ↗…to Analysis (Mattuck) - Elementary Differential Geometry (Pressley) both chosen because they have solutions in the book, which I find important for self-study. Also just got (hot off the presses) Visual Differential Geometry and Forms (Needham) Looks fantastic! Topology is next on the list...
on “Ask HN: Technical Summer Reading List” ↗…perpetual motion machine. Also makes me glad I moved into IT, though the bug never leaves you, for anyone in a similar position this is a wonderful book on general rel, and requires very little maths - "Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts"
on “What I learned as a hired consultant to autodidact physicists (2016)” ↗…had more geometry in their curriculum, I've noticed they don't have that intuitive spatial connection to reality other than through CAD or their lived experience. I am reading Tristran Needham's book, "Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts", and it is amazing. I love Sir Michael Atiyah's famous quote that Neeham uses at the start of the book: "Algebra is the offer made by the devil to the mathematician.…
on “The Geometry of Polynomials (2018)” ↗You will possibly like Needham's "Visual Differential Geometry and Forms" and even if you don't have much time to study it, it's quite beautiful to look at from time to time.
on “A pictorial introduction to differential geometry (2017)” ↗Needham is great and his Visual Differential Geometry and Forms is excellent.
on “Möbius Strips and Differential Equations” ↗As if. Take a look at the very first line in the description for the book "Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts". "FROM THE AUTHOR: All legitimate copies of VDGF produced by Princeton University Press are crisply printed on high-quality paper. If you obtain a shoddily printed…
on “Federal regulator says Amazon can be held responsible for faulty goods” ↗There is now also "Visual Differential Geometry and Forms", also by Needham.
on “Visual calculus” ↗