Vector calculus, linear algebra, and differential forms
by Hubbard, John H., John H. Hubbard, Barbara Burke Hubbard · first published 1999
89% recommend11% neutral
Why HN recommends it
Unified, intuitive treatment that interleaves multivariable calculus, linear algebra and differential forms, with applied examples from physics and machine learning. Rigorous yet chatty and easier than alternatives.
Summarised by Claude from recommending comments
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
Mentions per year
What Hacker News says
Related books
2010–2022Yet another introduction to analysis
Victor Bryant
Recommended by 4 · mentioned by 44 recommend · 4 mention4 recommend · 44 recommend
2019–2022Introduction to Topological Manifolds
John M. Lee
Recommended by 2 · mentioned by 22 recommend · 2 mention2 recommend · 22 recommend
2020–2022Euler's Gem
David S. Richeson
Recommended by 2 · mentioned by 22 recommend · 2 mention2 recommend · 22 recommend
2020–2023Common Sense Mathematics
Ethan D. Bolker, Maura B. Mast
Recommended by 2 · mentioned by 22 recommend · 2 mention2 recommend · 22 recommend
STROUD:ENGINEERING MATHEMATICS
K. A. Stroud
Recommended by 3 · mentioned by 43 recommend · 4 mention3 recommend · 43 recommend
2018–2023Arithmetic
Paul Lockhart
Recommended by 4 · mentioned by 54 recommend · 5 mention4 recommend · 54 recommend
2008–2023Number theory
George E. Andrews
Recommended by 5 · mentioned by 65 recommend · 6 mention5 recommend · 65 recommend
…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…
on “Ask HN: How or where to begin learning mathematics from first principles?” ↗…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…
on “Any recommended crash course on Maths?” ↗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…
on “Ask HN: Serious mathematics books that can replace a good teacher?” ↗…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.
on “What do Bill Gates and Richard Stallman have in common ?” ↗…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…
on “What Would You Recommend to a Bright 14 Year Old?” ↗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...
on “Ask HN: Want Math/CS books that teach both the how and the why of the subject.” ↗along these lines check out: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard and Hubabrd http://www.amazon.com/Vector-Calculus-Linear-Algebra-Differe...
on “Learning Math” ↗I'm currently enrolled in a class that uses this book: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard and Hubbard. http://matrixeditions.com/ This book should totally be listed. Though it doesn't fit particularly well in any category, it provides a pretty good intro to…
on “Math Books Organized by Area of Mathematics” ↗…Introduction series http://www.amazon.com/Mathematics-Short-Introduction-Timothy... that should be helpful to you. On the particular subject you are studying right now, see if Hubbard and Hubbard's book Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach http://matrixeditions.com/UnifiedApproach4th.html helps your understanding.
on “Ask HN: Tips for learning maths” ↗…http://www.amazon.com/Calculus-Vol-One-Variable-Introduction... http://www.amazon.com/Calculus-Vol-Multi-Variable-Applicatio... Those are all lovely, interesting books. A good bridge to mathematics beyond those is Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard and Hubbard. http://matrixeditions.com/UnifiedApproach4th.html A very good book series on more advanced mathematics is the Princeton University Press series by Elias Stein.…
on “Ask HN: How to become smarter?” ↗Not specifically as a pair with that book, but I found the following books help to build some background to start on Data Science and Machine Learning: 1. Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach http://www.amazon.com/Vector-Calculus-Linear-Algebra-Differe... 2. OpenIntro Statistics 2nd Edition https://www.openintro.org/stat/textbook.php
on “Data Science from Scratch: First Principles with Python” ↗> I'd recommend Hubbard and Hubbard over that as it's a little easier read with the same material. John Hamal Hubbard, Barbara Burke Hubbard - Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach
on “Down with Determinants (1995)” ↗…Calter is a single volume that covers stuff up through calculus in a, well, technical manner. For a more understanding way, try Elements of Mathematics by Stillwell. If you get past Calculus, I recommend Vector Calculus, Linear Algebra, and Differential Forms by Hubbard. It gives an amazingly clear viewpoint on the higher level analysis and algebra topics, both numerically and abstractly. For statistics, you might try something like Think Stats by Downey…
on “Ask HN: How to self-learn math?” ↗Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by Hubbard is good book, written somewhat from the point of view that these subjects are better presented interleaved than as a self-contained book.
on “Ask HN: Mathematicians, what textbooks are best for learning these math topics?” ↗…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 to the multi-dimensional aspects, but it is a book that should happen after knowing one dimensional calculus. . If your child hasn't been exposed…
on “Ask HN: Recommend a maths book for a teenager?” ↗