Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Ask HN: Are there books for mathematics like Feynman's lectures on physics?

news.ycombinator.com

Post reply on HN
Print view View original

111–120 of 180 posts

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#111

Post by Mugwort »

sacrificedcapon wrote: post #105

Not as encompassing as Feynman's lectures on physics, but Euclid's Elements is an excellent mathematical text.

Always. Robin Hartshorne's "Geometry: Euclid and Beyond" is the best book of its kind. It does Euclidean geometry with Hilbert's axioms and cleans up some of the loose ends of Euclid's classical treatment. Hartshorns book also covered the 5th postulate very thoroughly and non-Euclidean geometry. Hyperbolic geometry is treated axiomatically. He also has a nice treatment of axiomatic projective geometry which you can download for free. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475...

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#112

Post by rcpt »

jordigh wrote: post #11

Spivak's Calculus. It's "just" calculus... but it's also everything else leading up to it. It's a wonderful book, written in a very engaging style, and it shows you how mathematicians think and how they play. It shows you why we have proofs, why things go wrong, and all that had to happen before we came up with a definition of derivatives and integrals that we're happy with (and of course, all of the things we can do…

Apostols Calculus was huge for me. Probably the main reason I majored in math.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#114

Post by avyfain »

metastart wrote: post #98

If you're looking for a book that's both easy and stimulating to read, but that discusses a lot of mathematics in reasonable detail, I highly recommend the novelist David Foster Wallace's Everything and More: A Compact History of Infinity. It's probably the best book on mathematics I've read. It's not a textbook the way the Feynman lectures are, but it's stimulating and a good read. Other books mentioned like Visual…

+1 on DFW's book. It's odd, and really it's more a discussion on the history of modern mathematics than an in depth explanation of the concepts themselves, but it is a great read.

I wrote a short review after reading it, which you might be interested in checking out: https://faingezicht.com/articles/2017/10/27/infinity/

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#115

Post by m31415 »

cosmic_ape wrote: post #99
nabla9 wrote: post #51

"Mathematics : Its Content, Methods and Meaning" by A. D. Aleksandrov, A. N. Kolmogorov ,M. A. Lavrent'ev. (3 Volumes) This is a classic and exactly what you are seeking for. I think it was originally published in 1962. https://www.goodreads.com/book/show/405880.Mathematics https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

I'd add V. Arnold's books on Differential Equations and Geometry to that list. Wikipedia summarizes it nicely: "His views on education were particularly anti-Bourbaki." :)

Some problem collections by Arnold:

* Problems for Children from 5 to 15: http://jnsilva.ludicum.org/HMR13_14/Arnold_en.pdf

* A mathematical trivium pt. 1: http://www.physics.montana.edu/avorontsov/teaching/problemof...

* A mathematical trivium pt. 2: https://www.latroika.com/mathoman/exos/arnold-exos-math-engl...

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#116

Post by cardimart »

tchalla wrote: post #21

"Calculus Made Easy" by Silvanus P. Thompson (1910). It is availably freely online via the Gutenberg project and many other forms too. Chapter 1 is probably the best mathematics chapter I have ever read [0]. In two paragraphs, it beats most other calculus books. [0] http://calculusmadeeasy.org/1.html

Came to say the same. CMD+F didn't disappoint.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#117

Post by amagumori »

nabla9 wrote: post #51

"Mathematics : Its Content, Methods and Meaning" by A. D. Aleksandrov, A. N. Kolmogorov ,M. A. Lavrent'ev. (3 Volumes) This is a classic and exactly what you are seeking for. I think it was originally published in 1962. https://www.goodreads.com/book/show/405880.Mathematics https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

Oh shit, it’s authored by the Kolmogorov!

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#118

Post by rramadass »

SSLy wrote: post #89
nabla9 wrote: post #51

"Mathematics : Its Content, Methods and Meaning" by A. D. Aleksandrov, A. N. Kolmogorov ,M. A. Lavrent'ev. (3 Volumes) This is a classic and exactly what you are seeking for. I think it was originally published in 1962. https://www.goodreads.com/book/show/405880.Mathematics https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

There is some quality in Russian math books that western authors seem to lack.

Somebody from Russia/Former Soviet Countries from Eastern Europe ABSOLUTELY NEEDS to setup a publishing company (eg. Dover Publications) to bring all of their Science/Engineering books back into print. They will do very well in today's education market where the emphasis seems to have shifted to huge tomes/useless multiple editions/pretty colouring etc. rather than succinctly presenting the knowledge itself. The Mir (and other) publishers books were huge in many countries of the world and are remembered fondly to this day.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#119

Post by kooshball »

lkesteloot wrote: post #103
beagle3 wrote: post #19

When I was studying physics, I found Feynman’s books in the library, read them all, and had the feeling I understand everything! But then I tried to solve some final exams from previous years, and realized the feeling is false. These books gave me great intuition - but they made all the math look deceivingly simple, and as a result it is hard to develop the actual problem solving skills and intuition. I know my exper…

Came here to say this. The professors I've learned the most from were the ones who weren't awesome at explaining things. I didn't understand them and had to struggle through the material. That struggle made the material stick more. I think ideally you want a professor who's 80% good at explaining things, but leaves enough gaps and says things just confusingly enough that you have to engage your brain. Feynman was too…

disagree here. you're judging society on the most naive ranking a student would give. in an ideal world you can optimize for the perfect amount of understanding and imperfect leaps for each student to best address long term understanding and success.
Post reply on HN