151–160 of 180 posts
"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...
Not to be taken literally, of course. But there is some truth in that. If you are an engineer it makes sense to skim all kinds of math books. If you are a mathematician then I would say rather look for something that gels well with your personality and run with it.
Nobody has mentioned yet "Geometry and the Imagination" by Hilbert and Cohn-Vossen. If there is a Feynman equivalent in math it is certainly this book.
For elementary geometry, the Feynman equivalent is probably "Introduction to Geometry", by H.S.M.Coxeter. Beautifully written, figures on every page, covers all geometric topics (affine, projective, ordered, differential, ...)
For differential geometry, nothing beats "A Panoramic view of Differential Geometry" by Berger. It is a stunning comprehensive overview of the whole field, focused on the meaning and the applications of each part and, strangely for a math book, with no formal proofs. Only the main ideas of the proof and the relationships between them are given, but this allows to fit the whole subject into a single, manageable whole.
I'm currently learning group theory, matrices, and graph theory.
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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…
I remember when one of my professors told me how AVL trees were invented by mathematicians in the Soviet Union. It was in a paper titled “An algorithm for organizing information”. It was a side project for them, and it’s humbling to hear how simple the idea was to geniuses.
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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...
"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...
Earlier quoted context omitted.
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…
I absolutely agree about the quality of Russian math books. "Bronshtein and Semendyayev" and "Abramowitz and Stegun" come to my mind. I doubt that a publishing company bringing back those titles into print would be very successful. One thing is that many of these titles are mostly of historical value. Who needs a book with mathematical tables nowadays? Many of the books are still available as used books too. The most…
Much of "modern" textbooks are full of excessive verbiage obscuring the essentials, "pretty printing" disguised as "easy comprehension" and a racket for the publishers to make money. Why in the world do i need so many editions of books containing Mathematics which has not changed in centuries? Why do they cost an arm and a leg? Education is as fundamental as Health services and both should be affordable in service of the population.
So again, somebody setup a publishing company (eg. Dover Publications) and bring ALL the forgotten books from the Soviet era back into print :-)
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…
If you find it intuitive, you find it correct and the brain doesn't change your neural structure; because why would it? No neural structure change -> you didn't learn anything.
If you find it difficult, do mistakes, can't get the correct answer -> your brain start to change its neural structure to be able to resolve these problems -> you learn.