By the end of this book reaches college levels. There's nothing better to show how interesting mathematics, to look at it with wonderment. Our education system is to blame.
https://www.amazon.com/Playing-Infinity-Mathematical-Explora...
Ask HN: Are there books for mathematics like Feynman's lectures on physics?
101–110 of 180 posts
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#102"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...
Free on archive.org: https://archive.org/details/MathematicsItsContentsMethodsAnd...
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#103When 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 clear, which allowed my brain to coast.
At a meta level, I think this means we'll never (as a society) be great at teaching, because teachers who make us work make us feel like we're learning less. We prefer (and rate more highly) the professors, like Feynman, who make us feel smart.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#104I suggest this "Map of mathematics" as a starting point that gives you a reasonable birds-eye view of the field.
https://www.youtube.com/watch?v=OmJ-4B-mS-Y
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#105Not as encompassing as Feynman's lectures on physics, but Euclid's Elements is an excellent mathematical text.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#106More general purpose problem solving but written by a mathematician and one of the best books I've ever read! https://en.wikipedia.org/wiki/How_to_Solve_It
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#107When 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…
Personally I thought the Feynman lectures were ok but with room for improvement.
Vol 1 was good. Vol 2 was good though overly repetitive, iirc it's 90 percent Maxwell's equations. Vol 3 was unintuitive to me. Still I learned qm from it and made this http://tropic.org.uk/~crispin/quantum/
I'm fairly confident I get qm now, but most of that understanding came from trying to code it in simulation. Which suggests there are better ways to learn than Feynman 3.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#108There are some really good suggestions here. I would like to add that learning calculus properly is of the utmost importance. It's no exaggeration when I say that this is unquestionably the single best, most profitable action you can take. Any one of these books can change your life.
1. Spivak Calculus
2. Apostol Calculus vol. I and II
3. Courant and Johns, Introduction to Calculus and Analysis vol. I, IIA and IIB
For the more casual computer science or physics major, I'd go with choice 3 which resembles the Feynmann lectures the most. All the rigour of the other two is there but in a more digestible form. It's hard for someone not accustomed to hard maths to digest long proofs, it could give you a bad case of indigestion. It's more a function of patience. Courant and Johns get to the point much more quickly while Spivak and Apostol take their time to do everything thoroughly. Courant and Johns does do everything thoroughly but they are kinder to the reader and delay lengthy rigoourous proofs as long as possible while giving plenty of motivation and intuition.
Also I strongly recommend any books by Ray Smullyan particularly his introduction to mathematical logic. "A Beginner's Guide to Mathematical Logic"
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#109More general purpose problem solving but written by a mathematician and one of the best books I've ever read! https://en.wikipedia.org/wiki/How_to_Solve_It
Agreed. Hard for some people to appreciate but so true.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#110When 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…
It's a very good start. From there I think the most productive thing anyone could do is make a very thorough study of Classical Mechanics. People underestimate how much a thorough knowledge will help them. Start with an easy book and work your way up. Goldstein and Laundau are excellent intermediate level choices. For a beginner I think Jakob Schwichtenbergs "No Nonsense Classical Mechanics" could work or Leonard Susskind's "Theoretical Minimum Classical Mechanics" . Personally, I really liked Jakob's book. You'll need a friend or a study group online to help you when you get stuck. Classical mechanics is very serious physics and I regard a thorough foundation in say Hamiltonian Mechanics as a solid achievement. a sure sign someone could go on and learn E&M, Statistical mechanics, Quantum mechanics, Relativity and Gauge theories. For a semi advanced book if you know some advanced maths try Spivak's Classical Mechanics and anything by V. Arnold.