171–180 of 180 posts
I am very much enjoying Evan Chen's "An Infinitely Large Napkin". https://venhance.github.io/napkin/Napkin.pdf I think this is in the spirit of Feynman's lectures inasmuch as it's not going to bring you to expert-level understanding, but it is going to do a good job giving you some intuitive understanding, which you might then be able to apply to re-studying the material in more detail. He even takes pull requests, I…
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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...
Thank you, Is there an answer key to those?
[1]: https://math.stackexchange.com/questions/24533/find-the-aver...
I am also been interested for the longest time - even with a degree in Mechanical Engineering - to understand mathematic like Calculus or the equations you see in neural networks papers. My longest problem has been I have no idea what is going in the formula or fundamental questions like, "why is there a square root there". It is hard to describe my issue, but I've been very horrible with math anyways. Can't do gas s…
Get some school/college textbooks (high school level onwards) and some "popular maths" books and start reading. Once something catches your fancy you can dive deep as needed. You are studying to gain "understanding" and not to get through an exam or prove something to somebody.
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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…
I disagree with you on the publishing front. Mathematics is fundamental and timeless (what do you mean "many of these titles are mostly of historical value"?) They may need some trivial editing (though i would much prefer that they be published as they were with a note explaining the historical aspects) but otherwise they were information dense and succinct with an eye to Applications. They were all excellent across…
Absolutely and you certainly have a point with what you wrote. May opinion is more along the lines of: "the content is still as valuable as it ever was but the presentation is not."
Take one of the examples I mentioned. Abramowitz and Stegun is a collection of mathematical tables. If you needed to calculate the sine of a value, would you rip out your chuffed copy of Abramowitz and Stegun or would you use your calculator? Even for the more obscure tables there is probably nothing in the book that isn't in Mathematica. If I really needed to look into the book for some reason I would be too lazy find my copy, given that online versions[1] as well as extended and improved versions[2] are just a few mouse clicks away.
Now, a book of mathematical tables is like an extreme example but I still feel the same sentiment for all my old math books. Why bother with a physical copy if I have a searchable online version right at my fingertips? When i comes to the books from the Soviet era I guess libgen has them all and I think most people would not buy a physical copy anyway.
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I disagree with you on the publishing front. Mathematics is fundamental and timeless (what do you mean "many of these titles are mostly of historical value"?) They may need some trivial editing (though i would much prefer that they be published as they were with a note explaining the historical aspects) but otherwise they were information dense and succinct with an eye to Applications. They were all excellent across…
> Mathematics is fundamental and timeless Absolutely and you certainly have a point with what you wrote. May opinion is more along the lines of: "the content is still as valuable as it ever was but the presentation is not." Take one of the examples I mentioned. Abramowitz and Stegun is a collection of mathematical tables. If you needed to calculate the sine of a value, would you rip out your chuffed copy of Abramowit…
You are very wrong here. It is the very presentation in those books viz; succinct and concise, no frills approach, high information density and with an eye to applications which makes them so valuable today. It is the best way of Science teaching distilled from the brains of a whole lot of smart people.
I am not sure why you are fixated on one book of tables. It is irrelevant in the broader scheme of things. For example none of the Mir books that i have, have anything to do with pre-calculated tables other than a few appendices.
There are a huge swath of students across the world who do not have the same access to technology as we do. Printed books are still the norm amongst the majority of students in the world. Printed books will also outlast any Digital media presentation of books due to its simplicity and robustness i.e no problems like DRM, unreadable extinct formats, availability of good ereaders, health aspects, etc (there is a whole lot more i can elaborate here).
Finally, and most important, research is beginning to show that we retain/understand less when using ebooks/ereaders than when we read a printed book. This is very much true of technical books (borne out by my own experience) where you need concentrated attention with body and mind. For example, we intuitively jump back and forth across pages, use our fingers as book marks, subconsciously create spatial maps of what we are reading etc. all of which have no analogues with current day ereaders. Cognitive Science is still trying to figure out how best to use modern technology. So don't throw away your old Maths books just yet :-)
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After doing the hard learning, you can lecture your intuitive mental model you have. But it's difficult to install that mental model into a beginner's mind. Often the intuitions are illusory mnemonics for the deeper understanding, which if you never learned in the first place would just point to nothing. You have to do the hard learning to arrive at the "intuitive" mental model.
While i see where you are coming from; i feel that you are putting the cart before the horse. While Intuition by itself is not enough, it should absolutely be the first thing you should focus on before doing the hard work through rigor and formalisms. The former can be "grasped" while the latter needs "practice and applications". This is how Science itself developed (a good example is Faraday vs. Maxwell's approaches…
Are there any equivalent of these books for kids? something 9-10 year olds can read and get interested in Math (or not afraid of it).
Goes well with the Art of Problem Solving site/books for practice.
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I had a teacher in the University who took some courses taught by Feynman and had the same experience. He even tried to record some of the lectures, but the result was similar. While he was listening, he felt like everything was very clear. But as soon as he stopped the tape, nothing made sense anymore.
The funny thing is, if I remember his autobiographies correctly, he wouldn't let anyone else get away with that. I think he said that if he didn't understand something, he would always ask about it.
Feynman's PhD advisor, John Wheeler, together with Charles Misner and Kip Thorns, wrote a textbook on general relativity called Gravitation. It's gigantic, 1200 pages, and its tone is similar to the Feynman lectures. And it is at least partially a math textbook, as it includes a fairly complete introduction to Riemannian geometry.
I think even among professionals in general relativity, MTW has developed a reputation as being too dense and old-fashioned, certainly so for a beginner. If you're first approaching GR, Sean Carroll's notes or books are much more approachable.
For actually learning GR, I prefer Wald.