Hamming, R.W., Numerical Methods For Scientists and Engineers [0] [1]
[0] https://www.amazon.com/gp/aw/d/0486652416/
[1] http://alvand.basu.ac.ir/~dezfoulian/files/Numericals/Numeri...
Ask HN: Are there books for mathematics like Feynman's lectures on physics?
161–170 of 180 posts
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#162The Best of All Possible Worlds: Mathematics and Destiny by Ivar Ekeland, https://www.goodreads.com/book/show/407320.The_Best_of_All_P... It is definitely not like Feynman's Lectures still one of the best books I've ever read.
For some reason, Ivar Ekeland's books are not that well known. I myself came across his book Mathematics and the Unexpected by random chance while browsing the Maths Section in the Library. I was hooked and set about getting/reading all three of his "popular maths" books; a) Mathematics and the unexpected b) The broken dice, and other mathematical tales of chance c) The best of all possible worlds: Mathematics and destiny.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#163If 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/
OT: Interesting blog you’ve got there.
I’ve seen Donella Meadows’ Thinking in Systems book recommended here a few times before, but your review really pulled the trigger for me, so thanks!
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#164When 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…
I daresay you would have the same experience with any other book. If you just read a book and don't work through problems yourself, you simply don't learn enough to do it yourself.
I agree in general, but Feynman’s books are different. I usually read textbooks cover to cover; then go on to solve the hardest problems I can find at that level (sometimes they are from the book, sometimes from different sources).
Most books, I make some progress on some problems, get stuck on others, and generally have a good grasp of the overall landscape and where I am lacking; then I go back and reread (and practice) the missing pieces.
But Feynman’s lectures are different in that they make you feel you understand a lot, without really giving you any tools to address things he did not address (and basically only address those things he did address in the same way).
I am not saying they are bad - 25 years later, I still remember (and occasionally use) some of them; most recently insights from the chapter on minimum principles. I am just saying that it only became useful after I already had a good (but not great) grasp of the material from other sources — despite giving that impression when read as introductory.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#165This may be a bit too elementary, but I recently read “Arithmatic” by Paul Lockwood and found it easy, provocative, and fascinating. https://www.amazon.com/Arithmetic-Paul-Lockhart/dp/067497223...
Did you mean Paul Lockhart? His book, "Measurement" is also good. He starts with some simple concepts, like length, and goes on to develop Geometry and then Calculus while encouraging the reader to consider various questions along the way.
Yes, Lockhart! This is why you shouldn’t post with jet lag.
He uses a similar approach in “Arithmatic”. He begins the book by describing different base number systems used throughout human history (the way different civilizations did “counting”). He does that in order to argue that a number itself shouldn’t be confused with its representation.
I might check out “Measurement” next! Thanks for the recommendation.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#166There is no royal road. Even Terry Tao said he didn't understand group actions (an undergrad concept) until he was near the end of his Ph. D. program. And this was a guy with a 160 I.Q. If you want to learn math you'll have to do problems until you start crying every day.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#167Earlier quoted context omitted.
We used that book for a course and I found it among my less favourite ones. its been a few years since I used it, but I remember it shallow and uninspiring. not trying to start an argument here, maybe just an outlier opinion since this seems a standard textbook.
It was one of my course books as well, but I think it's aimed at the American market and style of learning/presentation. I much preferred Stroud's "Engineering Mathematics" which was a course book for engineers at my university (I studied physics).
>>> aimed at the American style of learning
Ouch! Boas is maybe not as inspiring as Feynman. But when you see a copy on someone's bookshelf. It tends to be just as dog-eared and spine-cracked as Surely You're Joking
Another resource I just thought of. While not a textbook per se. Math competition problems from previous years can be very stimulating ;)
https://www.maths.cam.ac.uk/undergrad/pastpapers/past-ia-ib-...
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#168Penrose's 'Road to Reality' [1] is a kind primer on where the math comes from, as it applies to physics. Kind of a philosophical walkthrough of how math applies to physics. It is nowhere near as concise as Feynman's lectures, but it does complement them pretty well, while getting more into the math, and why the math is needed to describe various aspects of physical reality. [1] https://www.math.columbia.edu/~woit/wor…
I have a love-hate relationship with that book. It elegantly shows how to think about the topics, but it also left me with many unanswered questions to which I could never find answers with any amount of Internet searching (even though those answers are known to the humankind, buried in a set of complex topic-specific books).
Feynman's Lectures are much more complete in that sense, even though as other comments on this thread note, the reader may not be able to use the learning to solve practical problems without going beyond Feynman's lectures.
Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
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Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?
#170Earlier quoted context omitted.
Yeah, he was like that in person as well. When I was an undergraduate, he would "teach" a seminar on Tuesday afternoons called "PhysX" where you could go and ask any question you wanted. He'd go up to the blackboard and extemporaneously write things down and explain things in such a way that thought you really understood. But when you got back to your room and tried to replicate the chain of reasoning, there were alw…
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.
I also had a prof who took Feynman’s classes. He told us Feynman was a tough grader - he didn’t give partial credits, you either solved a problem or you didn’t.