Mathematics
It's Content, Methods and Meaning
by Andrei Nikolaevich Kolmogorov, M. A. Lavrentʹev, A.D Alexsandrov · first published 1962
80% recommend20% neutral
Why HN recommends it
Broad survey of advanced undergraduate mathematics that covers a lot of ground in a fairly short text; praised as a comprehensive overview of the field and a good companion to grad-level study.
Summarised by Claude from recommending comments
An overview of concepts and areas of research in the field of Mathematics, for a general audience.
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What Hacker News says
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…tables goes a long way. Another thing you have going for yourself is - you can basically skip high school math and jump right in for the good stuff. I’d recommend getting great and cheap russian recap of mathematics up to 60s [1] and a modern coverage of the field in relatively light essay form [2]. Just skimming these will broaden your mathematical horizons to the point where you’re going to start recognizing more…
on “Ask HN: How to self-learn math?” ↗What a conspicuous absence of Russian books! To mention only a tiny handful: - Mathematics: Its Contents, Methods and Meaning by Kolmogorov, Alexandrov, et al - Shafarevich's Basic Notions of Algebra - Arnold's Mathematical Methods of Classical Mechanics Another favorite (though German,…
on “Great Math Books as Recommended by Our Readers” ↗This isn't a course but this book has been consistently word-of-mouth recommended as a comprehensive survey of undergraduate mathematics. http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do...
on “List of Computer Science Courses” ↗This book is fantastic and should get you pretty far: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
on “Princeton University Math Major Course Guide” ↗This book is fantastic and pretty much takes you through an entire undergrad mathematics course: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
on “Ask HN: How to self-study mathematics from the undergrad through graduate level?” ↗…writing math books for kids, especially parents homeschooling kids, but it could be anyone. I would also recommend the following (Russian) books by Kolmogorov and Aleksandrov: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
on “On teaching mathematics (1997)” ↗…lot of advanced topics in math by Kolmogorov et al. It is nice because it covers a lot of topics w/o in a fairly short text --- it is a brick but it covers 2000 years of knowledge! http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do... For first-year stuff, I would recommend No bullshit guide to math and physics[1] and the No bullshit guide to linear algebra[2] of which I am the author. [1] http://minireference.com/ [2]…
on “Ask HN: Math books like SICP?” ↗This is awesome, thanks. Obligatory 'zoomout' recommendation: https://www.amazon.com/Mathematics-Content-Methods-Meaning-V..., which I learned about from HN (http://hackernewsbooks.com/book/mathematics-its-content-meth...). Wish I had read/pondered this before grad math classes.
on “Mathematics for Computer Science [pdf]” ↗…think like a mathematician: Keith Devlin, Kolmogorov/Alexandrov et al did 2 Dover books, and Houston: http://www.amazon.com/How-Think-Like-Mathematician-Undergrad... and http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199... and Ellenberg: http://www.amazon.com/How-Not-Be-Wrong-Mathematical/dp/15942... - Concrete Math by Patashkin, Knuth et al; Streetfighting Math by Mahajan and his newer, freely available:…
on “A Software Engineer’s Adventures in Learning Mathematics” ↗Feynman was a unique teacher of course, and pure math isn't quite as easy to teach intuitively. Something that might be close would be the survey _Mathematics: Its Contents, Methods and Meaning_ by Aleksandrov, Kolmogorov et al. https://www.goodreads.com/book/show/405880.Mathematics
on “Ask HN: Are there books for mathematics like Feynman's lectures on physics?” ↗…high. By comparison, most modern text books are so verbose and sometimes dumbed down that it becomes quite a chore to sift the wheat from the chaff. Dover publications has some good ones starting with Mathematics: Its Contents, Methods and Meaning by Kolmogorov et.al. There is also the I.M.Gelfand series; Functions and Graphs, The Method of Coordinates, Algebra, Trigonometry etc.
on “Soviet children’s books became collectors’ items in India” ↗If you like this approach, I highly recommend Mathematics: It's Content, Methods, and Meaning by Kolmogorov. He uses this same approach, but applies it to many more concepts in math (about 1,000 pages!). In fact, I think I actually heard about that book on…
on “The Lost Art of Logarithms” ↗…Engineering: * Reservoir Engineering/Characterisation (General + specific: NMR, sonic, induction logging, etc). * Electronics Engineering. * Physics (Landau & Lifschitz, Feynman Lectures, Atomic/Nuclear). * Mathematics (Old college courses : Piskounov, Demidovich. New ones: Kolmogorov). * Brush up my rational mechanics (well, basically stuff we did in college in the engineering course). * Signal Processing (Oppenheim,…
on “Ask HN: The “I want to do everything but end up doing nothing” dilemma” ↗This book looks awesome. Mathematics is so vast that as a student its hard to know what classes you should take, or even what the map of the territory looks like. That is one of the reasons I got frustrated with my pure math BS. The Russian…
on “The nicest math book I own” ↗Book is a collaborative effort of many mathematicians from different soviet regions https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...
on “Soviet children’s books became collectors’ items in India” ↗