_Mathematics for the Million_ by Lancelot Hogben.
Ask HN: Math books that made you significantly better at math?
271–280 of 323 posts
Re: Ask HN: Math books that made you significantly better at math?
#272In early high school in the 90s, I got my parents to buy me an (expensive) copy of Chaos and Fractals: New Frontiers of Science by Peitgen, Jurgens, Saupe. The end of each chapter was a Basic program for calculating and displaying various fractal/chaos theory images, and that's what got me started programming.
It also included a bunch of mathematics involving "neighborhoods", meaning the set of all points within a distance of an arbitrarily small epsilon from some point X. Although I never did any of the math problems from the book, that early exposure to epsilon made calculus vastly easier to understand, and for that, it's close to my heart.
Re: Ask HN: Math books that made you significantly better at math?
#273Lot's of good books already here! In the same spirit as Polya's book "Thinking mathematically" by J. Mason, L. Burton and K. Stacey I learned a lot in the early days with Demidovich book on 5000 problems on mathematical analysis. Tom Apostol books on calculus, but for me his book on analytical number theory. Alongside alan baker's thin book on number theory. Gilbert Strang book(s) on linear algebra. Rudin book on fun…
Came here to recommend Thinking Mathematically (text only) by J. Mason. If only every high school maths teacher had this book, the world would be a better place
This is a great book. Unlike any other book I've read. It helps with defining a process that I think every person working in a technical field uses one way or another. It helps you develop a way of thinking that reduces anxiety when you are stuck and helps develop paths to get unstuck. This book made me love math and I wish more people knew about it. It's also never too early or too late to pick it up.
Re: Ask HN: Math books that made you significantly better at math?
#274A lot of people have mentioned Keith Devlin's book "Introduction to Mathematical Thinking" by Keith Devlin but for me his other book "Mathematics: The Science of Patterns" was something that really had a huge impact on me just to put mathematics in perspective. Probably has something to do with my own personal character and education but I needed that perspective before I could take the next step. Then the "Introduction to Mathematical Thinking" is a great following read. So it depends where you are.
Re: Ask HN: Math books that made you significantly better at math?
#275As a child, I re-read The Number Devil constantly. It introduced me to some really cool mathematical ideas, couched in a cute story. The very last chapter includes a picture of the Principia Mathematica's proof of 1 + 1 = 2 -- mostly for shock value, I think, but also "even this is within your reach". I recently got to see a friend's copy of the Principia, and I realized just how much of it I actually did understand, which was a really nice closing of the loop.
As an adult, Imre Lakatos' Proofs and Refutations gave me a much richer understanding of definitions in mathematics -- what job they're meant to do, and when it makes sense to change your definitions instead of adding premises to your theorems.
Re: Ask HN: Math books that made you significantly better at math?
#276To add one more thing: the "thing" that has helped me most lately isn't a specific book or video or anything, but rather simply committing to spending 1 hour every day on math. I even set up a Google Calendar task to remind me of this every. single. day. And so far this year I haven't missed a day yet. Now what constitutes that hour can vary. It can be watching math videos, it can be solving problems on paper, and I…
Yeah, I've been doing the same thing, but with the rule that I have to do "a math problem". Right now I'm going through a stochastic processes book a bit at a time that way and really enjoying it.
Re: Ask HN: Math books that made you significantly better at math?
#277You know how Feynman has these lectures where he digs into physics but you don’t need to know any to get lots out of it?
Is there that for math? Books or lectures that talk about math without doing the math?
Re: Ask HN: Math books that made you significantly better at math?
#278You know how Feynman has these lectures where he digs into physics but you don’t need to know any to get lots out of it? Is there that for math? Books or lectures that talk about math without doing the math?
I've found YouTube videos can do a good job.
Entry level: 3 Blue 1 Brown, Mathologer
More advanced: Many random one offs which I haven't yet to establish a good pattern for, Richard E Brocherds seems to have a few series though I have to take them slowly as they are more akin to a college lecture.
Number crunching examples: Michael Penn. Also should have some more theory based videos but I have only watched his problem solving ones.
Avoid: Numberphile just ends up feeling empty and devoid of any depth. Maybe it works for someone so entry level that they don't follow along with Mathologer but I don't see any value and would like a way for YouTube to stop recommending their videos.
Re: Ask HN: Math books that made you significantly better at math?
#279Math magic
Https://www.amazon.com/Math-Magic-Calculator-Everyday-Problems/dp/0688104762
Re: Ask HN: Math books that made you significantly better at math?
#280The Road to Reality: A Complete Guide to the Laws of the Universe
In this book, Roger Penrose a Nobel Prize winner in Physics for his contributions in mathematical physics of general relativity and cosmology, provides background math to understand the book's contents in the first half of the book.