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I'd love to see recommendations of similarly "powerful" math books in circulation today. And I mean books that actually taught you a ton of math, not books tha

I'd love to see recommendations of similarly "powerful" math books in circulation today. And I mean books that actually taught you a ton of math, not books that contain a ton of interesting-looking math but mostly sit unread. Tim Gowers' Princeton Companion to Mathematics comes to mind, but I don't own it and I'm not sure if it's breadth-over-quality.

ctchocula 5y ago
Seconded. This brings to mind "Disturbing the Universe", a selection of autobiographical essays by physicist Freeman Dyson, where he mentions he learned differential equations as a 12-year-old by working through 700 problems in Piaggio's "Differential Equations" over the summer vacation, after which learning general relativity became a breeze.
annexrichmond 5y ago
Spivak's Calculus, which is really an introduction to Analysis, was that book for me. The way to approach it was to forget everything you learned about math in high school and learn it from the ground up in this book, as it will provide you with so much more insight and appreciation for how it all comes together Some of the book's best content is actually the exercises; notoriously difficult, but incredibly rewarding as spending the time to solve them them really prepares you for upcoming chapters
- AlexCoventry 5y ago
  Yeah, the exercises in that book were wonderful.
xNeil 5y ago
I'm sure you'd enjoy What is Mathematics? by Robbin and Courant. Take a look at it, hope it's kind of what you're looking for.
- khazhoux 5y ago
  Thanks. Looks pretty fantastic.
  - xNeil 5y ago
    Sounds good!
commandlinefan 5y ago
Not quite math, but TAOCP was like that for me: rather than having to force myself to work through it, I actually looked forward to spending time reading it or working the exercises.
- philiplu 5y ago
  If you think you'd like TAOCP, but with just the math, not the programming (hah), take a look at Concrete Mathematics by Graham, Knuth, and Patashnik. I haven't read anything else by Graham or Patashnik, so I don't know how much their voice comes through, but Knuth's playfulness and joy in the material comes through strongly. It's a blast just to read for fun.
  - dataangel 5y ago
    I must be built differently, I found Concrete Mathematics insanely inapproachable. I have a math stack exchange question where I ask for clarity on WTF he means on one question and got upvotes and comments from his students who were similarly flummoxed taking the course from him in real life!
kenny87 5y ago
MAA has its Basic Library List: https://www.maa.org/press/maa-reviews/the-basic-library-list-maas-recommendations-for-undergraduate-libraries https://www.maa.org/press/maa-reviews/the-basic-library-list...
- khazhoux 5y ago
  The list contains 2,963 books!
fao_ 5y ago
I found Precalculus Mathematics In A Nutshell by Simmons to be extremely valuable (as someone who got so stressed out by my maths teachers in primary school that I literally was not able to add up in my head until the age of 14). It teaches the concepts and cuts out all of the crap, but the diagrams and the clearly stated formulas make a lot of the implicit knowledge, explicit and extremely elucidating.

ctchocula 5y ago

Seconded. This brings to mind "Disturbing the Universe", a selection of autobiographical essays by physicist Freeman Dyson, where he mentions he learned differential equations as a 12-year-old by working through 700 problems in Piaggio's "Differential Equations" over the summer vacation, after which learning general relativity became a breeze.

annexrichmond 5y ago

Spivak's Calculus, which is really an introduction to Analysis, was that book for me. The way to approach it was to forget everything you learned about math in high school and learn it from the ground up in this book, as it will provide you with so much more insight and appreciation for how it all comes together Some of the book's best content is actually the exercises; notoriously difficult, but incredibly rewarding as spending the time to solve them them really prepares you for upcoming chapters

AlexCoventry 5y ago
Yeah, the exercises in that book were wonderful.

xNeil 5y ago

I'm sure you'd enjoy What is Mathematics? by Robbin and Courant. Take a look at it, hope it's kind of what you're looking for.

khazhoux 5y ago
Thanks. Looks pretty fantastic.
- xNeil 5y ago
  Sounds good!

commandlinefan 5y ago

Not quite math, but TAOCP was like that for me: rather than having to force myself to work through it, I actually looked forward to spending time reading it or working the exercises.

philiplu 5y ago
If you think you'd like TAOCP, but with just the math, not the programming (hah), take a look at Concrete Mathematics by Graham, Knuth, and Patashnik. I haven't read anything else by Graham or Patashnik, so I don't know how much their voice comes through, but Knuth's playfulness and joy in the material comes through strongly. It's a blast just to read for fun.
- dataangel 5y ago
  I must be built differently, I found Concrete Mathematics insanely inapproachable. I have a math stack exchange question where I ask for clarity on WTF he means on one question and got upvotes and comments from his students who were similarly flummoxed taking the course from him in real life!

kenny87 5y ago

MAA has its Basic Library List: https://www.maa.org/press/maa-reviews/the-basic-library-list-maas-recommendations-for-undergraduate-libraries https://www.maa.org/press/maa-reviews/the-basic-library-list...

khazhoux 5y ago
The list contains 2,963 books!

fao_ 5y ago

I found Precalculus Mathematics In A Nutshell by Simmons to be extremely valuable (as someone who got so stressed out by my maths teachers in primary school that I literally was not able to add up in my head until the age of 14). It teaches the concepts and cuts out all of the crap, but the diagrams and the clearly stated formulas make a lot of the implicit knowledge, explicit and extremely elucidating.