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Ask HN: Math books that made you significantly better at math?

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Re: Ask HN: Math books that made you significantly better at math?

#241

Post by jdkee »

chriswarbo wrote: post #204
salusinarduis wrote: post #74

Earlier quoted context omitted.

I've had this idea of starting back at basics and relearning math from the beginning since I never "really" learned it besides memorizing and skirting my way through it in school. Do you know a good path or book that's suitable for that?

Norman Wildberger's YouTube channels are the most thorough I've seen ( https://www.youtube.com/@njwildberger and https://www.youtube.com/@WildEggmathematicscourses ). There are hundreds of videos, organised in playlists, from undergraduate lectures ( https://www.youtube.com/playlist?list=PL55C7C83781CF4316 ) and research seminars ( https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF ) all the way to basic fundam…

"The reason I find them fascinating is that Wildberger doesn't agree with some of the conventional approaches, in particular with the use of infinity and taking limits."

So no transfinite ordinal analysis or large cardinals? Hard to take him seriously.

Re: Ask HN: Math books that made you significantly better at math?

#243

Post by bick_nyers »

Jimmc414 wrote: post #182

Some that stand out "Concrete Mathematics: A Foundation for Computer Science" by Knuth, Graham, and Patashnik - solid foundation in mathematical concepts and techniques, and it helped me develop a deeper understanding of mathematical notation and problem-solving. "Introduction to the Theory of Computation" by Michael Sipser - introduced me to the theoretical foundations of computer science, and it helped me develop a…

+1 for The Art of Problem Solving

Re: Ask HN: Math books that made you significantly better at math?

#245

Post by chkhd »

* The Language of Mathematics: Utilizing Math in Practice by Baber https://www.amazon.com/Language-Mathematics-Utilizing-Math-P... really helped me "get it", as I always found programming natural but math hard. This one is written by a CS professor and it really makes all the difference.

* How to Solve it by Polya https://www.amazon.com/How-Solve-Mathematical-Princeton-Scie... and How to Prove it by Velleman https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/... helped strengthen that understanding.

* This year I am trying to master https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... which focuses on how to "connect the dots".

* I am using Geometry and the Imagination by Hilbert https://www.amazon.com/Geometry-Imagination-AMS-Chelsea-Publ... as an attempt to "immerse" myself in Geometry. I just love this book.

Re: Ask HN: Math books that made you significantly better at math?

#246

Post by rs999gti »

yodsanklai wrote: post #23

I wonder how good you can get at maths just by casually reading books. You need to work on problems for hours and hours to get a grasp on the theories. Programming is different in the sense that it's something people routinely do as a hobby because it's quite fun and addictive. But maths? maybe if you have already strong foundations you can pick up a new topic and develop your culture. But I doubt one can get these f…

> You need to work on problems for hours and hours to get a grasp on the theories.

Very true. For maths, it is drill to win.

Re: Ask HN: Math books that made you significantly better at math?

#248

Post by chriswarbo »

jdkee wrote: post #241
chriswarbo wrote: post #204

Earlier quoted context omitted.

Norman Wildberger's YouTube channels are the most thorough I've seen ( https://www.youtube.com/@njwildberger and https://www.youtube.com/@WildEggmathematicscourses ). There are hundreds of videos, organised in playlists, from undergraduate lectures ( https://www.youtube.com/playlist?list=PL55C7C83781CF4316 ) and research seminars ( https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF ) all the way to basic fundam…

"The reason I find them fascinating is that Wildberger doesn't agree with some of the conventional approaches, in particular with the use of infinity and taking limits." So no transfinite ordinal analysis or large cardinals? Hard to take him seriously.

More than that: no Real numbers, no pi, no square root of 2, no sine/cosine, etc.

It's similar to 'reverse mathematics' (trying to find the minimum set of assumptions required to prove a known result)

Re: Ask HN: Math books that made you significantly better at math?

#250

Post by fghorow »

adamsmith143 wrote: post #41

A lot of comments about textbooks that helped in specific topics but I don't think that answers the spirit of OP's question. Sure working through ANY Linear Algebra textbook is going to improve your Linear Algebra skills. In the spirit of OP's question: How to Solve it by G. Polya Solving Mathematical Problems by Terrence Tao Introduction to Mathematical Thinking by Keith Devlin Are all amazing, How to Solve it in pa…

For my tastes, Strang's Linear Algebra book is a winner!

I'm somewhat surprised the nobody has mentioned it yet...

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