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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?

#51

Post by bombcar »

pen2l wrote: post #16
bombcar wrote: post #12

Earlier quoted context omitted.

Reading Euclid's Elements and Newton's Principia really helped me get an intuitive feel for geometry and calculus. They may not be entirely easy (at least the second) without some commentary, but well worth the study.

While it's laudable that you sought those texts and profited from them, I worry about what others might take away from this. When I was young I knew some geniuses who highly spoke of Principia and how it gave them great insights. And the teenager me said, okay cool, I'll have a go! The problem is that it's in Latin and quite impenetrable. We have some geniuses here and they would no doubt be able to take away a lot f…

I didn't read Euclid in Greek or Newton in Latin; there are quite good translations available - even free!

In general I find that if someone is insisting that you study the philosophy of someone in their original language, they don't have a good enough translation yet.

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

#54

Post by kxyvr »

1. Principles of Mathematical Analysis by Walter Rudin (baby Rudin) - I'd studied real analysis in the past, but this book is direct and rigorous and provided a good framework to move forward into things like functional analysis in a way that I was not prepared for with other books.

2. Differential Equations and Dynamical Systems by Lawrence Perko - Solidified for me how dynamic systems behaved and were solved. Very much helped my understanding of control theory as well.

3. A Concise Introduction to the Theory of Integration by Daniel Stroock - Helped solidify concepts related to Lebesgue integration and a rigorous formulation of the divergence theorem in high dimensions.

4. Convex Functional Analysis by Kurdilla and Zabarankin - Filled in a lot of random holes missing in my functional analysis knowledge. Provides a rigorous formulation of when an optimization formulation contains an infimum and whether it can be attained. Prior to this point, I often conflated the two.

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

#55

Post by fouronnes3 »

binarymax wrote: post #42

“Mathematical Notation: A Guide for Engineers and Scientists”[0] really changed my abilities with being able to read papers and decipher what was going on. I had university math experience but it was a long time ago. When I started reading papers for algorithms later in my career I couldn’t get past the notation. Once the symbols are explained, as a programmer, I was able to grok so much more. This should be on every…

As a programmer I really wish math notation was more rigorous: less ambiguity, more explicit typing, no implicit variables, etc. So much of it would never pass code review. We programmers figured out that code should be optimized for readability, not writtability ; I wish mathematicians did too.

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

#57

Post by krmboya »

I have not yet become significantly better, and not a math book, but I recently read A mathematicians Lament by Paul Lockhart and it resonated so much with me that I plan to take another stab at math different from how it is taught in school.

Waiting to get my hands on his book 'Measurement' and approach it more like art.

If what he says is true, perhaps many who would have turned out great at math are locked out by how it's taught in school.

For now, I have a test subject of one :)

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

#58

Post by tylerstorm »

scruple wrote: post #10

Calculus Made Easy and Probability Through Problems. I'm not sure that I'd have gotten through either my university Calculus courses or Probability and Statistics without these two books. I used them as supplementary material to the course textbooks and homework. They both have a style that is approachable and helped me build an intuition for the material unlike anything else I found.

I second this suggestion for Calculus Made Easy by Thompson. It's become a bit of a classic...was published in like 1915. Super unique approach to teaching calculus. It's an excellent supplement...lots of good insights. It may be particularly good for people who believe they're bad at math. His style may convince people otherwise.

Also, Vibrations and Waves, by AP French. Granted, this is a physics book, but I appreciate his style so much. He makes use of a lot of geometric methods to solving problems. It definitly expanded my math horizons! His other books are good too.

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

#60

Post by r-zip »

hackerbrother wrote: post #48

Rudin's Principles of Mathematical Analysis has a really special place in my heart. Chapter 3 is great- it's a great reference for derivations of a lot of fundamental identities about limits used in undergrad calculus. Chapter 4 is a great place to learn about topology for the first time. In general, it kicks up the mathematical rigor you're used to a notch. Seeing ">" defined as "not <" really blew my mind when I fi…

Wouldn't ">=" be "not <"?
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