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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?

#121

Post by agucova »

cccybernetic wrote: post #21

The best resource I've found is this random, somewhat obscure website (though I've learned that it has grown in popularity) called Paul's Online Notes. The professor has a real knack of pedagogy, and the problems are perfectly structured in terms of their difficulty. His explanations are clear and without jargon, and it goes from algebra to diff eq. A note: this isn't a resource for higher-level, proof based maths. I…

This page got me through my engineering calculus I, II and III, linear algebra and ODEs courses.

I'm eternally grateful ;)

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

#122

Post by bmitc »

While I have a ton of favorite math books, the two books that I felt really helped me the relevant subject are:

* An Introduction to Manifolds by Loring Tu

* The Elements of Integration and Lebesgue Measure by Robert G. Bartle.

These two books were instrumental to my studying for my qualifying exams.

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

#123

Post by college_physics »

Math always seemed a bit arbitrary to me. Why and how did all those fields and branches develop, why are some so much more intuitive than others etc. What helped me cope with that challenge (and ultimately be a better learner / user of mathematics) was digging into the history of mathematics. Many great books in that genre but a very influential one for me was the Concise History of Mathematics by Dirk Jan Struik

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

#124

Post by willhslade »

fouronnes3 wrote: post #55
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.

To pick a nit, Iverson did this with APL and I still think it's brilliant. Executable math. It's time will come, I hope.

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

#125

Post by geenew »

eddsh1994 wrote: post #90
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.

This is sort of like recommending the art of computer programming as a way to learn how to code, isn’t it? Starting very far down the stack if you’re working through a 2000 year old book in Ancient Greek!

Elements was a school textbook for 2000 years, up until ~100 years ago. It's a fine book to use for self-study.

Edit: Also, to state the obvious, it's been translated into English

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

#126

Post by vmilner »

salusinarduis wrote: post #74
enriquto wrote: post #49

The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on manifolds ) * Fourier Analysis by Körner * Arnold's books on ODE, PDE and mathematical physics are breathtakingly beautiful. * The shape of space by Weeks * So…

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?

I’m reading and like Thomas Garrity’s “All the mathematics you missed (but need for graduate school)” which is this but for people who did a bachelors degree but missed certain areas (or forgot them).

https://www.amazon.co.uk/All-Math-You-Missed-Graduate/dp/100...

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

#128

Post by wannabebarista »

phonebucket wrote: post #114

A lot of recommendations depend on what you're trying to learn. But I've enjoyed the following texts to a larger extent than others: - Algebra: Chapter 0 (Aluffi) - Real Mathematical Analysis (Pugh) - Mathematics and its History (Stillwell) - An Introduction to Manifolds (Tu) - Gauge Fields, Knots and Gravity (Baez) - A First Look at Rigorous Probability Theory (Rosenthal) - All of Statistics (Wasserman) There are so…

Great list! I want to call out John Stillwell's Reverse Mathematics as a fun and accessible introduction to the field.

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

#129

Post by [deleted] »

fouronnes3 wrote: post #55
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.

[deleted]

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

#130

Post by sthu11182 »

belter wrote: post #43

If you have a Love of Books and Math Books in particular, you can't miss this playlist by The Math Sorcerer: https://www.youtube.com/playlist?list=PLO1y6V1SXjjM-1azbCNYq...

I've really enjoyed the Math Sorcerer's overview of various math books. Such a breath of topics and levels.
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