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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?

#31

Post by wannabebarista »

dfan wrote: post #20

This is different from the other answers, but it does answer your question: When I was a kid I had tons of math and logic puzzle books. Two I remember specifically are "Aha! Insight" and "Aha! Gotcha" by Martin Gardner. Decades later, when a math problem comes up in my work, I have an apparently unusual ability to cut to the heart of it ("by symmetry, we must have X" or "looking at this extreme case, we must have Y"…

I had a similar experience with Raymond Smullyan's books, particularly The Gödelian Puzzle Book: https://www.raymondsmullyan.com/books/the-godelian-puzzle-bo.... Recreational math is quite underrated.

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

#33

Post by mohamez »

Mimmy wrote: post #17

Linear Algebra Done Right by Sheldon Axler for the following reasons: - I was revisiting a topic in greater depth, which is a common theme in university-level math courses. - It is a rigorous book, written in the style of definition, proposition, theorem, etc. - It was the first math book where the exercises don't just reinforce what you learned in the chapter, but teach you new material (another common theme in adva…

Linear Algebra Done Right by Sheldon Axler is indeed a good book if you are looking for a rigorous proof based book to learn linear algebra.

Here [1] you can find Sheldon Axler himself explaining the topics of the book in his YouTube channel! How wonderful is that!

Here [2] you can find the solutions to the exercises in the book.

This [3] Lectures might help as well, among the books this course follow is Algebra Done Right.

Good luck learning the subject of Linear Algebra you'll have fun doing so.

[1] https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmS...

[2] http://linearalgebras.com/

[3] http://nptel.ac.in/courses/111106051/

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

#34

Post by Penyngton »

Since I haven't seen many discrete maths books, he's my list:

Beginner: NL Biggs, Discrete Mathematics, Oxford University Press

Intermediate: PJ Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press

Advanced: JH van Lint & RM Wilson, A Course in Combinatorics, Cambridge University Press

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

#35

Post by mxkopy »

keiferski wrote: post #6

I would not call myself great at math – I struggled with it in school, in fact – but in recent years I’ve begun “correcting” my lack of mathematical knowledge. The single best decision I’ve made is to first start with the philosophy of mathematics. Maybe it’s because my background is in philosophy, but I also think that for certain people like myself, understanding what math is makes me far more interested in underst…

In that vein I highly recommend Foundations and Fundamental Concepts of Mathematics by Howard Eves. I think it might be a little dated, but it gives an amazing overview of the most important developments in mathematics that were relevant at the time. It's less focused on practice (though there are some problems) and more on the history and motivation behind the ideas. This book introduced me to axiomatics, non-Euclidean geometry, quaternions, and abstract algebra in my senior year of high-school.

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

#36

Post by enriquto »

wannabebarista wrote: post #8

Measure and Category by John Oxtoby. This book studies duality results between different notions of "small" sets in measure theory and topology. It's the first (and to some extent the only) math book where things just clicked and I didn't feel like I was drowning in a sea of notation and ideas. Here are some more thoughts on it: https://bcmullins.github.io/Top-Books-2019 .

I'm so happy to hear that! I've always loved this little book (even if it's completely independent of the math needed for my work).

In a similar spirit, but with a much more geometrical flavor, there is Evans-Gariepy.

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

#38

Post by pncnmnp »

During my undergraduate studies, I loved "Discrete Mathematics and Applications" by Kenneth Rosen. I really enjoyed reading through the various examples and biographies of famous mathematicians included in each chapter.

For those looking to delve into discrete mathematics, I highly recommend the lecture notes from L. Lovasz and K. Vesztergombi (Yale University, Spring 1999) and from Eric Lehman, Tom Leighton, and Albert Meyer (MIT, 2010).

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

#39

Post by Kaizeras »

Mathematik für Ingenieure und Wissenschaftler I, II and III from Lothar Papula (in German). The solutions are detailed, making it perfect for self-studying.

Book of Proof by Richard Hammack. A great introduction to proofs in mathematics. The book is available free online [0], but also I bought the physical version because I really enjoyed it.

[0]https://jdhsmith.math.iastate.edu/class/BookOfProof.pdf

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