linear algebra done right - sheldon axler
Ask HN: Math books that made you significantly better at math?
71–80 of 323 posts
Re: Ask HN: Math books that made you significantly better at math?
#72During 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 Alb…
On a similar subject I recall Concrete Mathematics by Donald Knuth being my favourite book from school.
Re: Ask HN: Math books that made you significantly better at math?
#73I 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…
I second this strongly, you can’t get better at math just by reading books. You need to hone your problem solving skills, you need to fight with the problems, have the mindset of a warrior, a conqueror, only then you’ll get the juice out of it and have a clear understanding of the subject. I’ll suggest starting with Concrete Mathematics by Donald Knuth, it’s a beautiful book that catches the essence of mathematics.
Art of problem solving(https://www.amazon.in/Art-Problem-Solving-Basics/dp/09773045...) is also a great start, especially if you don’t have much experience.
Re: Ask HN: Math books that made you significantly better at math?
#74The 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?
Re: Ask HN: Math books that made you significantly better at math?
#75Lot's of good books already here!
In the same spirit as Polya's book "Thinking mathematically" by J.
Mason, L. Burton and K. Stacey
I learned a lot in the early days with Demidovich book on 5000 problems on mathematical analysis.
Tom Apostol books on calculus, but for me his book on analytical number theory. Alongside alan baker's thin book on number theory.
Gilbert Strang book(s) on linear algebra.
Rudin book on functional analysis.
Oh Hardy's book on divergent series!
Ian Steward books on transcendental numbers and Galois theory.
Elements of algebraic topology by Munkres is a fantastic book.
So many books are invaluable to me in teaching not only math but mathematical thinking.
I guess if you want to learn thinking but not necessarily math "thinking mathematically" above mentioned is your friend.
Re: Ask HN: Math books that made you significantly better at math?
#76Not a direct answer, but I once read that the best book about a technical topic is the third book you read on it. Often you'll see things in comments sections like: "I have heard this explained so many times by others, but this explanation finally clicked!". The assumption is that that's the case because the explanation is better, rather than assuming it's the case because you've struggled with the material before and you're still going at it.
Re: Ask HN: Math books that made you significantly better at math?
#77The 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 think Khan Academy is pretty much made for this.
Re: Ask HN: Math books that made you significantly better at math?
#78Linear 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…
I have to second this. It's very well written and presents a clear view of what Linear Algebra is. Although it might be best used as a second book in Linear Algebra (depending on your preparation).
Re: Ask HN: Math books that made you significantly better at math?
#79Calculus 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.
>Probability Through Problems
First time I'm hearing about this one, thanks for the recommendation. Unlike Calculus or even a typical one semester Statistics course, probability is one of those topics where you need to see a lot of problems to really grok anything. The only way is to see a lot of solved problems and think about why that's the right answer.
Even highly recommended books (e.g. by Blitzstein) don't have enough solved problems, so it's nice to there's a problem focused book out there.
Re: Ask HN: Math books that made you significantly better at math?
#80Baby Rudin for analysis.
Dummit and Foote for algebra.