Going to echo the suggestions for the Art of Problem Solving books, particularly I recommend the contest books (vol 1 or 2). Several very talented people have said to me that these books taught them how to think. Maybe a bit exaggerated, but they’re very good.
Ask HN: Math books that made you significantly better at math?
181–190 of 323 posts
Re: Ask HN: Math books that made you significantly better at math?
#182Some 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 strong understanding of formal languages, automata, and complexity theory.
"A Course in Combinatorics" by J.H. van Lint and Wilson - provided a comprehensive introduction to combinatorics, and it helped me develop a strong understanding of combinatorial techniques and their applications.
"The Art of Problem Solving" by Richard Rusczyk - This book is a comprehensive guide to problem-solving, with a focus on mathematical problem-solving strategies. It helped me develop my problem-solving skills and learn how to think critically about mathematical problems.
Re: Ask HN: Math books that made you significantly better at math?
#183Books do not make you better at math. Working math problems makes you better at math. Go ahead, down vote all you want. Reading about running does not make you a better runner. You can watch 1000 marathons, sprinters, Olympians. You may get _ideas_ for running, but it will never make you a better runner. To be a better runner you have to do it. To be a better programmer/mathematician/physicist/whatever, you need to g…
So many great responses recommending all kinds of books and then there's... this. Lol. Such a jaded/cynical teacher thing to say, but sure, nothing is a substitute for what you get out of putting the effort into doing. For me, the biggest hurdle to succeeding at college-level math was a lack of motivation due to the meaninglessness of most of the content.
Re: Ask HN: Math books that made you significantly better at math?
#184Earlier quoted context omitted.
Honestly, unless you're very gifted, a book on its own is not going to be enough to really develop your skills. You need to work interactively with a teacher. Wouldn't that depend on what level of skill we're talking about? I believe that most people who need to learn just, say, high-school algebra/geometry/trigonometry/etc. can probably do so with "just books" if they are motivated. Heck, I'd even venture that most…
I basically agree with what you're saying. My response was based on the reader saying something about "mathematical thinking" in their post. In my experience, programmers talking about "mathematical thinking" usually have math insecurity and are referring to more advanced topics, thinking they need to consult tomes of deep mathematical wisdom to correct this deficiency (wrong). Could be totally off base, of course. B…
I'm not so sure about this. If, like you say, someone is in a job where they need to read some papers with some math in them, they should be organizationally near someone who can help them out. If possible, I think a better strategy (better even than getting a degree) would be to find these people and develop a relationship with them to the point where you can ask them questions.
Fair point.
One could also form a math "study circle" of some sort if you are in an area with enough mathematically oriented folks to find people to participate. I did this briefly and it was a valuable thing. It kind of fell apart for different reasons, but I could see doing it again at some point.
Re: Ask HN: Math books that made you significantly better at math?
#185Books do not make you better at math. Working math problems makes you better at math. Go ahead, down vote all you want. Reading about running does not make you a better runner. You can watch 1000 marathons, sprinters, Olympians. You may get _ideas_ for running, but it will never make you a better runner. To be a better runner you have to do it. To be a better programmer/mathematician/physicist/whatever, you need to g…
Problem sets are useful for improving your mathematical ability, as is looking at an expert's attempt at a problem after your attempt. Both are a core part of reading books well. So when someone asks for books to improve their mathematical ability, a likely interpretation is just "they want books with good problem sets, clear presentation and elegance". Another interpretation is "what's a book which, when after I intrepret all the individual sentences into a vague impression, will make me good at maths?"
Your answer is somewhat helpful in the latter sort of world where OP didn't know how to read a textbook (which is unfortunately common) but not in the former sort. You seem to be venting though, which is understandable. But venting with a side of helpful content would be even better.
For instance, advising OP on how to to read a maths book (generate content yourself, check dependancies, connect things to what you know etc.) or suggest books which contain advise like this alongside their main content (I think Tao's analysis texts might do this?)
Re: Ask HN: Math books that made you significantly better at math?
#186How To Solve It by G. Polya https://press.princeton.edu/books/paperback/9780691164076/ho...
A Logical Approach to Discrete Math by David Greis and Fred Schneider, https://link.springer.com/book/10.1007/978-1-4757-3837-7
I'm self-taught so for me it was learning how to write proofs that gave me a big boost in being able to branch out into different area of interest and not give up. :)
Re: Ask HN: Math books that made you significantly better at math?
#187[dead]
Re: Ask HN: Math books that made you significantly better at math?
#188Velleman's How to Prove It greatly helped my ability to construct set theoretic proofs, which better prepared me for Spivak's calculus and Baby Rudin. Hamkins' Proof and the Art of Mathematics is designed as a a good, less set-theory heavy, introduction to proof writing that leads more naturally to analysis. OpenStax books are FREE.
Surprised to see Velleman's book so far down. It taught me that proofs are fun and do not in general require clever tricks. As a bonus, it provided plenty of practice with foundational objects such as sets, relations and functions. All this made me much better at doing mathematics and prepared to texts in real analysis, CS, algebra.
Re: Ask HN: Math books that made you significantly better at math?
#189Jeffreys, Harold, and Bertha Swirles Jeffreys. Methods Of Mathematical Physics. Cambridge At The University Press, 1950. http://archive.org/details/methodsofmathema031187mbp.
Re: Ask HN: Math books that made you significantly better at math?
#190A pair which I am most of the way through:
_Make: Geometry: Learn by coding, 3D printing and building_ https://www.goodreads.com/en/book/show/58059196
and
_Make: Calculus: Build models to learn, visualize, and explore_ https://www.goodreads.com/book/show/61739368-make
I'd really like to find a similar book on conic sections --- my next major project seems to need them, and when I tried to solve it using trigonometry alone, I wound up 7 or 8 levels deep in triangles and wasn't much more than half-way to where I needed to be.