Not a book. But a course by Prof Keith Devlin on Coursera called Introduction to Mathematical Thinking.
I jumped into the first analysis class (using baby Rudin) completely unprepared and this course saved me!
Ask HN: Math books that made you significantly better at math?
11–20 of 323 posts
Re: Ask HN: Math books that made you significantly better at math?
#12I 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…
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.
Re: Ask HN: Math books that made you significantly better at math?
#13I 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…
Is that entire course just wading through the wreckage wrought by Gödel?
Re: Ask HN: Math books that made you significantly better at math?
#14Meta comment: might be good to add the level of mathematical maturity needed to enjoy the book.
Re: Ask HN: Math books that made you significantly better at math?
#15Significantly better I don't know but when I was a child I was given Der Zahlenteufel. Ein Kopfkissenbuch für alle, die Angst vor der Mathematik haben (The Number Devil) and I liked it very much
Re: Ask HN: Math books that made you significantly better at math?
#16I 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…
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 from these texts, but for you normals out there: don't optimize too much, you're quite alright in taking the normal approach of just taking a class at a community college, doing the exercises the teacher assigns, etc.
Re: Ask HN: Math books that made you significantly better at math?
#17Linear 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 advanced math textbooks).
- Linear Algebra is arguably the most important math subject these days.
Re: Ask HN: Math books that made you significantly better at math?
#18I 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…
History of mathematics as well, it will give you a very subtle entry into the minds of mathematicians and the motivation behind their theorems.
This will surely make you more appreciative of subjects and concepts you are learning.
Re: Ask HN: Math books that made you significantly better at math?
#19From Mathematics to Generic Programming - Stepanov & Rose
Gödel, Escher, Bach: an Eternal Golden Braid - Hofstadter
Euclid's Elements
Re: Ask HN: Math books that made you significantly better at math?
#20This 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" or "this looks like a special case of Z" sort of things) instead of starting by soldiering through equations, and I credit a lot of that to all the puzzle-solving I did as a kid.