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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?

#151

Post by MrMan »

DoingIsLearning wrote: post #139
Philip-J-Fry wrote: post #101

Earlier quoted context omitted.

I had the same idea. I bought myself a Remarkable 2 and signed up to Khan Academy. Now I'm revising algebra basics and I plan to go as advanced as Khan Academy lets me. I was really bad at maths in school (UK A Levels). But I'm a successful software developer today. I felt like knowing more advanced maths could make me a better developer and not feel intimidated by a lot of the things I see. I'm actually enjoying it…

If you don't mind the question how is the Remarkable helping you in this. Just to avoid the clutter of paper? Or does it some how OCR you're handwriting?

I have a remarkable 2 and a Microsoft Surface Pro, intended to de-clutter math coursework. Both work, but I found that the real estate on the remarkable was too limited, even though its a great device, so I tried the Surface Pro. I can fit just about any sized work onto it, and you can endlessly scroll down which was something I couldn't figure out on the remarkable. It makes doing math easy or at least takes away some housekeeping which I find really distracting. And saving and organizing work and being able to import and export files is a bonus.

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

#152

Post by macrolocal »

bombcar wrote: post #12
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…

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.

Ditto for Euclid. Doing this early in life pays huge dividends.

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

#153

Post by bee_rider »

orm wrote: post #106
orm wrote: post #96

Earlier quoted context omitted.

3Blue1Brown videos seem like a good resource to use along any book. My experience as a math major (in the distant past) is that the kind of visualization the author shows you is also something you want to imitate in your head when you are learning new concepts. I find things I learned in this level tended to stick in my head 10+ years later, other stuff less.

I should mention focusing on doing a few interesting problems, rather than many not so interesting ones, is also one way to help yourself understand more deeply.

Lots of easy problems is a good way to build up muscle memory, though. IMO the brute-force method of, say, Saxon Math really makes sense for things like basic elementary school algebra and probably intro calculus, where the student is sort of learning the math equivalent of how to walk. Not sure where the switch over ought to be, though.

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

#155

Post by mharig »

mohamez wrote: post #9

Any good book about the history of mathematics that will teach you a natural historical development of concepts to reach more generalizations. History of mathematics 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.

Foundations and Fundamental Concepts of Mathematics, by Howard Eves

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

#156

Post by jsenn »

* The Art of Probability by Hamming. An opinionated, slightly quirky text on probability. Unlike the text used in my university course its explanations were clear and rigourous without being pedantic. The exercises were both interesting and enlightening. The only book in this list that taught skills I've actually used in the real world.

* Calculus by Spivak. This was used in my intro calculus course in university. It's very much a bottom-up, first-principles construction of calculus. Very proof-based, so you have to be into that. Tons of exercises, including some that sneakily introduce pretty advanced concepts not explicitly covered in the main text. This book, along with the course, rearranged by brain. Not sure how useful it would be for self-study though.

* Measurement by Lockhart. I haven't read the whole thing, but have enjoyed working through some of the exercises. A good book for really grokking geometric proofs and understanding "mathematical beauty", rather than just cranking through algebraic proofs step by step.

* Naive Set Theory by Halmos. Somewhat spare, but a nice, concise introduction to axiomatic set theory. Brings you from nothing up to the Continuum Hypothesis. I read this somewhere around my first year in university and it was another brain-rearranger.

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

#157

Post by Philip-J-Fry »

DoingIsLearning wrote: post #139
Philip-J-Fry wrote: post #101

Earlier quoted context omitted.

I had the same idea. I bought myself a Remarkable 2 and signed up to Khan Academy. Now I'm revising algebra basics and I plan to go as advanced as Khan Academy lets me. I was really bad at maths in school (UK A Levels). But I'm a successful software developer today. I felt like knowing more advanced maths could make me a better developer and not feel intimidated by a lot of the things I see. I'm actually enjoying it…

If you don't mind the question how is the Remarkable helping you in this. Just to avoid the clutter of paper? Or does it some how OCR you're handwriting?

I hate the clutter of paper and how hard to organise it is for me. Plus, how messy I am writing on paper and crossing things out all the time.

The Remarkable, at least for me, is good because I can organise my notebooks into folders by certain math lessons or concepts. And I can undo any mistakes, so my notes are clean. Even if I am quickly working something out I am clean it up and make it a good note for future me. The feel of writing on it is much nicer as well versus my laptop's pen or my iPad's pen.

Also, I like that it basically just does notes. There's no Android bullshit, it's just no nonsense note taking. Some competitor tablets have Android and all that baggage.

It can OCR you writing, but I don't know how good that would be for math.

The Remarkable isn't the only tablet that can do this, but it's the one I bought because I like the style and the simplicity of the software.

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

#158

Post by boothby »

No specific book, but generic advise about how to use a math book. Homework, homework, homework. Read the whole thing, but focus on the exercises. Do every exercise as soon as you can manage: don't wait until you've read the whole chapter -- once you get confused and stumped, the lesson of the chapter becomes urgent and I find that sharpens my attention.

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

#159

Post by ask_b123 »

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…

I used this a lot while in school, very useful!

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

#160

Post by mindcrime »

theusus wrote: post #142

> Discrete Mathematics with Applications by Susanna S. Epp Fantastic book for Discrete Mathematics with lucid explanation and good exercises. The other one would be concrete mathematics.

Epp's book is my favorite Discrete Math book by far. Her writing style is very clear and easy to follow. And as you say, there are good exercises. And if you buy an older edition, used copies can be had for a (relatively) reasonable price.
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