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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?

#221

Post by imranq »

Counter-intuitively, reading Tim Ferris and his DSSS approach made me much better at math

Deconstruct: Break down the math you want to know into big problems and concepts. Pick a math-related goal that is Measurable and Time-Bound

Selection: What the 20% of math concepts, that if made really strong, would solve 80% of math problems

Sequencing: What order of material should you study for maximal progress

Stakes: Find some incentive to complete the problem. Some nice view of mathematical terrain, as part of a masters program, applications to another field, a prize, a cookie. Anything that motivates you to actually make progress towards the goal

This approach helped me learn a bunch of high level math like abstract algebra, analysis, linear algebra, etc.

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

#224

Post by bee_rider »

skyde wrote: post #210
TjZkxkxeky wrote: post #202

Earlier quoted context omitted.

I like Saxon math for kids. It implements spaced repetition with their exercises, so the kids actually retain what was taught.

we tried "Saxon math", Singapore math dimensions, and Beast Academy. And my impression was that Saxon Math was the worst. What I mean by worst is that it just make you practice an algorithm by doing lot of repetition but doesn't force you to have a deep understanding or problem solving skill.

Saxon math worked out for me, although we didn’t shop around as far as I remember, so maybe Singapore would have worked fine as well.

My experience is that I didn’t really feel like I was memorizing an algorithm. Because the problem set includes assignments from all of the old sets, it is hard to memorize all of the algorithms. So you instead memorize the different moves that are allowed and have a general idea of what types of moves might be useful.

I dunno. I went on to do engineery stuff as an undergrad rather than pure math stuff, it seems like a good match because engineering problems are also often in the “no need to be super clever, just don’t mess up” vein, so it could be just a lucky match. This is what I mean by muscle memory — I’ll use the famous names theorems when necessary but sometimes you just need to bash the math until the thing you want is on that side of the equal sign and the other stuff is on the other side.

I think anything that results in

1) actually reading some textbook

2) actually working through problems for a couple hours a week

will compare well to the typical US math education pretty well anyway.

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

#225

Post by jordibc »

For sure I got significantly(?) better with classics like Spivak, Apostol, Rudin.

"Real and Complex Analysis" by Rudin, and the two books both named "Calculus" from Spivak and Apostol. But also from Apostol his more concise and far-reaching "Mathematical Analysis". And from Spivak his small gem "Calculus On Manifolds" made quite a dent on me.

Other than more "classic math" books, I also wanted to mention two outliers that I found eye-opening and generally awesome:

* Street-Fighting Mathematics, by Mahajan (http://streetfightingmath.com/). Intuitive, useful and fun.

* Geometric Algebra for Physicists, by Doran and Lasenby. I found the power and elegance of geometric algebra mesmerizing, and even if this book is also about physics and there may be more appropriate math-only books about geometric algebra, this is the one that made it for me.

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

#226

Post by rahimnathwani »

skyde wrote: post #208

On a similar note: Does anyone have book they would recommend to teach Algebra or pre-algebra to young kid?

Not a book, but I recently had my son look at the pre-algebra track brilliant.org, and it looks nice. I'm not sure whether there's a paywall.

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

#228

Post by 6gvONxR4sf7o »

Probabilistic Graphical Models by Koller & Friedman. In anything statistics and ML related, being able to deal with complicated probabilitistic things that are all related is really useful. This book gives you that toolkit. It's a "strong foundations" kind of book, rather than a bunch of methods you'll use directly.

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

#229

Post by ForHackernews »

The Art and Craft of Problem Solving https://archive.org/details/the-art-and-craft-of-problem-sol...

This is only math book I've ever read that teaches the mindset needed to work mathematics problems, rather than mathematical concepts or techniques.

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