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Ask HN: How to self-learn math?

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Re: Ask HN: How to self-learn math?

#51

Post by mkl »

elcapitan wrote: post #41
mkl wrote: post #37

Earlier quoted context omitted.

Personally, I wouldn't recommend Wolfram Alpha, or anything proprietary. If you have some programming knowledge (as OP is likely to), Sympy and Matplotlib are much more capable and controllable (and free!). I think if you're building up skills and knowledge, it should be towards something you have control over and can use in any situation without worrying about licences, cost, etc. At my university, we teach undergra…

I think for starting from scratch these software library interfaces (that is what they are) create way more problems than they solve, if OP is not experienced enough to use them. That doesn't mean they can't get around to use them finally, but for exploring a space a tool like Alpha that is both evaluating as well as explaining seems much more useful. Interacting with Sympy and Matplotlib seems like something you wou…

I'm not so sure. I use Sympy, Matplotlib, Numpy, etc. even when I am just exploring, and have little idea what I want to achieve.

I do use and recommend http://desmos.com, which is proprietary (but pretty limited and easily translated to Python). It doesn't lock features behind a paywall like Wolfram Alpha.

Re: Ask HN: How to self-learn math?

#52

Post by MikkoFinell »

hamad wrote: post #6

haskell(common knowledge) -> category theory(compare it with set theory here you will read about math foundation crisis) -> type theory(curry howard correspondence or logic == program) personal perspective

It's better to do it the other way around; begin at the low level and work your way up to the abstractions:

* Foundations of proofwriting and mathematical thinking: Velleman

* Going further into logic: Hindley and Seldin, Lambda-Calculus and Combinators

* Apply what you learned just learned: Sussman and Abelson, SICP

* Getting serious: Awodey, Category theory

* You're there: Haskell

Re: Ask HN: How to self-learn math?

#53

Post by elcapitan »

mkl wrote: post #51
elcapitan wrote: post #41

Earlier quoted context omitted.

I think for starting from scratch these software library interfaces (that is what they are) create way more problems than they solve, if OP is not experienced enough to use them. That doesn't mean they can't get around to use them finally, but for exploring a space a tool like Alpha that is both evaluating as well as explaining seems much more useful. Interacting with Sympy and Matplotlib seems like something you wou…

I'm not so sure. I use Sympy, Matplotlib, Numpy, etc. even when I am just exploring, and have little idea what I want to achieve. I do use and recommend http://desmos.com , which is proprietary (but pretty limited and easily translated to Python). It doesn't lock features behind a paywall like Wolfram Alpha.

I was just guessing from OPs post saying that they don't even have basic highschool math knowledge, from which I would assume that translating mathematical concepts into concepts in Python would probably create more difficulties than necessary, whereas in Alpha you can just dump an equation and then get an interpretation. Matplotlib in particular is kind of an expert interface for a library, at least when I last checked it out.

Desmos looks interesting.

Re: Ask HN: How to self-learn math?

#54

Post by sidcool »

synthmeat wrote: post #50

I’m going to go with a few assumptions here: a) You don’t do this full time. b) By “bottoms up” you just mean “with firm grasp on fundamentals”, not logic/set/category/type theory approach. c) You are skilled with programming/software in general. In a way, you’re ahead of math peers in that you don’t need to do a lot of problems by hand, and can develop intuition much faster through many software tools available. Eve…

What's your opinion of Mathematics for computer science?

Re: Ask HN: How to self-learn math?

#55

Post by ll350 »

I almost lol'ed when I read this, but I think I have good suggestion for you. "Maths - A Student Survival Guide" by Jenny Olive: https://www.amazon.com/Maths-Students-Survival-Self-Help-Eng... She basically starts out with the simplest algebra (fractions) and gradually works up to topics in 1st semester Calculus. And she starts each chapter with a short quiz to test yourself and skip ahead if already know the material. This book is great for what you are describing, if I'm understanding you. I picked it up when I was preparing to return to college after being away for many years. I supplemented it with another book I highly recommend: "Mastering Technical Mathematics" by Stan Gibilisco and Norman Crowhurst: https://www.amazon.com/Mastering-Technical-Mathematics-Third...

I found that Jenny Olive's book was well designed and preferred it's style to any math textbook I have ever used. Even so occasionally I would get bored while working thru it. That is when I flip thru the Stan Gibilisco's book, which was full of interesting looking problems and examples. When I would try to solve one of them, it would become apparent that I still need to work on the fundamental concepts that were prerequisites for solving the problem. Thus I would return to Jenny Olive's book right where I left off, re-energized by the desire to master those fundamentals that she covers so well.

Re: Ask HN: How to self-learn math?

#56

Post by Zeule »

IvanK_net wrote: post #21

Whenever I tried to self-learn anything, it was a very bad idea. Some parts of the subject I enjoyed and other parts I hated. I tend to make my own conclusions, which parts are useful and wich are a waste of time (so I tend to skip them). I tend to filter out the material this way, in order to make learning less painful and more fun. My conclusions (what is useful and what isn't) were always wrong and I ended up not…

This answer is absurd, and only true for people with little motivation. Self-learning does require more motivation and "grit" to keep going, and some planning early on, and there is a higher dropout rate. But in many cases, it is the best option. I've found that this is especially true for many parts of STEM fields. It is a far more productive and effective use of time to work through problems than listen to lectures. Of course, it is also helpful to have people you can ask questions when you don't understand as comes with a class, but that can also be found online. I also find that I often understand things I learn on my own more deeply because I can go at my own pace and have more time (time not spent listening to lectures or preparing for exams on a fixed deadline) to draw from a variety of resources.

One of the most important skills someone can learn is how to learn, and especially how to solve problems and keep going when it is difficult.

For math through high school level/early university, I'd suggest Art of Problem Solving (if you can handle it). It teaches by having people solve problems rather than presenting mathematical techniques to memorize. Some of them are straightforward, but many are tricky problems and fun puzzles with elegant solutions. It helps you gain a good sense for numbers and problem solving, and an appreciation for the beauty of math. The teaching method helps you intuitively understand rules rather than memorize them. They also have a nice gamified online practice system (Alcumus) to go along with the first half of their books.

For some higher level, more applied areas like linear algebra there are some good coding-based courses like codingthematrix.com. Project Euler is also another good option for practicing math with programming.

Re: Ask HN: How to self-learn math?

#58

Post by nhaehnle »

I'll make an unconventional suggestion that, in addition to just brushing up on high-school mathematics, you should read Gödel, Escher, Bach by Hofstadter. It's a very meandering book, but it contains a lot of interesting ideas related to math and probably one of the best ways of teaching you about formal systems, which is really crucial to the axiomatic approach of "real" math.

Re: Ask HN: How to self-learn math?

#59

Post by IndrekR »

jimnotgym wrote: post #44

I studied my 'college level' maths with the Open University. The materials were excellent, being designed specifically for self learning and they offer access to a tutor too. OU courses also give you proper qualifications. I am not sure how it works for non UK students. open.ac.uk However I did mine before the cuts to higher education in the UK and the courses are much more expensive now. This is very sad as it enabl…

Second that! OU math courses were really good. This involves the materials and tutor support. Took them in 2003..2004, so things may have changed.
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