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Ask HN: How to self-learn math?

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

#41

Post by elcapitan »

mkl wrote: post #37
elcapitan wrote: post #26

Method-wise it could be helpful to get a (lightweight) computer algebra software and learn how to use it and how to explore knowledge using it. One thing you won't have when you're out on your own is a method to just try out stuff and verify that it is correct, or to get better visualizations quickly. Often you will get stuck with something and need a different angle (which teachers or other students could normally p…

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 would do when you have already a solid understanding of what you want to achieve.

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

#42

Post by jpineman »

mkl wrote: post #37
elcapitan wrote: post #26

Method-wise it could be helpful to get a (lightweight) computer algebra software and learn how to use it and how to explore knowledge using it. One thing you won't have when you're out on your own is a method to just try out stuff and verify that it is correct, or to get better visualizations quickly. Often you will get stuck with something and need a different angle (which teachers or other students could normally p…

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…

At my university we also use Matlab a lot. However, I've found that Octave is a very suitable replacement for all packages except Simulink, which is widely used for Control. The alternative here would be Scilab/Xcos.

I also use python/sympy/matplotlib/scipy/jupyter a lot and it's absolutely great -- highly recommend to the OP.

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

#43

Post by alexdowad »

watwut wrote: post #35

I would suggest to browse through coursera and pick something free and easy (since you labeled yourself pre-highschool). If it turns out too difficult, dont worry, unsign and pick something else. I never tried Khan Academy, but people seem to praise that too. Moreover, maybe just taking high school math book and exercises book would be fine. Most importantly, at stage you are at, learning math should consist of doing…

I found Khan Academy really helped with high-school algebra, single-variable calculus, and especially multi-variable calculus (the visualizations were great). Khan Academy's linear algebra course was awful and I dropped out there.

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

#44

Post by jimnotgym »

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 enabled me to change careers.

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

#45

Post by bryanph_ »

There is no such thing as "bottoms up" in mathematics, I think a relatively broad examination of mathematics might be useful so that you can discover what is relevant to the subjects you are actually interested in. I learned this the hard way. Here you have Feynman talking on this: https://www.youtube.com/watch?v=YaUlqXRPMmY Finding a real world use case for the math you learn will be crucial if you self-study to keep yourself motivated to keep going.

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

#46

Post by Entalpi »

dvddgld wrote: post #27
mikevm wrote: post #19

Ok, I'll take a crack at this: Up to high-school level: 1. Precalculus: Precalculus: A Prelude to Calculus - Axler 2. Calculus: The Calculus Tutoring Book - Ash. College: 3. Preparation for Collegel-level maths: 3a. General prep for high level maths: How to Study as a Mathematics Major - Alcock 3b. Proof writing: How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!) 4. Ma…

Two quick things I can recommend without hesitation, which focus on an intuitive understanding of concepts: 1. Essence of Linear Algebra mini-series - https://m.youtube.com/watch?v=kjBOesZCoqc 2. Better Explained website - https://betterexplained.com YouTube has a lot of high quality math content, it definitely helped through university. It's also worth mentioning the Stanford U courses. The main takeaway I have for…

My two cents are whenever something seems hard/impossible/infuriating/etc, take a break then seek dofferent sources on the material. A lot of times I have been hung up on something only to find that things make much more sense when approaching it from a different viewpoint. :)

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

#47

Post by dvddgld »

Entalpi wrote: post #46
dvddgld wrote: post #27

Earlier quoted context omitted.

Two quick things I can recommend without hesitation, which focus on an intuitive understanding of concepts: 1. Essence of Linear Algebra mini-series - https://m.youtube.com/watch?v=kjBOesZCoqc 2. Better Explained website - https://betterexplained.com YouTube has a lot of high quality math content, it definitely helped through university. It's also worth mentioning the Stanford U courses. The main takeaway I have for…

My two cents are whenever something seems hard/impossible/infuriating/etc, take a break then seek dofferent sources on the material. A lot of times I have been hung up on something only to find that things make much more sense when approaching it from a different viewpoint. :)

Absolutely! Not having to hit your head against a wall helps prevent burnout as well as just plain being more effective

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

#48

Post by PyComfy »

mikevm wrote: post #19

Ok, I'll take a crack at this: Up to high-school level: 1. Precalculus: Precalculus: A Prelude to Calculus - Axler 2. Calculus: The Calculus Tutoring Book - Ash. College: 3. Preparation for Collegel-level maths: 3a. General prep for high level maths: How to Study as a Mathematics Major - Alcock 3b. Proof writing: How to Prove It - A Structured Approach - Velleman OR Book of Proof (2nd ed) - Hammack (it's free!) 4. Ma…

for linear algebra, may i add http://immersivemath.com/ila/index.html

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

#49

Post by undecidabot »

I really enjoyed reading "Discrete Mathematics with Applications" by Susanna S. Epp. It's very accessible. Having a good understanding of algebra should be enough.

For programmers, Discrete Mathematics is arguably the most relevant discipline of Math. Yegge wrote a long but interesting post on this subject [1].

[1] http://steve-yegge.blogspot.com/2006/03/math-for-programmers...

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

#50

Post by synthmeat »

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. Even charting simple tables goes a long way.

Another thing you have going for yourself is - you can basically skip high school math and jump right in for the good stuff.

I’d recommend getting great and cheap russian recap of mathematics up to 60s [1] and a modern coverage of the field in relatively light essay form [2].

Just skimming these will broaden your mathematical horizons to the point where you’re going to start recognizing more and more real-life math problems in your daily life which will, in return, incite you to dig further into aspects and resources of what is absolutely huge and beautiful landscape of mathematics.

[1] https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

[2] https://www.amazon.com/Princeton-Companion-Mathematics-Timot...

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