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Ask HN: How to self-learn math?

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

#71

Post by evanb »

RossBencina wrote: post #30
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…

To the above I would add: How to Think Like a Mathematician - Kevin Houston (an excellent book to read before starting) How to Read and Do Proofs - Solow The Keys to Advanced Mathematics: Recurrent Themes in Abstract Reasoning - Solow Calculus - Spivak (Actually a Real Analysis book, not a Calculus book, see e.g. https://math.stackexchange.com/questions/1811325/spivaks-cal... ) Linear Algebra Done Right - Axler (Inte…

There's also How To Solve It by Polya. Small, accessible, casually written.

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

#72

Post by synthmeat »

tzs wrote: post #70

> My current proficiency level is pre-high school mathematics as I didn't pay much attention in high school, learning effectively nothing. I took a look at your other comments and submissions, to try to get an idea of whether or not you are a programmer. The fact that you are on HN makes the odds pretty good that you are or were, but there are enough people here who are not that I didn't want to assume. It's relevant…

> I'm not normally suspicious of these types of questions...but something seems off here.

Really doesn't need to be off. Some shitty decisions on where to put attention in past and now probably in position where one can play catch-up with ambitions or just doesn't play well with authority and wants to conquer things with a more individualistic touch...

..or really any number of scenarios that can explain this not being "off" at all.

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

#73

Post by baby »

Go in a store, look at math books and find out one that looks like it:

* teaches you things you don't know

* relies on things you know for the most part

* do it well

You're in luck, a few years ago pedagogy in math was not really a thing. Now we have khanacademy and plenty of other courses (Coursera, Udemy, ...) and youtube videos to help you.

There are different goals when you're learning math. Do you just want to get more exposure? Then focus on youtube videos (subscribe to some math channels) and novel-type of books.

You want to get a deep understanding of some area in math like algebra or number theory? Then you're going to have to buy these books I told you about and do the exercises in them. If you've chosen your book well, they will have good explanations on how to solve these if you get stuck. In any case, exercising is the way to go.

For those who recommend a good teacher, I think this is only a good advice if you're just starting and too many concepts are scary to you, but if you're already have a good basis then good videos, online courses and text books are enough and even better than a teacher.

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

#74

Post by chris_wot »

dvddgld wrote: post #47
Entalpi wrote: post #46

Earlier quoted context omitted.

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

That’s how I got to grips with trigonometry... I tried to understand why sine, cosine, tangent, cotangent, secant and close can’t we’re named like they were... then I found a bunch of stuff on the unit circle. Never looked back!

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

#75

Post by iliketosleep »

mathgenius wrote: post #64

Nothing beats having a (good) teacher. Self-learning, no matter how smart you are, is pitifully slow without a teacher. Half an hour with a good teacher can save you weeks of table head-butting. (But obviously you can't rely only on the teacher.) As for books, it's not a spectator sport: you gotta do it yourself. Read a sentence, then work it out yourself with pen & paper. You can't get it just from reading alone. Fi…

I disagree with the general statement that leaning maths is "pitifully slow without a teacher". So long as one has structure (e.g. some kind of syllabus) and has access to google, then learning can proceed very efficiently indeed. In addition, by being able to work through difficulties independently you can "be your own master" so to speak, earning the confidence to solve new and difficult problems without assistance.

Having said that, I have come across people who have absolutely no apitutude for maths and definitely need a teacher. In a matsh class, there's usually one one set of people who kind of just "get it" straight away, and another set who struggle despite studying hard.

As you said, there are many roads to Rome, and the best road may or may not involve a teacher depending on the individual.

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

#76

Post by lordnacho »

I'm looking for recommendations for the same question, but for someone who did graduate Engineering and Econ, and does a lot of coding.

There's a lot of mathematical fundamentals they don't teach you while you're learning a whole variety of applied math.

Off the top the pieces we did:

- Linear Algebra

- Computation (big-O etc)

- Vector calculus

- Finite Element methods

- SDEs, PDEs

- Discrete math (graphs, cryptography, number theory, etc)

- Complex analysis (used a lot in EE)

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

#77

Post by chris_wot »

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…

I find there are things I’m missing. Does the precalculus stuff cover geometry and polynomials?

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

#79

Post by realharo »

mathgenius wrote: post #64

Nothing beats having a (good) teacher. Self-learning, no matter how smart you are, is pitifully slow without a teacher. Half an hour with a good teacher can save you weeks of table head-butting. (But obviously you can't rely only on the teacher.) As for books, it's not a spectator sport: you gotta do it yourself. Read a sentence, then work it out yourself with pen & paper. You can't get it just from reading alone. Fi…

>Half an hour with a good teacher can save you weeks of table head-butting.

That says more about the poor quality (or bad fit) of the book/video/material than it says about the skill of the teacher.

I guess online courses where students can post comments and talk to each other partially address this. These comments may help point out the parts that the material failed to convey properly (and in an ideal world, such feedback would then be incorporated into the next revision of the material).

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

#80

Post by tzs »

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…

> 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!).

If one doesn't mind proprietary, though, and wants even more capable and controllable, Mathematica on a Raspberry Pi is pretty cool, and is free (beer) and is included in the default install of Raspbian.

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