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Ask HN: How to self-learn math?

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

#201

Earlier quoted context omitted.

I'm still working on generating the MATH eBook, but the 3-in-1 book (MATH+MECH+CALC) is available here: https://gumroad.com/l/noBSmath Chapter 1 of the 3-in-1 book is essentially the same as the No Bullshit guide to Mathematics. You can see a preview here: https://minireference.com/static/excerpts/noBSguide_v5_previ...

what is the difference between no bs guide to mathematics and the 3-in-1 book?

The 3-in-1 book contains a high school math review, a mechanics course, and a calculus course (450pp). The No bs guide to math is just the high school math review and is much thinner 170pp. (I'm essentially cutting up the 3-in-1 book and releasing it as split books because I realize 450pp can be intimidating for some readers).

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

#202
Where do you live? In most Europe public university is free and you can attend courses. I don’t know about US or other parts of the world.

If you just “show up one day”, you’ll be seen as pretty weird, but hey, it’s math, there will certainly be people more weird than you. My recommendation would be to introduce yourself to the teachers and be very careful/polite/diligent in attending the course. Some teachers can be very opinionated, just go with the flow.

Given your initial level, I’d recommend to focus on breadth instead of depth. It’s likely the case that you don’t know enough yet to make an informed decision.

For example, in my case I love algebraic geometry, number theory, and cryptography. And I hate calculus with a passion, including analytical number theory. None of this was clear to me until the 2nd-3rd year of university, foundamentally because what you learn in high school (liceo, in Italy) is kind ok fixed and biased towards calculus.

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

#203

I'd like to learn vector calculus (to better understand Maxwell's Equations). Does anyone have any learning resources they could recommend? I've got this video in my Watch Later queue on YouTube, but if there are any other resources that give a clear introduction to the material I'd be interested in them. To give a bit of background, I learnt the basics of calculus back in school but I haven't used it in over 15 year…

Edward Frenkel's UC Berkeley course:

https://www.youtube.com/playlist?list=PLaLOVNqqD-2GcoO8CLvCb...

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

#204
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…

6,7,8 can be done alongside 2 there's no reason to leave those 4 foundation topics to late IMHO.

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

#205

find a problem without an answer(o) and try to answer it research as much as you can about the problem until you understand it well enough to explain it to someone else when you come across new concepts, research them.. recurse ;p if you like to program then try to write your own implementations of concepts as you learn them if you are unfamiliar with programming i would recommend trying it, you get to build this mat…

good answer p . saying hello from canada, c.

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

#206
post #113

I know people are recommending a lot of books here but I want to say this, I know a lot of you guys might going to shit on me but telling someone about 5-6 book in order to self-learn maths is never going to help. I see that when someone people ask for help instead of relating what he is really asking for that he wants to understand and learn math people start telling the names of these books that they knew about not…

I agree with the basic thrust of your comment, which as I interpret it boils down to saying it's unhelpful to throw book titles at a person without any context or guidance. However, I disagree with this point: > If some 2-minute video gives you something actionable to do rather than going through a 2-hour chapter in textbook there is no point of going through 2-hour chapter. Knowledge is all about applying not learni…

> it's unhelpful to throw book titles at a person without any context or guidance

Here's one reason it's unhelpful; After 4 or 5 people list a bunch of books, you now have a long list of books, and no way to know which to start with, unless there is a lot of overlap - you could just as well google/search amazon and look at ratings, which would give you far better results.

Furthermore, many people tend not to read multiple math books on the same subject, so they just recommend what they know w/o having any knowledge of how that book fares against other suggestions.

If they expand on either their own credentials, and reading on the matter, so you have the context of their knowledge; or give reasons why that book is good, this gives a better basis for comparison.

As an aside; I like the coursera structure of following video lectures with content summaries of what was covered in the video. The advantage is 1) quick reference of material without having to search through a video; 2) if you already understand the topic, you can often just read the summary, and skip the video if you think you already know the material.

Another aside; one problem with books versus videos is often books are long compendia of a field, where as videos are shorter. if you already know topic A and want to learn B, then there may already be a video on topic B, where as a book might cover B in some chapter. For these cases, it might be good to discuss individual chapters/sections of book, but that assumes you can ready them somewhat independently given prior knowledge.

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

#207

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…

> I disagree with the general statement that leaning maths is "pitifully slow without a teacher".

How do you check your work then? I remember specific experiences in college math classes where I thought I understood something, took a test, and then got something wrong. And it was because of a misunderstanding of something I thought I understood. I have those misunderstandings occasionally in math. And that can make self-teaching really difficult. At least with cs/software development you can check your understanding by writing code.

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

#209

Earlier quoted context omitted.

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…

> I disagree with the general statement that leaning maths is "pitifully slow without a teacher". How do you check your work then? I remember specific experiences in college math classes where I thought I understood something, took a test, and then got something wrong. And it was because of a misunderstanding of something I thought I understood. I have those misunderstandings occasionally in math. And that can make s…

By downloading question papers that have worked solutions. If you get something wrong, check your solution against the worked solution and then error in your understanding should become apparent. This works well up to about college level, after which it's harder to find resources.

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

#210

Earlier quoted context omitted.

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…

I think for most people though, not having a teacher doesn't mean "pitifully slow", it means they will eventually forfeit the endeavor. The option to self-study has always been there, and now Khan Academy is here too, but I think there's a reason why we haven't seen an education revolution just yet, and I think it's because an interactive teacher who monitors your state and thinks about the road ahead is key. There a…

They feel anxiety about basic math because they've lost touch with the basics, and this is a massive problem. They could and should go back and review the basics; otherwise they will not make great teachers.
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