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Ask HN: How to self-learn math?

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

#181

Post by tdaniels »

aphextron wrote: post #112

>My current proficiency level is pre-high school mathematics as I didn't pay much attention in high school, learning effectively nothing. Advice from someone who was in the same position: Take a class. Multiple classes. Go sign up for a Mathematics AS at your nearest community college right now. You will never know enough of what you don't know to learn this stuff on your own. A lot of it is just doing the painful re…

I second this. Having studied to the postgrad level, I've come to appreciate just how broad the subject is. Looking back, I feel it would have been near impossible for me (personally) to get here without the help of lecturers and tutors - often prerequisite knowledge creeps in unexpectedly, and you come to rely on them to guide you through this.

I agree also that regular grading and a lesson schedule help to both push you to learn, and for you to assess your progress in an unbiassed fashion.

Personally, though, I am biassed - and am thrilled when people say they want to learn more maths. I love maths, and find it very rewarding. The best of luck with your journey!

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

#182

Post by princeb »

InitialLastName wrote: post #146
Ultimatt wrote: post #122

Earlier quoted context omitted.

Depends what your goal is. I cant imagine anything worse than High School style teaching of mathematics. Its awful. That repetitive calculation, entirely unnecessary for almost any real world situation. Almost every time you are doing repetitive calculation what you should have been taught was a second or third conceptualisation of whatever maths you are looking at. So linear algebra I was only ever taught numericall…

I disagree about the repetitive calculation being "entirely unnecessary". Background: I (probably like many here) excelled at high school and undergraduate mathematics. I have a graduate degree in a heavily mathematics-focused branch of engineering (digital signal processing) and much of my work involves applying that math at a conceptual level. I'm currently tutoring an adult I'm close to who is approximately at GP'…

> 1) It helps to build a sort of mental "muscle memory", and 2) it helps with developing intuition, since your mind eventually gets bored with the mechanics and starts to notice patterns.

muscle memory is super important in math.

the last thing you want is to be struggling with foundation when you're trying to progress through concepts. everything needs to be available to you at the snap of your fingers.

trying to progress math knowledge without the basics is doable, but it's a ton of mental overhead and frustration that you can cut down if you just get the practice out of the way.

plus it's super cool if you're one of those guys who have the ability to quickly apply 10-20 different models on a real world problem. that's what we think of when we think "good at math".

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

#183

Post by 8bitsrule »

Depends on what kind of math you enjoy doing. If you're interested in practical applications, start by becoming an algebra ninja ... so good that just looking at a problem makes it fall apart.

If you find something that's 'beautiful' (I never did :-( ), then scratch that itch.

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

#186

Post by ethbro »

ams6110 wrote: post #162
wrs wrote: post #150

Earlier quoted context omitted.

My high school calculus and physics teachers synchronized their classes, so shortly after we learned something in calculus, we would use it in physics. Since then I’ve learned this is not as common as it should be! Perhaps it works especially well in that case because calculus was literally invented to do the kind of physics you learn in high school, so it’s a very natural combination. Linear algebra (e.g.) is so gen…

My high school only taught physics without calculus. In 12th grade when I took calculus separately I was sort of annoyed to realize how much easier physics would have been using calculus.

This was my experience too.

I remember doing integrals in high school, but didn't take calculus-based physics until my second year of college.

Jesus christ, it explained a lot of things.

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

#187

Post by ethbro »

elbear wrote: post #144
Ultimatt wrote: post #122

Earlier quoted context omitted.

Depends what your goal is. I cant imagine anything worse than High School style teaching of mathematics. Its awful. That repetitive calculation, entirely unnecessary for almost any real world situation. Almost every time you are doing repetitive calculation what you should have been taught was a second or third conceptualisation of whatever maths you are looking at. So linear algebra I was only ever taught numericall…

Thank you for saying this. I've been learning math from Khan Academy for the last 200 days. I've reached calculus and I feel more and more the need for examples of how to apply the math that I'm learning to truly understand what it's useful for. I was actually thinking of learning how to build video games (or at least parts of it) to properly understand linear algebra. Someone else also suggested physics for calculus…

Fwiw, I found electromag (typically undergrad physics 2) the best application of calculus.

Classical physics of motion (physics 1) used some superficial calculus, but none of the use cases that would let you spread your mathematical wings cropped up in the material we studied.

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

#188

Post by HaoZeke »

I think you need to first decide your application before starting such a thing.

There's no way to remember the entirety of mathematics, even if you do rote memorize and practice your way through it.

You need to figure out which sub-discipline you can apply and follow through with it,

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

#189

Post by budadre75 »

rizn wrote: post #140

I was in your position as well and my recommendation is to buy a good book. I personally chose Precalculus by James Stewart and it works for me. It's a thick 1000 pages book with excercises and tests. It quite well explains all topics, which you would have in high school (from basic arithmetics to everything you need to start calculus). I do maths in my spare time (a few hours a week) and I completed 700 pages over p…

You are very persistent! But the efficiency is too low, not to put you down but precalculus is not something you should spend so much time on, there are so much more to learn and so much more fun after precalc. At this rate, it's probably going to take you 10 years to complete calculus and differential equations, which typically college students take a year to finish and start applying. Plus there are abstract algebra, discrete mathematics, etc. I know you are probably having fun with the precalc topics, but trust me it's more fun afterwards. Imagine what you are learning now is from times before 17th Century, and you wanna catch up to all the fun today at that rate, it doesn't sound fun.
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