Do the homework if you want to really understand it. Reading math isn't like reading fiction. You need to go slow, and you need to do the problems and the proofs to get it. Yes, ask for help when you get stuck. But there's really no way around grinding through the problems.
Ask HN: How to self-learn math?
141–150 of 215 posts
Re: Ask HN: How to self-learn math?
#142Earlier quoted context omitted.
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…
That being said, there is something for the pressure cooker environment that forces you to consider and learn the hard topics. I have gone back to school twice as an adult, first for a pure math degree, and now for comp sci - machine learning. Both times, the amount of pain it takes is just not something a person with average or above average motivation would go through on their own.
True, though on the flip side sometimes it is easier to take the time needed for deeper understanding outside the pressure cooker environment of classes. Pressure cooker environments can be motivating to keep moving forward, but sometimes at cost of depth and intuitive understanding.
Re: Ask HN: How to self-learn math?
#143Earlier quoted context omitted.
> The Princeton Companion to Mathematics is a good resource... I think Princeton Companion to Physics curated by Frank Wilczek, a Nobelist, is due to be published this year. > Whoever reads it from cover to cover is my hero... Yeah, I'd die an accomplished man if I would grok just a few books I treasure, amongst which are TPCTM and MICMAM. > Don't just be a consumer but write something as soon as you're inspired. Abs…
What is MICMAM? Whitepapers, lectures, and speech transcriptions are also good motivation, and useful resources. Sometimes overwhelming, especially if reading mathematical text is as a foreign language. And sometimes it takes you down a rabbit hole. My biggest block for learning math has really been all the unlearning. After a while ideas like negative numbers and zeros and processes like addition and subtraction sto…
> What is MICMAM?
Check my [1] at root.
> Where to go from there - philosophy or computation?
For me, there's plenty of fun in mathematics without venturing even near the edges of it. Maybe one day I'll grow bored of it, who knows - it's a lifelong process.
Re: Ask HN: How to self-learn math?
#144>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…
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.
Re: Ask HN: How to self-learn math?
#145May I recommend the NCERT math textbooks used in India. They are simple to follow and nicely organized as different levels. They are available for free on the NCERT website (website maybe a bit tough to navigate). The books cover stuff from basic algebra, geometry and calculus. After this you should be good to go for collegiate mathematics like analysis, multivariable calculus etc.
Re: Ask HN: How to self-learn math?
#146>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…
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's starting level and has a strong anxiety reaction to math. I'm finding that the repetitive calculation aspect is important to being able to developing an intuition for the concepts.
The process that's working well for us so far involves alternating between practical word problems (to establish a motivation for learning the material), theoretical/background explanations (to hit the understanding at a high level) and repeated simple problems (to practice the mechanics).
I'm finding that, in terms of process, the repeated problem-solving is critical for two reasons. 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.
Remember that mathematics at that level is all about building blocks. Every concept/problem-solving practice you learn is part of a tower of strategies; if earlier mechanisms aren't almost mindless, it's MUCH harder to build on top of that knowledge.
Re: Ask HN: How to self-learn math?
#147By your early 20s you should know if you need a teacher, or just a guide, or no one but yourself(plus textbooks&internet), for medium level difficulty and down. If you have to ask, I'm pretty sure you need a teacher.
For example, by the time I was in my last year of college, I regularly skipped 90% of class time, and showed up to take tests. I handed in assignments at instructor's office.
I don't process auditory information all that great, but I'm extremely efficient and robust in my processing of visual information including the written word, graphics, pictures, and video.
On some topics I have sought a mentor, with whom can provide a little guidance, and bounce ideas off of. But his is extremely far from the traditional instructor role.
So in conclusion, most people do far better in class. But for me it's slow, tedious, distracting, and out of sync with my normal learning processes. The few other people that I know who are like me, also skip the classes and have done well. You'll know because from birth, you'll be an excellent test taker, get bored silly in classroom environments, and have likely read 1000 books or more in just two or three years. We never asked "do I need a class", we just stopped going.
Re: Ask HN: How to self-learn math?
#148>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…
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…
Having another interest to tie it to (especially if it's something you're more comfortable with) is huge. I have a CS degree, and for me, what bridged the gap into being comfy with "pure" mathematics (and appreciating it outside of any specific application), was my theory of computation class.
Re: Ask HN: How to self-learn math?
#149Nothing 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'm curious about the need for a teacher. Because I'm learning math by myself and I don't have a teacher. Except for math.stackexchange.com, essentially. How many hours of tutoring/hour of self-study do you recommend? What can tutors help you with that is hard or impossible to learn on your own?
An experienced teacher, in a one-on-one situation, can identify the areas you're struggling with much more quickly than you can, and can guide you on a path out that you might not be able to see.
I've found that sole self-study can make it easy to convince yourself you're more comfortable with some set of material than you are, which can make it hard to see why you're struggling with the next conceptual layer up.
Re: Ask HN: How to self-learn math?
#150>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…
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…
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 general-purpose that the overlap with another course might not be so continuous.