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Ask HN: How to self-learn math?

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

#151

Post by zenhack »

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'…

One of the earliest memories I have of really enjoying math was a unit on modular arithmatic from my 6th grade math class. The teacher introduced the concept with a hands of a clock metaphor, gave us a whole bunch of drill problems, and told us to watch for patterns. We had an easel in the class room where he collected the insights students had gained. Discovering the relationship with remainders by ourselves was incredibly cool.

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

#152

Post by elbear »

ivansavz wrote: post #15

I have just the book for you: the essentials of high school math for adults: http://www.lulu.com/shop/ivan-savov/no-bullshit-guide-to-mat... If you like this one, you can followup with the MATH&PHYS book which covers mechanics (PHYS101) and calculus. And if you like that one, you can follow up with the liner algebra book. All along the way, I recommend you try solving exercises and problems using pen and paper. Ideal…

Thank you for your work. Your books look great!

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

#153

Post by hackernewsacct »

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…

This is a great list. Thank you.

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

#154

Post by mkl »

elcapitan wrote: post #53
mkl wrote: post #51

Earlier quoted context omitted.

I'm not so sure. I use Sympy, Matplotlib, Numpy, etc. even when I am just exploring, and have little idea what I want to achieve. I do use and recommend http://desmos.com , which is proprietary (but pretty limited and easily translated to Python). It doesn't lock features behind a paywall like Wolfram Alpha.

I was just guessing from OPs post saying that they don't even have basic highschool math knowledge, from which I would assume that translating mathematical concepts into concepts in Python would probably create more difficulties than necessary, whereas in Alpha you can just dump an equation and then get an interpretation. Matplotlib in particular is kind of an expert interface for a library, at least when I last chec…

I use Desmos all the time when teaching. It's accessible to students with no programming knowledge, and the killer feature is that I can just give students a link so they can interact with a demo I've made.

For example:

Quadratic through 3 points (drag the points around): https://www.desmos.com/calculator/tf1f80zgug

Pythagoras's Theorem (drag the sliders): https://www.desmos.com/calculator/dbjxbeuzk7

Why shearing preserves area (drag the slider): https://www.desmos.com/calculator/1vykaqf7je

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

#155

Post by ZenoArrow »

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 years, so I'm likely to need to get the basics down first.

https://www.youtube.com/watch?v=wsOoClvZmic

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

#156

Post by InitialLastName »

zenhack wrote: post #151
InitialLastName wrote: post #146

Earlier quoted context omitted.

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'…

One of the earliest memories I have of really enjoying math was a unit on modular arithmatic from my 6th grade math class. The teacher introduced the concept with a hands of a clock metaphor, gave us a whole bunch of drill problems, and told us to watch for patterns. We had an easel in the class room where he collected the insights students had gained. Discovering the relationship with remainders by ourselves was inc…

I had a similar experience when I learned about factoring (not sure what age). I got a little obsessed with finding prime numbers by hand, and eventually figured out that I only had to search for factors up to the square root. I distinctly remember that as the first time I realized how powerful a simple mathematical insight can be to speeding up a process.

Now, of course, I use mathematical insight to speed up processes occupationally; I guess that experience stuck with me.

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

#157

Post by elbear »

KodiakLabs wrote: post #5

The simplest approach I think would be to start with Khan Academy. Well spoken clear and concise. You can go from a Highschool level towards subjects from first year university. Once there, it should be easier to self teach from books.

I agree, because I'm on this path myself and have been for 200 days. I started by brushing up on my algebra and now I've reached integrals in AP Calculus AB.

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

#158

Post by noobhacker »

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…

Do you also think that one can only learn Computer Science effectively by taking classes?

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

#159

Post by Jhsto »

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…

> 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.

Just so that you know this was my impression at a university as well. In fact, calculus courses are translated into "basic mathematics." I think this underlines how much these courses are about learning the tooling for practical applications taught in later classes.

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

#160

Post by ivansavz »

ZenoArrow wrote: post #155

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…

Wow, Herbert Gross is an amazing lecturer. Everything is planned out, and he's careful to avoid jargon. I wish all eLearning material was of this quality.
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