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Ask HN: How to learn math from zero for adults?

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Ask HN: How to learn math from zero for adults?

#1
I am a 26 year old learner who is really into Machine Learning. But my lack of understanding in math has held me back. Skipping and hating math classes in high school have been my biggest regret.

Now, I am slowly trying to learn, but I don't know where to start. I need some guidance.

Re: Ask HN: How to learn math from zero for adults?

#3
Run through the math on Khan Academy to fill in your gaps for at least Algebra I, II and Precalculus. Then you need to Calculus I-III, Linear Algebra and basic Statistics which are also on Khan Academy.

Also I have created some youtube channels aggregating quite a bit of the quality university courses organized into playlists of playlists.

https://youtube.com/channel/UCjgQ2pJDjZlhdI4Ym7NQdUw

Note: You have to click on the titles of the topics on the home page that slide left/right (or up/down on a phone) to see the whole list of courses because YouTube truncates the lists on the home page.

Re: Ask HN: How to learn math from zero for adults?

#4
Once we're outside a formal academic setting, the way to start learning is to start learning.

The first high hurdle is accepting that starting out everything (to a first approximation) is over our heads.

There's no perfect first resource because hard subjects are hard and take time.

But because we are out of school, we have decades to learn.

There's no final in sixteen weeks and only a pop-quiz tomorrow if we are in the middle of applying what we learned.

So just start learning math and figure out what works for you as you go along.

Good luck.

Re: Ask HN: How to learn math from zero for adults?

#7
Everything that can be learned can be studied through some mix of these techniques:

1. Rote learning/memorization. Copying, tracing, flash cards and so forth. This is how you learned to read and write, and while in school math it tends to be applied to calculation(memorizing results from adding and multiplying and so on) it can also be applied to build up recall of mathematical concepts like postulates and theorems.

2. Logic and problem solving strategies. Math "homework" is usually about finding a result through a mix of deductive, inductive and abductive strategies. When the result is calculation-focused it becomes very mechanical and "follow the steps you've memorized", and so can usually be delegated to a computer program now, but higher level math is more about integrating the concepts together to prove something is correct, which means having a really clear understanding of the definitions you're working with.

3. Dividing and conquering. Sometimes it's hard to see a concept in totality but you can understand a particular limited context and then generalize on it. This is typically where math research starts: there's a flash of insight into a concept and then progressive attempts to generalize it and reuse it to solve more problems or define its relationship to other concepts, like how there are multiple ways to define coordinate systems in geometry.

When reading a math text, it can be hard to get started because skimming the text doesn't really grant any access to the concepts: you have to follow through on internalizing them first, which means a mix of the rote learning and posing problems for oneself to solve, and looking for analogies in things you already know to find the differences and so gain more detailed understanding. By the time you've done that, you probably have read the same words hundreds of times and "slept on the problem" for weeks.

This quality of not really understanding math until you've grappled with the problems means that research mathematicians tend to only have a really detailed understanding of their own specialty, but have a more limited background in others, enough to communicate a little bit but not necessarily participate in the discussion substantially. To get "there", look at what's offered in college courses: you can reuse their textbooks and problem sets. Following an online course is also a valid method. You don't have to attend classes or lectures to study math, although sometimes you may want to ask questions to clarify - but the internet exists for that and lots of people are willing to help, at least up until you actually get to a research level problem.

Re: Ask HN: How to learn math from zero for adults?

#10
You don't say how much you already know.

Your first stop would be Khan Academy and knowing your gaps.

Fill your gaps.

Learn HS level Calculus, Linear Algebra, and Statistics.

You will need more Calculus and Linear Algebra later. But not now.

Then try studying "Machine Learning for Absolute Beginners" book. It not very mathy.

Then just keep going through ML courses. Learn what you need on the way.

The "way" of math needed in Machine Learning is not the same "way" that brings you scores in school/college exam.

You need absolutely crystal clear concepts in Linear Algebra, Multivariable Calculus, and in some areas of ML, Statistics.

Corporate "Data Science" and Machine Learning research/projects are wildly different beasts. Learn what you will pursue, and decide your path based on that.

And most importantly, you have to be patient. Machine Learning and Math for it takes time- not days or weeks, but months and years.

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