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Mathematics for the Adventurous Self-Learner

neilwithdata.com

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Re: Mathematics for the Adventurous Self-Learner

#2

Post by hackernews7643 »

One thing I don’t think is discussed enough is the process of how self-learners in math get critical feedback. Most advanced level math textbooks do not have solutions to check their work against nor do they have a way to get feedback by an expert and this is essential for learning. Least with programming, you can get immediate feedback and know whether what you did is correct or not.

Re: Mathematics for the Adventurous Self-Learner

#3

Post by yuanshan »

hackernews7643 wrote: post #2

One thing I don’t think is discussed enough is the process of how self-learners in math get critical feedback. Most advanced level math textbooks do not have solutions to check their work against nor do they have a way to get feedback by an expert and this is essential for learning. Least with programming, you can get immediate feedback and know whether what you did is correct or not.

Usually, some people will post some or almost all of the solutions online if the textbook is really famous, for instance, baby rudin.

Although rarely, some authors do provide solutions, like Knuth's books, Stephen Abbott's Understanding Anaylsis, etc.

For immediate feedback, maybe you can checkout [0] to learn some formal proof by doing interactive proving.

[0] http://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_game...

BTW, you can always ask questions on https://math.stackexchange.com

Re: Mathematics for the Adventurous Self-Learner

#5

Post by clircle »

hackernews7643 wrote: post #2

One thing I don’t think is discussed enough is the process of how self-learners in math get critical feedback. Most advanced level math textbooks do not have solutions to check their work against nor do they have a way to get feedback by an expert and this is essential for learning. Least with programming, you can get immediate feedback and know whether what you did is correct or not.

It's not immediate feedback, but you do learn when you right and when you are wrong. You learn when you are bullshitting yourself. You learn that you need to be able to justify every step in a proof, and if you can't do, then you are wrong. Trying to bullshit the right answer is the most common way to end up with a faulty proof. Of course, you can also end up with a faulty proof because you can't differentiate your own bullshit from truth, but this is less common.

Re: Mathematics for the Adventurous Self-Learner

#6

Post by gavinray »

I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make:

I have yet to find a guide that does not start with the assumption that you graduated highschool.

That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to assume the people you are surrounded by did not have a fundamental base of mathematics.

But the times I have tried to go through these teach-yourself materials, it went from zero to draw-the-rest-of-the-fucking-owl real quick. [0]

I have been programming for 14 years, but stopped doing schoolwork around age 12, and never did any math beyond pre-algebra.

Does anyone know of materials for adults that cover pre-algebra -> algebra -> geometry -> trigonometry -> linear algebra -> statistics -> calculus? At a reasonably quick pace that someone with a family + overtime startup hours could still benefit from?

[0] https://i.imgur.com/RadSf.jpg

(Also, curse the Greeks for not using more idiomatic variables. ∑ would never pass code review, what an entirely unreadable identifier)

Re: Mathematics for the Adventurous Self-Learner

#8

Post by kyawzazaw »

gavinray wrote: post #6

I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make: I have yet to find a guide that does not start with the assumption that you graduated highschool. That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to…

khanacademy has content for those school work level.

Re: Mathematics for the Adventurous Self-Learner

#10

Post by quaquaqua1 »

gavinray wrote: post #6

I know this is going to be the case for likely nobody, but I have browsed most of the self-study math threads that pop up here as a forever-on-my-todo-list thing and I have a remark to make: I have yet to find a guide that does not start with the assumption that you graduated highschool. That is a very reasonable assumption to make. We are in a community of technology and engineering, it would be a bit ridiculous to…

SAT prep books such as those from Kaplan or Princeton Review tend to be extremely cheap, if not free, and cover almost all of those topics pretty succinctly :)

Speaking as someone who was kicked out of precalc and then never touched math again despite working as a dev, your point resonates with me :)

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