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File: 1609363355162.jpg (1.12 MB, 3718x2150, topology.jpg)

I know this is kind of a meme on boards like this, but is it actually possible to learn university-level mathematics on your own? Not a full mathematics program, just the equivalent of some select courses. How would one go about it?

What type of math were you looking to learn? Learning anything on your own is possible, you just have to be motivated enough.

You'll have to learn all the math that comes before the select courses you want to learn about.

You'll have to learn all the math that comes before the select courses you want to learn about.

One could read a textbook on the subject and do relevant problems.

It's how i learned most math in university anyways.

It's how i learned most math in university anyways.

>>479

yes, but unless you van back that up with some actual tests or practical applications nobody is gonna believe you.

yes, but unless you van back that up with some actual tests or practical applications nobody is gonna believe you.

>>481

I'd like to start with geometry, because I remember being very bad at it in school. After that probably calculus, single and then multi-variable, plus differential equations, with the goal of studying physics in mind.

>>482

I have learned a lot about programming from books. But the difference there is that you have the compiler and you can run your code, both of which guarantee that you have understood things pretty well. I'm afraid that with maths I will get lazy and just reassure myself that yeah I understood it and can continue reading only to realize a few pages later that I have completely lost track and need to reread half of the book again and then I get discouraged, feel like a failure and give up.

>>483

I don't care about that, it's not for my CV or something.

I'd like to start with geometry, because I remember being very bad at it in school. After that probably calculus, single and then multi-variable, plus differential equations, with the goal of studying physics in mind.

>>482

I have learned a lot about programming from books. But the difference there is that you have the compiler and you can run your code, both of which guarantee that you have understood things pretty well. I'm afraid that with maths I will get lazy and just reassure myself that yeah I understood it and can continue reading only to realize a few pages later that I have completely lost track and need to reread half of the book again and then I get discouraged, feel like a failure and give up.

>>483

I don't care about that, it's not for my CV or something.

>>484

I'd say algebra is the most important building block, the rest should come easy. Study order of operations really well. Once you have some single variable calculus under your belt you can start getting into physics.

I'd say algebra is the most important building block, the rest should come easy. Study order of operations really well. Once you have some single variable calculus under your belt you can start getting into physics.

>>485

Do you have anything to recommend to master it? Books, study methods, whatever that comes to your mind?

Do you have anything to recommend to master it? Books, study methods, whatever that comes to your mind?

>>486

I don't have any books in mind but I found this for you.

http://www.sci.wsu.edu/math/HS/problems.html

I don't have any books in mind but I found this for you.

http://www.sci.wsu.edu/math/HS/problems.html

>>484

If you can do relevant problems, that would guarantee that you have understood things pretty well.

You should be able to find solutions for introductory problems.

If you can do relevant problems, that would guarantee that you have understood things pretty well.

You should be able to find solutions for introductory problems.

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Cool, another autodidact mathanon!

I'm trying to do the exact same thing as you - university-level maths for pure enjoyment of the abstract knowledge. I stopped studying maths formally at age 16.

I don't know what kind of maths you like the look of, but bear in mind that there is a*lot* out there - whole, gigantic, overarching fields - which they don't even tell you exist during high school. Topology. Group theory. Linear algebra. Mathematical logic. If you haven't already done this, I'd recommend scouring popular maths content for inspiration about what to learn. Some example sources:

>YouTube (Numberphile, especially)

>books (e.g. Simon Schama's*Fermat's Last Theorem* is excellent)

>wikisurfing

If you have a feeling for the fields that are out there, you might be able to skip some high-school stuff and move straight onto the more abstract fruits of mathematics. I don't know shit about trigonometry and, so far, that hasn't harmed me in any way. At university level, my impression is that a 2D triangle is a laughably specific object - the things being studied by university students nowadays are much more general in nature. However, as another anon said, algebra is everywhere so definitely get an intuitive feeling for manipulating equations.

Logic and set theory. You might have heard of these subjects in the context of the 'foundations of mathematics'. It is pretty much accurate to say that all other fields pre-suppose them, in the sense that almost all mathematical constructions (real numbers, vector spaces, etc.) are, ultimately, set-theoretical constructions. And, of course, mathematical proofs must use logic.

[1/2]

I'm trying to do the exact same thing as you - university-level maths for pure enjoyment of the abstract knowledge. I stopped studying maths formally at age 16.

I don't know what kind of maths you like the look of, but bear in mind that there is a

>YouTube (Numberphile, especially)

>books (e.g. Simon Schama's

>wikisurfing

If you have a feeling for the fields that are out there, you might be able to skip some high-school stuff and move straight onto the more abstract fruits of mathematics. I don't know shit about trigonometry and, so far, that hasn't harmed me in any way. At university level, my impression is that a 2D triangle is a laughably specific object - the things being studied by university students nowadays are much more general in nature. However, as another anon said, algebra is everywhere so definitely get an intuitive feeling for manipulating equations.

Logic and set theory. You might have heard of these subjects in the context of the 'foundations of mathematics'. It is pretty much accurate to say that all other fields pre-suppose them, in the sense that almost all mathematical constructions (real numbers, vector spaces, etc.) are, ultimately, set-theoretical constructions. And, of course, mathematical proofs must use logic.

[1/2]

If you can spare some time, I would familiarise yourself with the conventions of first-order logic and Zermelo-Fraenkel set theory. Paul Halmos' book *Naïve Set Theory* is short and covers a lot of useful stuff. (Even just the first 15 sections would be sufficient for a good grounding in the subject.)

My friend, who did maths at undergraduate level, also said that linear algebra is important for understanding other areas, so it's what I picked to study this year (along with some topology if I have time).

Apart from doing exercises, you can also really test your understanding by programming mathematical algorithms - e.g. an algorithm to produce the prime factorisation of any natural number.

Some links:

https://mathoverflow.net/questions/28158/a-learning-roadmap-request-from-high-school-to-mid-undergraduate-studies - introductory textbook recommendations from MathOverflow users

https://libgen.fun - Library Genesis gives you free access to basically any textbook you want. This portal downloads the book you request via IPFS.

[2/2]

My friend, who did maths at undergraduate level, also said that linear algebra is important for understanding other areas, so it's what I picked to study this year (along with some topology if I have time).

Apart from doing exercises, you can also really test your understanding by programming mathematical algorithms - e.g. an algorithm to produce the prime factorisation of any natural number.

Some links:

https://mathoverflow.net/questions/28158/a-learning-roadmap-request-from-high-school-to-mid-undergraduate-studies - introductory textbook recommendations from MathOverflow users

https://libgen.fun - Library Genesis gives you free access to basically any textbook you want. This portal downloads the book you request via IPFS.

[2/2]

>>490

>>491

I should also have mentioned lectures on YouTube. Several universities post full undergraduate lectures under a Creative Commons licence. MIT does this with its OpenCourseWare channel. Here is a lecture series about topology and geometry, given by one of the academics who appears occasionally on Numberphile: https://www.youtube.com/watch?v=SXHHvoaSctc

>>491

I should also have mentioned lectures on YouTube. Several universities post full undergraduate lectures under a Creative Commons licence. MIT does this with its OpenCourseWare channel. Here is a lecture series about topology and geometry, given by one of the academics who appears occasionally on Numberphile: https://www.youtube.com/watch?v=SXHHvoaSctc

>>489

What about proving things, how can I make sure that I am not making mistakes or even deluding myself in a proof?

What about proving things, how can I make sure that I am not making mistakes or even deluding myself in a proof?

>>497

If you read a lot of proofs in the textbook, you will gradually get a feeling for the level of precision required for a proof.

If you are paranoid about your answer to a particular exercise, pretend that you are a sceptical mathematician examining the purported proof. Ask yourself things like:

>does statement X really imply statement Y?

>can I find a counter-example to the statement Z which I'm not sure about?

>am I allowed to assume this?

For the last one, basically: if it's part of the statement of the theorem you are asked to prove, then yes. If not, then you have to prove the assumption as well.

If you read a lot of proofs in the textbook, you will gradually get a feeling for the level of precision required for a proof.

If you are paranoid about your answer to a particular exercise, pretend that you are a sceptical mathematician examining the purported proof. Ask yourself things like:

>does statement X really imply statement Y?

>can I find a counter-example to the statement Z which I'm not sure about?

>am I allowed to assume this?

For the last one, basically: if it's part of the statement of the theorem you are asked to prove, then yes. If not, then you have to prove the assumption as well.

>>493

Thanks anon. The course looks interesting, I'll give it a try. Do you usually take notes while watching these? I guess for courses it is a must, but what about the "edutainment"?

Thanks anon. The course looks interesting, I'll give it a try. Do you usually take notes while watching these? I guess for courses it is a must, but what about the "edutainment"?

I know hobby programmers can contribute to open-source and post their programs on github, but what do hobby mathematicians do? Is there some forum where they share the proofs they come up with or something?

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>>513

>Is there some forum where they share the proofs they come up with or something?

Yes! There is a small effort to make "massively multiplayer mathematics" a reality, where randos on the internet shoot out ideas about unsolved problems:

https://asone.ai/polymath/index.php?title=Main_Page

It's a bit dead, but still.

>Is there some forum where they share the proofs they come up with or something?

Yes! There is a small effort to make "massively multiplayer mathematics" a reality, where randos on the internet shoot out ideas about unsolved problems:

https://asone.ai/polymath/index.php?title=Main_Page

It's a bit dead, but still.

>>515

I was thinking of something more analogous to rewriting fizzbuzz for the thousandth time, but this is really cool.

I was thinking of something more analogous to rewriting fizzbuzz for the thousandth time, but this is really cool.

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