Need opinions on a roadmap i found

[nimble fiber]

I'm starting from zero so i'd like to know if this is worth following and using as my main resource.

roadmap: https://raw.githubusercontent.com/TalalAlrawajfeh/mathematics-roadmap/master/mathematics-roadmap.jpg

(posted link because higher quality)

[urban badge]

Looks cool

Btw, how can you start from zero if you probably know a lot already?

[barren raptor]

I would do some of the ordering differently

E.g. they do linear algebra and only then introduction to proofs

But if you do linear algebra properly right away, that'll already be enough of an introduction to proofs

Also, I would skip all of the philosophy stuff

Pretty sure in no real math major at a uni is that required

[nimble fiber]

it's been a while since i've done any math so starting from zero doesn't necessarily mean learning from zero

i want to self-study math and i think refreshing my memory on everything from the ground up could be beneficial

[urban badge]

ok

[nimble fiber]

no skip the philosophy and skip the introduction to proofs. would you say that the rest is fine?

[barren raptor]

I'm not really saying "skip intro to proofs", I'm just saying if you want to do that, I'd do it before linear algebra. But overall, I don't think you can well-order mathematics learning. Obviously there are some pre-requisites to some topics, but you can jump into e.g. Topology after having only done some analysis, and so on.

In many unis (atleast it's like this in Germany), you can choose courses yourself having done the fundamental ones (like linear algebra and analysis)

[nimble fiber]

i see what you mean. my only dilemma is understanding what's considered pre-requisite, hence the reliance on a roadmap

i probably wouldn't know that i could get into topology after doing only a bit of analysis if you haven't told me for example. that may only be a problem with people who self-study

[barren raptor]

Well, I'm in uni and I face the same problem, having the freedom to choose courses, lol

I could choose topology in my first semester

I need to talk to people to find out if that makes sense

Well, atleast there is a course page, and some pre-reqs are listed

[nimble fiber]

so i should probably follow the roadmap and ask the people in this server if it makes sense to move on to the next thing

[barren raptor]

What about following a uni curriculum?

Are you preparing for college or just self-learning?

[nimble fiber]

if the uni curriculum has pre-reqs listed, i'm okay with that idea

[nimble fiber]

just self-learning

[barren raptor]

Are you from the US? Generally, college in the US is structured a bit differently than in the EU

[nimble fiber]

i'm from australia, so neither lol

but i'm not preparing for uni. as i said, i'm self-studying

i wouldn't mind either curriculum as long as i'm following something well-structured with pre-requisites laid out

[barren raptor]

This is how the structure looks like at my uni

First column is first semester, second is second semester and so on

You start with linear algebra and analysis 1 here

In the US, you generally take calculus 1, 2, 3 before analysis, which is basically the same but less proof-based

Also, linear algebra is proof-based right away, not computational, here

Wahl-Kernmodul is a course of choice

But yeah, you can see what is a requirement

[barren raptor]

Btw, also, check out https://ocw.mit.edu/. It offers recordings of courses at MIT (for free)

So e.g. if you search for "linear algebra", you get https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/video_galleries/video-lectures/

and you can basically follow along

[barren raptor]

Generally, #advanced-lounge is good for these types of questions (if you don't have access to it, go to id:customize and claim the undergraduate role), more active than the forum

[nimble fiber]

thanks a lot. i'll use that MIT link you sent as a resource. i've just claimed the undergraduate role - do you think i can ask for opinions of this roadmap on there or are links not allowed?

[barren raptor]

You can, links are generally allowed