/sci/ - Science & Math

>>14520013
All math is derived from geometry, and how it changes.

>>14520013

You seem not to understand that PhD is about research. PhD is about contributing to the field with knowledge that does not exist yet. Also, math has lots of branches. People specialize in a few.

>>14521166
Do most learn geometric algebra?

>>14520013
>>14520705
Listen to this anon, just learn as much geometry as you possibly can. You'll eventually be forced to learn Analysis and Algebra to provide a bridge to the interesting stuff : )

>>14521199
All engineering and math students learn linear algebra in their undergrad... it's a basic requirement for postgraduate studies in these fields.

>>14521225
Of course linear algebra is

>>14520013

It's definitely possible. I say this because there are clear cut cases in existence:

https://ncatlab.org/toddtrimble/published/topogeny

A self-taught mathematician named Victor Porton produced work at the research level, which was verified by mathematicians who run ncatlab.


This isn't to say it is easy. Read mathematics texts up to the Masters level, then contact local universities to get into research. Or, you can dive into the literature yourself.


Check this out for some advice:

https://math.mit.edu/~cohn/Thoughts/advice.html

>>14521243
Me again.

Here are interesting links (not exactly related to mathematics) that could give you motivation and inspiration:

https://www.harshsikka.com/the-diy-phd/

https://nadiaeghbal.com/phd

https://news.ycombinator.com/item?id=15435371

>>14521249
https://andreas-madsen.medium.com/becoming-an-independent-researcher-and-getting-published-in-iclr-with-spotlight-c93ef0b39b8b

>>14521243
>then contact local universities to get into research
at which point if you're lucky, you'll hook up with a professor or two that will work with you.

at worst? you're a crank to them

>>14521199
Are you the geometric algebra anon from the other thread?
Why dont you just start learning this subject?

>>14521204
Where to start anon? Any book recommendations?

>>14521166
Wasn't this back in the day? I'd heard modern PhDs are a wholly different story, where sadly, morons can get in and devalue the certificate.

>>14521225
linear algebra ≠ geometric algebra
linear algebra ⊂ geometric algebra

>>14523586
his phd paper was less than 1000 words, none of them meaningful, but he still got awarded the degree. now he is the world's most famous astronomer.

>>14520013
There's no "average" mathematics PhD, they are all specialising in different fields. The common ground they have is undergrad knowledge.

There's some advice in the sticky about maths undergrad topics.
I haven't checked this out but probably curriculum and lecture notes for some prestigious university are available online, you could use that as a guide .

Why do you want to self-teach PhD level maths? If you are looking to do research it is much easier to worth with a university than to do independently.

>>14523575
but seriousy, read the wiki
https://sites.google.com/site/scienceandmathguide/subjects/mathematics

>>14520013
Bad frown man

>>14523586
If you have 6 figures to spend on paying for a PhD out of pocket without an assistantship, you can certainly manage to pass and get the credentialing process from a crappy 3rd rate university. You might then be able to get a job at a private business and make math PhDs look less like the 300k starting geniuses they are supposed to be, but you will never actually contribute to mathematics even if you do take a teaching job from someone who could.

OP, you can probably learn in 3-4 years all the theory, and if you are some kind of autistic math savant you could totally end up learning how to prove theorems, but you really need to be able to talk to a teacher when studying most fields of math at a higher level to make sure that your proofs arent retarded and you actually understand it, basically

>>14523616
I love these asshole charts.

>>14521199
>Do most learn geometric algebra?
Not, unless they are studying mathematical physics.

>>14523616
Thanks anon. Looks good.

>>14523215
I think there would be a few receptive to this. If they think you're a crank for coming at research from a different route, they're probably insufferable to work with anyway.

>>14523400
I've tried learning about it a few times but can never get it, so always wonder if it's worth it to keep trying

>>14524183
Ok,but why do you want to lewrn it? What is your motivation?
Also what books have you tried?

>>14524230
I want to learn more advanced physics but can't understand anything after Calculus and Linear Algebra.
I've tried various internet sources, including https://marctenbosch.com/quaternions/..
For book I tried Linear and Geometric Algebra by Macdonald.

>>14524431
Quantum theory mainly uses linear algebra

>Geometric Algebra
Its just repackaged Clifford algebra for mongoloids
No reason to care about it, when you can open up Lang, Serre, Samelson, and Olver and learn how lie theory, Clifford algebras, and spin representations work.
Hestenes did it because he didn't understand how physics or physicists picks up mathematics and opted to introduce it to physicists the way linear algebra is introduced in undergrad.
Meanwhile, it was already known in physics, he could have capitalized on that, but he didn't.

https://twitter.com/johncarlosbaez/status/1101225401097961472?s=20
https://twitter.com/johncarlosbaez/status/1101891416270168066?s=20

>>14524431
try https://youtu.be/60z_hpEAtD8
I've been teaching myself from MacDonald's books as well, keep at it.

>>14524688
Thanks, I'll check it out