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Great resource. This was my area of graduate study, and I would say this material is quite hard, in the beginner to advanced PhD range. And this inspiring tex

Great resource. This was my area of graduate study, and I would say this material is quite hard, in the beginner to advanced PhD range. And this inspiring textbook I think has high overlap with these topics: https://www.amazon.com/Stochastic-Integration-Differential-Equations-Protter/dp/3540003134 https://www.amazon.com/Stochastic-Integration-Differential-E...

markisus 2y ago
Yes, by advanced undergraduate, I meant very advanced undergraduate. But when I was in undergrad I always heard about some students like this who were off in the graduate classes. And then in grad school, there was even a high school student in my Algebra course who managed to correct the professor on some technical issue of group theory. So I don't assume you have to be a PhD to work through this material.
3abiton 2y ago
I was traumatised by fluid dynamics course back in the days before youtube tutorials were a thing and we had to rely on a good teacher to explain some concepts.
krick 2y ago
Can perhaps someone suggest some resources that are, uh, less advanced undergraduate? Is this possible? Or perhaps just the resources for the prerequisites themselves? Like, what's the route from "not advanced undergraduate"?
- hrududu 2y ago
  The links above are for studying this as a pure mathematician would. If you want to study it that way, you would take most of the core classes in the undergrad curriculum: Calculus (without proofs) Linear Algebra Real Analysis (proofs of calculus) Measure Theory There are also higher level courses that are worth taking, because they motivated a lot of this theory. They would be imo, Functional Analysis (real analysis applied to spaces of functions), and Partial Differential Equations. If you've knocked off some of the undergrad prereqs and feel good about proofs, this could be the right book for you: https://www.amazon.com/Probability-Martingales-Cambridge-Mathematical-Textbooks/dp/0521406056 https://www.amazon.com/Probability-Martingales-Cambridge-Mat.... Another gem of a book.

markisus 2y ago

Yes, by advanced undergraduate, I meant very advanced undergraduate. But when I was in undergrad I always heard about some students like this who were off in the graduate classes. And then in grad school, there was even a high school student in my Algebra course who managed to correct the professor on some technical issue of group theory. So I don't assume you have to be a PhD to work through this material.

3abiton 2y ago

I was traumatised by fluid dynamics course back in the days before youtube tutorials were a thing and we had to rely on a good teacher to explain some concepts.

krick 2y ago

Can perhaps someone suggest some resources that are, uh, less advanced undergraduate? Is this possible? Or perhaps just the resources for the prerequisites themselves? Like, what's the route from "not advanced undergraduate"?

hrududu 2y ago
The links above are for studying this as a pure mathematician would. If you want to study it that way, you would take most of the core classes in the undergrad curriculum: Calculus (without proofs) Linear Algebra Real Analysis (proofs of calculus) Measure Theory There are also higher level courses that are worth taking, because they motivated a lot of this theory. They would be imo, Functional Analysis (real analysis applied to spaces of functions), and Partial Differential Equations. If you've knocked off some of the undergrad prereqs and feel good about proofs, this could be the right book for you: https://www.amazon.com/Probability-Martingales-Cambridge-Mathematical-Textbooks/dp/0521406056 https://www.amazon.com/Probability-Martingales-Cambridge-Mat.... Another gem of a book.