/sci/ - Science & Math » Thread #11778265

17KiB, 200x267, 23007443 (1).jpg

View Same Google iqdb SauceNAO

Anonymous Tue 09 Jun 15:10:44 2020 No.11778265 View Reply Original Report

Quoted By: >>11779585 >>11779914

What's a good resource for learning algebraic geometry?

Is it worth learning? It appears to be useful for optimizing for computational efficiency.

What is compactness? What makes something locally compact or globally compact?

That is all. Thanks.

Anonymous

Anonymous Tue 09 Jun 2020 21:46:13 No.11779585 Report

Quoted By: >>11779603 >>11779628

>>11778265
Depends on what you mean with algebraic geometry.
You either mean geometry done with cartesian variables or you mean a branch of modern Algebra in which case it is closely tied to the theories of differential geometry and manifolds.

>Is it worth learning?
No, not really except you're into PhD mathematics or general relativity.
>It appears to be useful for optimizing for computational efficiency.
I don't know where you got that from.
>What is compactness? What makes something locally compact or globally compact?
This is topology. Are you interested in Topology? Munkin's topology is a good book.

Anonymous

Anonymous Tue 09 Jun 2020 21:52:32 No.11779603 Report

Quoted By:

>>11779585
>No, not really except you're into PhD mathematics or general relativity.
Nope, it has practical applications in cryptography.

Anonymous

Anonymous Tue 09 Jun 2020 22:00:51 No.11779628 Report

Quoted By:

>>11779585
I mean mapping systems or functions into Euclidean spaces as a set of vector fields representing the parameters, and an eigenvector of the resulting outcome on the set of differential equations, mapped bijectively across dimensions to form a geometrical shape by connecting the neighboring points with a surface between. This can be generalized to map any problem really into a geometry, and if you can find its algebraic variety, then you can perform calculus and trigonometry to perhaps perform aggregate calculations on a large or infinite set with a single operation.

I may have used some incorrect terminology there but I'm sure you get what I mean.

Anonymous

Anonymous Tue 09 Jun 2020 23:26:05 No.11779914 Report

Quoted By: >>11779938

>>11778265
>What is compactness?
The ideas of closedness and boundedness on their own do not behave well, in that those conditions depend on the ambient space of the set. On the other hand, a set that is both closed and bounded will be so regardless of the ambient space. We call such a set compact. As it turns out, you can generalize the idea of compactness to any topological space.

Anonymous

Anonymous Tue 09 Jun 2020 23:35:59 No.11779938 Report

Quoted By:

>>11779914
Brilliant explanation, thank you my friend.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches