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Algebra, Topology, Differential Calculus, and Optimization Theory for CS [pdf]

cis.upenn.edu

31–35 of 35 posts

Re: Algebra, Topology, Differential Calculus, and Optimization Theory for CS [pdf]

#31

Don't know what to make of these notes. A bit of a kitchen sink. And too brief for learning the materials.

like many other PDFs like this what they really are the author's personal notes, which served the purpose of firming up the author's own understanding of the material.

Re: Algebra, Topology, Differential Calculus, and Optimization Theory for CS [pdf]

#33
post #29

Earlier quoted context omitted.

Except for the “borderline mathematics” parts of computer science (algorithms, PL semantics, etc.), the scientific rigor in CS publications is much, much, much lower than in math or physics publications. Scientific progress is to be measured in terms of advances in human understanding, not in number of publications, our current “publish or perish” culture notwithstanding.

Again, if you want to coast, collect grade inflated Bs and Cs, you can do without much rigor. If you want As and are ambitious, you have to master both CS and related math. Publish or perish is terrible, I agree; if you focus only on super hard high risk problems that might advance humanity, you'll get kicked out of university in no time. And as a professor, 90% of your time will be spent on chasing grants.

I am talking about scientific rigor, not grades. A more relevant question (at least to my interests) is “What tests does a scientific proposal have to pass to become an estabilshed scientific result?”

Re: Algebra, Topology, Differential Calculus, and Optimization Theory for CS [pdf]

#34

I wonder where is topology used in comp sci other than computer vision (?) ?

It's part of a good foundation for measure theory which is part of a good foundation for probability which can be used in any type of computational role. Also, understanding a bit about manifolds, neighborhoods, and things like that are a big part of deep learning theory. I am only acquainted with undergrad topology, but I would say it has had more of an impact on my work and projects and future learning than quick sort ever has or .

Tangentially, it is a great topic to learn in general for those with a math interest and a bare minimum requirement for any higher math learning.

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