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

cis.upenn.edu

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

#21

Post by bitL »

dang wrote: post #20
bitL wrote: post #18

CS is basically math++, i.e. a CS graduate is considered elite, capable of mastering in 1 year what math graduates do in 2 years. Deal with it!

Please don't post unsubstantive comments here.

World's elite universities will tell you right away that as their CS student you are considered the best group they have and that math students go slower than you are, and increase your load to crazy levels. I am not going to post "unsubstantive" comments that I haven't heard at those places. As a CS student, you are expected to master (continuous) calculus, discrete calculus (discrete math proofs, hypercubes for parallel algorithms), optimization (machine/deep learning, compilers), category theory (functional programming), logic (up to automated proofs, i.e. including set theory), differential equations, topology (computational geometry, distributed algorithms), probability and statistics (reinforcement learning, queueing), number theory (cryptology), graph theory (almost everywhere)... There is no functional analysis needed yet, but it's heavily used for PhD degrees anyway. You need to know all this down to the level of proving theorems if you want to achieve anything in CS.

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

#22

Post by yeukhon »

ychen306 wrote: post #16
yeukhon wrote: post #6

Earlier quoted context omitted.

A lot of the math in the notes are not covered in the standard engineering mathematics curriculum. Chapter 1 is not. No one taught me about rings except in discrete (just briefly), and the next time I visited it would be in algorithm and cryptography class. I honestly cannot recall my exact curriculum, but a quick glance at the table of content, more than half unknown to me. Now, different school, different teacher w…

Schools usually have two or three abstract algebra classes just to cover materials in Chapter 1 and a couple later chapters (polynomials, modules, etc).

Not really (though again I emphasize every school is different). At least my school doesn't teach these abstract algebra covered in Chapter 1 except in discrete mathematics, which is not offered to most engineering students.

Sure some axioms, vector spaces, some polynomial, logic, here and there would be covered in calculus, differential and linear. But large part of the content would not be part of a CS/Engineering classes. Only what is relevant.

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

#24

Post by jcoffland »

bitL wrote: post #21
dang wrote: post #20

Earlier quoted context omitted.

Please don't post unsubstantive comments here.

World's elite universities will tell you right away that as their CS student you are considered the best group they have and that math students go slower than you are, and increase your load to crazy levels. I am not going to post "unsubstantive" comments that I haven't heard at those places. As a CS student, you are expected to master (continuous) calculus, discrete calculus (discrete math proofs, hypercubes for par…

Looks like you got of easy.

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

#25

Post by jacobolus »

bitL wrote: post #21
dang wrote: post #20

Earlier quoted context omitted.

Please don't post unsubstantive comments here.

World's elite universities will tell you right away that as their CS student you are considered the best group they have and that math students go slower than you are, and increase your load to crazy levels. I am not going to post "unsubstantive" comments that I haven't heard at those places. As a CS student, you are expected to master (continuous) calculus, discrete calculus (discrete math proofs, hypercubes for par…

I know several CS PhDs from “world elite universities” with undergraduate math or physics degrees who switched to CS for grad school because they decided that math/theoretical physics were too difficult or too competitive, and found their CS programs comparatively much easier mathematically, with most CS fields requiring much less background to get to the academic cutting edge (as should be expected for a much younger and more application focused field), with an easier path for newcomers to publish meaningful results in high-impact journals. YMMV.

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

#26

Post by Edmond »

v64 wrote: post #13
Edmond wrote: post #10

Earlier quoted context omitted.

You may be taking too rigid a notion of CS...a lot of CS programs at least in American Universities are math programs...I got a minor in Applied math merely by declaring my desire for it without any extra classes. I would have gotten a double major in Applied Math and CS if I was willing to spend another semester in undergrad...point being Math and CS are not as far off.

Out of curiosity, what university did you go to? I attended the University of Texas and there was very little overlap between the math and CS curriculums [1]. The classes in common were lower division calculus (8 or 12 hours, depending if you took the condensed accelerated version), linear algebra (3 hours), and probability (3 hours). Students could of course take more math electives, but you could get a CS degree wi…

I attended the New Jersey Institute of Technology (it's been >10yrs so things may have changed)...the curriculum may not exactly overlap but with thoughtful selection of electives you can get pretty close.

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

#27

Post by bitL »

jacobolus wrote: post #25
bitL wrote: post #21

Earlier quoted context omitted.

World's elite universities will tell you right away that as their CS student you are considered the best group they have and that math students go slower than you are, and increase your load to crazy levels. I am not going to post "unsubstantive" comments that I haven't heard at those places. As a CS student, you are expected to master (continuous) calculus, discrete calculus (discrete math proofs, hypercubes for par…

I know several CS PhDs from “world elite universities” with undergraduate math or physics degrees who switched to CS for grad school because they decided that math/theoretical physics were too difficult or too competitive, and found their CS programs comparatively much easier mathematically, with most CS fields requiring much less background to get to the academic cutting edge (as should be expected for a much younge…

Ok, I should quantify it as "some of world's Top 10 engineering universities" then. YMMV as you say; imagine you are required to read 100 papers a term in a single subject in CS these days. Moreover, you should be almost assured that most of the facts you learn will be/are already obsolete due to crazy pace CS is having in some areas. I am not aware of math/physics having such a crazy pace, but I might be ignorant there.

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

#28

Post by catnaroek »

bitL wrote: post #27
jacobolus wrote: post #25

Earlier quoted context omitted.

I know several CS PhDs from “world elite universities” with undergraduate math or physics degrees who switched to CS for grad school because they decided that math/theoretical physics were too difficult or too competitive, and found their CS programs comparatively much easier mathematically, with most CS fields requiring much less background to get to the academic cutting edge (as should be expected for a much younge…

Ok, I should quantify it as "some of world's Top 10 engineering universities" then. YMMV as you say; imagine you are required to read 100 papers a term in a single subject in CS these days. Moreover, you should be almost assured that most of the facts you learn will be/are already obsolete due to crazy pace CS is having in some areas. I am not aware of math/physics having such a crazy pace, but I might be ignorant th…

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.

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

#29

Post by bitL »

catnaroek wrote: post #28
bitL wrote: post #27

Earlier quoted context omitted.

Ok, I should quantify it as "some of world's Top 10 engineering universities" then. YMMV as you say; imagine you are required to read 100 papers a term in a single subject in CS these days. Moreover, you should be almost assured that most of the facts you learn will be/are already obsolete due to crazy pace CS is having in some areas. I am not aware of math/physics having such a crazy pace, but I might be ignorant th…

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.

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

#30

Post by asafira »

bitL wrote: post #18

CS is basically math++, i.e. a CS graduate is considered elite, capable of mastering in 1 year what math graduates do in 2 years. Deal with it!

Unfortunately, I am compelled to make sure people don't read too far into this: this is phenomenally far from the truth. I am sure some schools have stronger engineering schools than math departments, but to say this generalizes is honestly borderline absurd to anyone that has gone to a school with a good math department.
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