
Algebra, Topology, Differential Calculus, and Optimization Theory for CS [pdf] - lainon
https://www.cis.upenn.edu/~jean/math-basics.pdf
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ychen306
Don't know what to make of these notes. A bit of a kitchen sink. And too brief
for learning the materials.

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mlevental
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.

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

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judis
Topological data analysis[0] is a new application of topology.

[0]
[https://en.wikipedia.org/wiki/Topological_data_analysis](https://en.wikipedia.org/wiki/Topological_data_analysis)

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CardenB
Does anyone know some good supplemental exercises to pair with this text?

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nud
You can check out the homeworks from the class these notes were intended for:
[http://www.cis.upenn.edu/~cis515/cis515-hw-mid-
fin-16.html](http://www.cis.upenn.edu/~cis515/cis515-hw-mid-fin-16.html)

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llamaz
CS shouldn't be in the title. If you learn everything in this set of notes you
will have learned something close to a standard 3 year undergraduate math
curriculum. So the only way it's related to CS is that undergraduate math is
applicable to CS, as expected.

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yeukhon
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 will have additional materials.
That's possible. Most importantly, the author of this PDF created this for the
CS students, so it CAN be in the title.

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ychen306
Schools usually have two or three abstract algebra classes just to cover
materials in Chapter 1 and a couple later chapters (polynomials, modules,
etc).

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yeukhon
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.

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craigching
Previous discussion not too long ago:

[https://news.ycombinator.com/item?id=15923338](https://news.ycombinator.com/item?id=15923338)

Though I note that this link has been updated by one day.

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eggpy
That discussion appears to be in regards to a different paper. Or do you mean
to relate it to a previous relevant discussion?

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craigching
Maybe an interesting discussion that would keep the link relevant is what the
difference actually is? The table of contents do differ, but are very similar.
Thanks for pointing that out, I was mostly going on memory, but looking at the
ToC there are some differences between the two, but how much would be
interesting to ascertain.

~~~
yeukhon
They are very different. They might have some overlap, but they each have many
unique contents.

The one you linked: Fundamentals of Linear Algebra and Optimization

The one here is: Algebra, Topology, Differential Calculus, and Optimization
Theory

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bitL
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!

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dang
Please don't post unsubstantive comments here.

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bitL
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.

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jacobolus
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.

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bitL
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.

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catnaroek
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.

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bitL
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.

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catnaroek
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?”

