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Algebra, Topology, Differential Calculus, and Optimization Theory for CS [pdf]
- craigching 9y agoPrevious 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.
- eggpy 9y agoThat discussion appears to be in regards to a different paper. Or do you mean to relate it to a previous relevant discussion?
- craigching 9y agoMaybe 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 9y agoThey 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
- llamaz 9y agoCS 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.
- yeukhon 9y agoA 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.
- GameOfTrolls 9y agoNo.
- ychen306 9y agoSchools usually have two or three abstract algebra classes just to cover materials in Chapter 1 and a couple later chapters (polynomials, modules, etc).
- yeukhon 9y agoNot 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.
- luyi06 9y agoWe shouldn't be confused with CS and programmer.
- Edmond 9y agoYou 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.
- CardenB 9y agoDoes anyone know some good supplemental exercises to pair with this text?
- nud 9y agoYou 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
- ychen306 9y agoDon't know what to make of these notes. A bit of a kitchen sink. And too brief for learning the materials.
- mlevental 9y agolike 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.
- bitL 9y agoCS 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!
- dang 9y agoPlease don't post unsubstantive comments here.
- bitL 9y agoWorld'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.
- jcoffland 9y agoLooks like you got of easy.
- jacobolus 9y agoI 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.
- hulkisdumb 9y agoI wonder where is topology used in comp sci other than computer vision (?) ?
- aje403 9y agoIt'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 <insert random CS degree topic here>. 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.
- judis 9y agoTopological 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