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Theoretical Computer Science Cheat Sheet [pdf]
- nlitsme 5y agoThis seems to be the original publication: https://dl.acm.org/doi/10.1145/242581.242585 https://dl.acm.org/doi/10.1145/242581.242585
- g42gregory 5y agoI don’t know if Pythagorean theorem needs to go on any cheat sheet, whether it’s Math or CS. If you can’t remember that, maybe you are in the wrong place to begin with!
- LoyCgg 5y agoDo you have a cheat sheet for this cheat sheet?
- BruceEel 5y agoMore like a cheat booklet ;-) Very nice!
- eloeffler 5y agoIs this generated with LaTeX and is there a source for this? I love the arrangement of cells
- garethl 5y agoSeems to be here: https://www.tug.org/texshowcase/cheat-20131114.tar.gz https://www.tug.org/texshowcase/cheat-20131114.tar.gz (via https://www.tug.org/texshowcase/ https://www.tug.org/texshowcase/)
- eloeffler 5y agoThanks!
- stevesimmons 5y agoThe original source is very old. Written in plain TeX. Most source files in the TUG TeX Showcase archive [1] are dated 1998. Undoubtedly the first versions were much earlier. As the TeX Showcase master page [2] notes, the author was Steve Seiden, from LSU. He died in a bike accident in 2002. [1] https://www.tug.org/texshowcase/cheat-20131114.tar.gz https://www.tug.org/texshowcase/cheat-20131114.tar.gz [2] https://www.tug.org/texshowcase/ https://www.tug.org/texshowcase/
- eloeffler 5y agoThanks! And sorry to hear that...
- raxxorrax 5y agoUseful. I would add maybe abstract algebra, definitions of fields, rings, etc. and their respective operations. LaPlace/Z-Transformation from system theory.
- sannee 5y agoGenerating functions are already there (that is just math-speak for the Z-transform).
- tartoran 5y agoI never ran into Escher’s knot before although Im somewhat familiar wit Esche’s work. Does anyone know what its relevance in this context?
- lordnacho 5y agoAlso, how does the picture of it become useful in the way that all the formulas are useful?
- gxnxcxcx 5y agoJust like the quotes sprinkled around the pages, it seems to be there to avoid a white gap while keeping a more uniform content density across cells.
- thuccess129 5y agoOn which side does it land on the question of utility or futility as to ORM or SQL?
- mdp2021 5y agoDoes any gentlemember have something similar for statistics?
- lordnacho 5y agoEngineering version is a whole huge book with lots of interesting things to search for: https://link.springer.com/book/10.1007/978-94-010-9314-9 https://link.springer.com/book/10.1007/978-94-010-9314-9 Not just math, but properties of matter, physical constants, thermodynamics and fluids (oblique shocks!), electricity (Semiconductors, Verilog!), solid mechanics, and random stuff like screw threads. They had us get this in undergrad, all the Engineering students at Oxford know it as HLT.
- GuB-42 5y agoInteresting that the periodic table doesn't go beyond element 103 (as Lw, not Lr), we are at 118 (Og) now. Periodic table are a good way to date things. Looking at the footnote, the edition is from 1972. How can you have Verilog, btw? It is from 1984.
- lordnacho 5y agoI found an updated version online
- jonsen 5y agoI own this one. More relevant in my opinion: https://www.amazon.com/Handbook-Mathematics-Computational-Science-Harris/dp/0387947469/ https://www.amazon.com/Handbook-Mathematics-Computational-Sc...
- choeger 5y agoI have to wonder about the big-O notation. Do people really write f(x) = O(g(x)) ? Because that doesn't seem to make sense. It could make sense if we read O as an operator (so f is the upper bound on g, but the definition is the other way around) but saying that a function is equal to an upper bound is just odd, even leaving aside the fact that the definition uses "f(x)", i.e., the application of f, to express the function itself.
- mk12 5y agoSome textbooks use set membership notation instead: f(x) ∈ O(g(x)). This makes sense if you think of O(g(x)) as the set of all functions with that upper bound. However, the (abuse of) equality notation is often more convenient. For example, f(x) = x^2 + O(x) reads “f(x) is x^2 plus (something bounded by) a linear term”. Writing f(x) = x^2 + g(x) where g(x) ∈ O(x) is more of a hassle.
- whimsicalism 5y agoIs there not a special symbol for the usage you are using for error? A sorta cursive O rather than the standard O. I prefer O to remain the set of functions usually.
- FeepingCreature 5y agoYes they do, and yes this is wrong and everyone knows it, and no we can't do anything about it.
- TuringTest 5y agoIt's not wrong, they just overloaded the = operator for the RuntimeComplexity class ;-P Jokes aside, in my college we would write something like: O( f(n) ) = O(n^2) + O(n)
- bjourne 5y ago> O( f(n) ) = O(n^2) + O(n) Naively, one would assume that that implies O( f(n) ) - O(n) = O(n^2), which is not correct. However, O( f(n) ) = O(n^2) + O(n) implies O( f(n) ) = O(n^2), which would have been obvious if proper notation had been used.
- W0lf 5y agoI clearly remember my heureka moment when I discovered back in university that I don't have to actually learn and remember all that stuff that was taught but to recognize patterns and tricks that will reduce the problem domain down to a few things from which everything else can be deduced. After that most of the lectures boiled down to: ok, what is important to learn and remember here :-)
- tester34 5y agoit's just cs math, not cs?
- TuringTest 5y agoMy thoughts exactly. Where are the lambda functions, ADTs, lattices, pre/post conditions for formal derivations, category theory? Boolean logic?
- agumonkey 5y agoYeah it lacks a few layers. But the embedded ~basics are worth it
- dandanua 5y agoIt's just math. In my view, CS theory is about computations as a whole. That is – formalisations, languages, algorithms, structures, and design principles.
- qsort 5y agoIt reminds me of the cheatsheets we used to make before math competitions. Many of those things are forever etched in my brain. The only difference is that the ones I made tended to have a lot more freaking triangles.
- fjfaase 5y agoA nice collection formuleas that seem usefull when doing theoretical computer science. Maybe could improve it with adding the definition for NP-complete, context free grammars, Turing complete, and such.
- osivertsson 5y agoThis is only a showcase of TeX, the actual value of this cheat-sheet seems pretty low. I used to know most of this when I was in uni, including how to derive it when I needed it. Back then this kind of cheat-sheet would not have helped me apply my knowledge. The actual knowledge was very clear in my head from solving problems, or I remembered some key idea used during derivation and from there could work out the rest. If you need this kind of cheat-sheet you don't understand the concepts deep enough. Unfortunately most of this knowledge is now 15 years later either very fuzzy or completely lost from my mind. I guess that happens when it is not being refreshed/applied during the career I chose. This cheat-sheet serves a reminder of how much knowledge I have lost ;)
- OskarS 5y agoI dunno, this seems like a perfectly reasonable tool. Saying "what was the double angle formula for sin, again?" or "what was the error term in Stirling's approximation" doesn't mean that you don't understand the fundamentals.
- whimsicalism 5y agoI find I don't really need to remember trig as long as i remember how imaginary exponentials and the unit circle works. Def agree on Stirling's though.
- JadeNB 5y ago> I find I don't really need to remember trig as long as i remember how imaginary exponentials and the unit circle works. Or, to phrase it differently, trigonometry is just a different language for the restriction of the complex exponential to the imaginary axis, and you are remembering the facts in translated form. (Which I agree is much better—it's certainly the only way I can ever remember the thicket of identities! But I'd argue that it's still remembering trigonometry.)
- gonzus 5y agoAnybody knows what the grid of numbers on the last page, grouped under "Fibonacci Numbers", is?
- Item_Boring 5y agoGoogle (Books) yields this: https://books.google.de/books?id=6fJdDwAAQBAJ&pg=PA11&lpg=PA11&dq=00+47+18+76+29+93+85+34+61+52&source=bl&ots=kMYq7enGu0&sig=ACfU3U135G1Y0IN5uask4patgUoMXQUkEQ&hl=en&sa=X&ved=2ahUKEwjl6LGV3rX0AhXD_rsIHQdCByUQ6AF6BAgPEAM#v=onepage&q=00%2047%2018%2076%2029%2093%2085%2034%2061%2052&f=false https://books.google.de/books?id=6fJdDwAAQBAJ&pg=PA11&lpg=PA... An Eulerian Square of order 10.
- rattyc 5y agoI don't understand any of that
- deleted 5y ago[deleted]
- tzs 5y ago1. I was a pure math major so I've always liked neat representations of pi such as Wallis' identity and Brouncker's continued fraction, both given on that cheat sheet, but I've never actually seen them used for anything. Where do they come up in CS? 2. If you have to deal with a lot of sums involving hypergeometric terms (such as a many series involving binomial coefficients), the book "A=B" by Marko Petkovsek, Herbert Wilf, and Doron Zeilberger might be of interest. It is downloadable from Wilf's site [1]. [1] https://www2.math.upenn.edu/~wilf/AeqB.html https://www2.math.upenn.edu/~wilf/AeqB.html
- xore 5y agoI was expecting something like known NPC problems and their reductions plus complexity of algorithms and data structures. This seems like a math cheat sheet that can be improved removing simple derivations of some formulas. However it can be handy.
- monopoledance 5y agoMaaaan, I was expecting friendly pictures and stuff. Every computer science book looks like this cheat sheet!
- alpaca128 5y agoMaybe it's just me, but when a cheatsheet reaches 10 pages and includes multiple areas like this one I'd just split it up into multiple ones. It almost feels like this needs a table of contents. And I think a bit more theoretical CS stuff, maybe a few diagrams, would be more helpful than e.g. the Pythagorean theorem or the powers of 2 which shouldn't be a problem to just memorize at that level.
- lqet 5y agoI am confused, this seems more like a general math cheatsheet. The only thing that truly has anything to do with theoretical CS are the definitions for the O-notation on the first page (and most CS students don't need a cheat-sheet for that) and the master theorem. Nothing on P, NP, NP-hardness or completeness, formal languages (Chomsky hierarchy?), finite automata, Turing machines, halting problem, decision problem, reduction proofs, Pumping lemma, Gödels incompleteness theorem, etc. This sheet would have been of very little help in any theoretical computer science exam I ever took. The only cheat sheet I ever needed in theoretical CS was Schönings book "Theoretische Informatik - kurz gefasst" ("A short overview of theoretical CS", well, it has ~180 pages...), which is pretty standard in German universities. It was completely worn out after my first semester + exam of theoretical CS... here is a TOC: http://www.gbv.de/dms/hebis-mainz/toc/094349797.pdf http://www.gbv.de/dms/hebis-mainz/toc/094349797.pdf
- SkeuomorphicBee 5y agoMore of a "Math for CS" cheatsheet. I agree that we can't call it a CS sheet as it has very few actual CS concepts (besides the O notation, I would also consider Graph Theory as CS), but I also wouldn't call it a general math sheet because it encompasses only an arbitrary small subset of math. Having said that, as a Math-for-CS sheet I found the section on matrices a bit light (missing quite a lot of linear algebra), and I missed the Fourier transform.
- emteycz 5y agoIsn't graph theory a very general (and generally used) math concept that is useful in CS, not the other way around?
- whimsicalism 5y agoYes
- zazen 5y agoYes, and so is asymptotic analysis and the associated big-O notation.
- pyentropy 5y agoIt's nice, but it doesn't cover any topic of Theoretical Computer Science [1]. It's just the math required for undergrad general CS courses. [1] - https://en.wikipedia.org/wiki/Theoretical_computer_science https://en.wikipedia.org/wiki/Theoretical_computer_science
- d33 5y agoI just had this thought that it might be super interesting to see a cheat sheet with the current state of academic knowledge in computer science compressed to as few pages as possible. Things that we didn't know at - let's say - 10 or 20 years ago in a format that could be understood by people from those times.
- antegamisou 5y agoFor anyone complaining about the length of the document, I suggested it as a shorter alternative to a original submission [0] where apparently a 212 page document was called a cheatsheet and in fact TCS Cheat Sheet was seen as too concise! [0] https://news.ycombinator.com/item?id=27468908 https://news.ycombinator.com/item?id=27468908
- Tade0 5y agoNo mention of (Shannon) entropy? Sort of an important concept.
- killjoywashere 5y agoIt's like the front section of CRC Handbook of Chemistry & Physics. Very dense.
- arethuza 5y agoNo definition of the Y Combinator ;-)
- waynecochran 5y agoThe formula for the nth prime number has a bound of O(n / ln n) which makes the lesser terms noise (?) Same w pi(x) (?) Using a bound is more useful: n ln n + n(ln ln n - 1) < p_n < n ln n + n ln ln n (for n >= 6)
- AstroDogCatcher 5y agoFeels like this exists mostly as a prop for immature CS students to "impress" people with.
- unbanned 5y agoSeems like some eager undergrad's notebook; an exercise in productive procrastination. Not sure how useful this is in practice. Probably not very. Thanks nonetheless
- deleted 5y ago[deleted]
- slmjkdbtl 5y agoAs someone who has no training at all in related subject I really like the graphical aspect of this pdf, it brought me a sense of complete alienness and makes me want to explore. It almost look like something you can find at an art book fair.