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Mathematics all-in-one cheat-sheet (2013) [pdf]
- chris_wot 7y agoDon't see any logic equivalencies... I think they are kind of neat!
- mhartl 7y agoSomeday the cover will read e^iτ = 1 and all will be right with the world.
- deleted 7y ago[deleted]
- alanbernstein 7y agoSome believe the pi version is superior due to the inclusion of three operators (+, *, exp), and five numbers (0, 1, i, e, pi) which are all fundamental in some sense. The tau version omits the + and the 0.
- gizmo686 7y agoe^iτ + 0 = 1 Fixed.
- lisper 7y agoe^iτ = 1 + 0 Fixed^2
- simongr3dal 7y agoe^iτ = 1 + 0i Fixed for real this time-final.final.v2.docx
- EGreg 7y agoYou mean fixed for all real values of i?
- ngcc_hk 7y ago-1 not 1 ... e^iπ+1=0 from e^ix=sinx + icosx with x=π
- gizmo686 7y agoThats why we are using τ not π.
- deleted 7y ago[deleted]
- mhartl 7y agoAs the author of The Tau Manifesto, I’m well aware of this (pseudo-)argument, which is dealt with explicitly here: https://tauday.com/tau-manifesto#eq-euler_tau_zero https://tauday.com/tau-manifesto#eq-euler_tau_zero
- deleted 7y ago[deleted]
- pgreenwood 7y agoNot LaTeX; didn't read.
- Ghost_of_USSR 7y agoThis, some formulas quite hard to read.
- stevesimmons 7y agoThe first thing I look for in a math paper is whether the typesetting is up to TeX's standard. If it's not good enough, I'll just skim the text. I'm not sure whether this pro-TeX prejudice is a good or bad thing...
- dngray 7y agoI have to admit it's a pretty ugly manual. Some of those formulas were really blurry, while some of the tables spanned weirdly over pages. The hosting issues could have been fixed as well if it was LaTeX as it would have been neat in a git repository. Gitlab also has continuous integration for LaTeX * https://www.vipinajayakumar.com/continuous-integration-of-latex-projects-with-gitlab-pages.html https://www.vipinajayakumar.com/continuous-integration-of-la... * https://sayantangkhan.github.io/latex-gitlab-ci.html https://sayantangkhan.github.io/latex-gitlab-ci.html
- nicklaf 7y agoWhile we're on the topic of this kind of thing: https://en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics https://en.wikipedia.org/wiki/Synopsis_of_Pure_Mathematics
- yannis 7y agoThis is an excellent book, but perhaps a bit dated despite the fact that Mathematical Books have a long shelf-life. Factoid: The book is noteworthy because it was a major source of information for the legendary and self-taught mathematician Srinivasa Ramanujan who managed to obtain a library loaned copy from a friend in 1903...
- karmakaze 7y agoI hate how often these sprawly things are called cheetsheets: LOGIC SYMBOLS Symbol Symbol Name Meaning / definition Example & and x & y
- sdan 7y agoFirst time I've seen someone use Keybase.pub. Last time I checked they gave out 250gb for free for everyone... this is a good use of that!
- ac29 7y agoI wonder how long that can last before abuse kills the system. Some quotes from their page about KBFS [0]: "The 250GB free accounts will stay free" "we'll never run an ad-supported business" "we're not trying to make money" [0] https://keybase.io/docs/kbfs https://keybase.io/docs/kbfs
- sdan 7y agoProbably why they don't market it. If they did... like Dropbox, Dropbox would have to say goodbye to a lot of users, given that these users understand that Keybase doesn't have the efficiency or reliability that Dropbox has.
- ashton314 7y agoHow is Keybase funded anyway? They say they’re hiring, so money is coming from somewhere.
- justusthane 7y agoFunding from Stellar: https://keybase.io/blog/keybase-stellar https://keybase.io/blog/keybase-stellar
- johnnyRose 7y agoTheir Series A raised $10.8M back in 2015: https://keybase.io/blog/2015-07-15/keybase-raises-series-a https://keybase.io/blog/2015-07-15/keybase-raises-series-a
- daurnimator 7y agoPages 168 to 262 seem to be missing?
- SubiculumCode 7y agoFermat’s Lost Theorem?
- hollasch 7y agoReally? That's odd -- I see pages 1-212 (213+ are missing).
- daveFNbuck 7y agoI got a B in probability because I didn't write a proof of the central limit theorem on the allowed cheat sheet for the final exam. So of course it's the first thing I looked for on this one. It's not there.
- creddit 7y agoAren't most proofs of the CLT pretty extensive?
- AstralStorm 7y agoThere are a few short ones going from area integral comparisons.
- crdrost 7y agoThe easiest is to look at characteristic functions and cumulants; for a random variable T with PDF p(t) we say T ~ p and define φ_T[f] = ∫ dt p(t) exp(-2πift) = ⟨ exp(-2πifT) ⟩ If two variables X ~ r and Y ~ s are independent then you can prove [from ⟨f(X) g(Y)⟩ = ⟨f(X)⟩ ⟨g(Y)⟩ or X+Y ~ q where q(z) = ∫ dx r(x) s(z — x)] that their sum has a characteristic function φ_{X+Y} = φ_X + φ_Y And therefore the “sample mean” M of n IID variables is itself a random variable with characteristic function φ_M[f] = ( φ[f/n] )^n. So we find that log φ_M[f] = n log φ[f/n] ≈ 0 + i a f – b f²/n + O(f³/n²). These terms [a, b] from expanding the log of the characteristic function constitute the cumulant expansion and for large n the other terms shrink to zero, so that the characteristic function is to first order in 1/n a Gaussian. The characteristic function was a Fourier transform of a PDF, so an inverse Fourier transform gets it back: p(t) = ∫ df φ_T[f] exp(2πift) But the Fourier transform of a Gaussian is just a Gaussian.
- ngcc_hk 7y agoSurprise you can use those character like “∫ φ π”. Thought you need to say pig etc.
- lucb1e 7y ago
- trilinearnz 7y agoI like the idea of this, but I'm not sure that "cheat sheet" is the best term for it, given that it weighs in at quite a few pages (191 physical).
- _emacsomancer_ 7y ago"cheat ream" ?
- dominicwllmsn 7y agoYes, cheat tome.
- derefr 7y agoI believe that this sort of collection of tables is commonly called an “almanac”—but maybe only when the subject is of practical use.
- Sharlin 7y agoThe sort of ~100 page softcover reference book that we were permitted to use in highschool math, physics, and chemistry exams is called around here, literally translated, a book of tables. The term is probably a remnant from a time before pocket calculators when it contained actual trig and log tables. "Book of formulas" would probably be a more apt name nowadays. Not sure if there's a common word for such a thing in English.
- mcnamaratw 7y agoThis kind of thing? https://en.wikipedia.org/wiki/Abramowitz_and_Stegun https://en.wikipedia.org/wiki/Abramowitz_and_Stegun I'm not sure there's really an English word for it. That's strange.
- paxys 7y agoUh, this is a book.
- symplee 7y agoLast page says "Page 212 of 330" Pages 213+ are probably where they discuss cardinality.
- imedadel 7y agoOne day, I'll make an Anki version of this.
- james_s_tayler 7y agoJust start with one small section :P
- imedadel 7y agoLast year, when I was in high school, I turned most of my math (and physics) textbook into an Anki deck :D It's really good, especially when the final exam covers +4 years of mathematics.
- zhte415 7y agoI remember for Maths, Further Maths and Computing A-Levels typing in mini programs for everything into my TI-85, from stats to bubble sort or curvature. It took so long typing that on a numerical keypad I could remember everything and no longer needed it. Still, a good exercise in basic programming and not unlike remembering from a flashcard deck. Four years later in banking, I discovered the entire industry does the same, but in Excel. Enjoy your studies!
- r-w 7y agoPost it when you do! Might be worth making it open-source so not only one person has to do it :P
- taliesinb 7y agoSpeaking of, can anyone commend some good Anki mathematics decks?
- mathnmusic 7y agoThere is just one link here: https://learnawesome.org/learn-awesome/mathematics.html https://learnawesome.org/learn-awesome/mathematics.html If people share links here, I'll send a PR to learnawesome to add those under mathematics#flashcards section.
- zw123456 7y agoReminds me of the old Schaum's Outlines, I still have a couple of them on the book shelf from college days, saved my bacon many times.
- sunstone 7y agoYou know you're in for a head banging when the Table of Contents is 25 pages long! :o
- kwoff 7y agohttps://archive.org/details/elementsquaterni00hamirich/page/n13 https://archive.org/details/elementsquaterni00hamirich/page/... Hamilton's "Elements of Quaternions"'s table of contents is about 60 pages long and includes footnotes.
- halfelf 7y agoFind a bug in page 39: y' is Lagrange's notation while dx/dy is Leibniz's.
- te_platt 7y agoNice touch: 4.15 FERMAT’S LAST THEOREM: ... General case when n>2 was proved by Andrew Wiles (1994). The proof is too long to be written here. See: http://www.cs.berkeley.edu/~anindya/fermat.pdf http://www.cs.berkeley.edu/~anindya/fermat.pdf
- throwawaymath 7y agoI actually can't tell if that was an intentional "margin" joke, or if the author is just bluntly stating a fact about Wiles' proof... EDIT: Nope, probably intentional. The author doesn't say something similar for any other proof based on a quick CTRL+F :)
- piqufoh 7y agoFermat wrote that in the margin of his book Arithmetica that a proof existed, but there wasn’t space in the margin to write it. It took Wiles 385 years to find a proof, and it won’t fit in a margin. https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem https://en.m.wikipedia.org/wiki/Fermat%27s_Last_Theorem That’s the allure of the theorem; that a simple unknown proof may exist.
- barking 7y agoYes, I remember when news of his proof broke, being disappointed at how voluminous and obscure (to someone like me) it was. I'd been hoping for something I might be able to get my head around. (Hard as it was, I don't think Wiles spent 385 years coming up with it btw!)
- nurettin 7y agoWhether there is an existing and verified proof or not, there is still a great mystery to be solved by figuring out what Fermat actually meant by what he thought as an elegant solution, whether it is an actual solution or not.
- 7y ago
- amitport 7y agonice work. I would have removed most of 'PART 1: PHYSICAL CONSTANTS', 'PART 8: APPLIED FIELDS', 'PART 18: ELECTRICAL', and some of 'PART 99: CONVERSIONS'. "all-in-one" math seems enough :). Other stuff seems arbitrary and leaning towards physics (which could have its own giant book).
- Aromasin 7y agoI'm biased as I'm an EE, but I'd say that the Laplace transforms within the Electrical section are firmly in the realm mathematics, so keep them. It just so happens that they are only really useful in the domain of digital signal/control processing, and I think to get the true form or radioactive decay(?) though I may be mistaken. I'd put it next to information on Fourier transforms. The circuit theory may be a bit unnecessary though I agree.
- remarkEon 7y agoWoof. Flashbacks to Sister Mary's Calculus class in 12th grade.
- alister 7y agoI think the author's page (Alex Spartalis) deserves to be mentioned: https://www.alexspartalis.com/cheat-sheet.html https://www.alexspartalis.com/cheat-sheet.html He has the same version (v2.10) there and mentions that, "The Web version does not include the distribution functions due to file size restrictions. Email me if you would like a copy of these." That explains why pages 213-330 are missing. Someone should offer to upload the full copy to keybase.pub (or someplace) since his personal site can't handle the load. People sometimes do tremendous work creating a program/book/artwork, and want the world to see it, but don't get around to really share it or promote it.
- behnamoh 7y agoIt'd be nice if there was a cheat sheet for Category Theory as well. I thought that part could be found in the link you provided, but seems like the author hadn't (2013) included CT in this almanac.
- lucb1e 7y agoI sent a message using the contact form. Thanks for mentioning this.
- samirm 7y agoIf you do end up reuploading it, please look into fixing all the typographical issues too. Ty!
- _underfl0w_ 7y agoIf you do re-upload it, you should let us know here and/or post a link to the full version on HN.
- iagovar 7y agoJust use torrent! It's easy, and potentially free!
- lucb1e 7y agoDistributing new versions is an issue though, as there is no way to tell anyone who is currently seeding the old torrent. But it's not a terrible idea if it turns out there is really a lot of bandwidth (I don't expect that), then I could use my server for seeding at least.
- pencillr 7y agoIt's awesome. Though I prefer my Bronshtein :D https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev https://en.wikipedia.org/wiki/Bronshtein_and_Semendyayev
- amelius 7y agoRussian version?
- GlenTheMachine 7y agoBronshtein is excellent, but a bit dated. For me in particular it's lacking coverage of modern ideas on function approximation. Also, it isn't free ;)
- zwieback 7y agoInteresting - I've had the German version from my university days (every ME student had one) and it's spelled "Bronstein". The English spelling makes me a little dizzy.
- billfruit 7y agoIIRC it does not cover probablity and statistics, a strange omission considering the Russian heritage.
- r-w 7y agoThings get kind of pixelated for me around page 123. Anyone else?
- trymas 7y agoYou are not alone. Seems like formula's are not vector anymore from page 121.
- killjoywashere 7y agoAh, 10% of the first section of the CRC Handbook of Chemistry and Physics, with amateur typography. Sort of like Greenspun's tenth rule, but for math.
- digitalsushi 7y agoI've heard of mathematicians handwriting proofs in the margins of books. Like an MVC, I can appreciate the data without appreciating the presentation.
- TorKlingberg 7y agoI remember using something similar called "Mathematics Handbook for Science and Engineering" in university. https://www.amazon.co.uk/Mathematics-Handbook-Science-Engineering-Lennart/dp/3540211411 https://www.amazon.co.uk/Mathematics-Handbook-Science-Engine... I assume there are many others, and this is a free alternative.
- nn3 7y agoSeems very similar to a classic formula collection like https://dlmf.nist.gov/ https://dlmf.nist.gov/
- orangewindhoek 7y agomisprint PART 2: MATHEMTAICAL SYMBOLS
- rplnt 7y agoCheat-sheet we were allowed to use during math exams at university: Theoretical Computer Science Cheat Sheet https://www.tug.org/texshowcase/cheat.pdf https://www.tug.org/texshowcase/cheat.pdf It's 10 pages, so 3 papers with one page free for something that might be missing.
- archi42 7y agoI often used this when solving assignments and can recommend it to any computer science student.
- daodedickinson 7y agoIt's organized like a debate file. Fascinating.
- FerretFred 7y agoAwesome! It only serves to remind me I know practically nothing about Mathematics. "Good Primes" and "Happy Primes" .. who'd have thought it ...
- pja 7y agoMore “Cheat Book” than “Cheat Sheet” :) Looks like it could do with typesetting in LaTeX - I think the author started doing this here: http://mathscheats.weebly.com/ http://mathscheats.weebly.com/ but never entirely completed it. Plenty there to chew on though.
- karthie 7y agoQuiet handy and amazing thank you very much for sharing this over.
- andrepd 7y agoI really didn't want to be that guy, and props for the author for such comprehensive reference work, but god, what an appalling typography. Bad tables with too many lines bitmap formulas with misadjusted size, poor spacing, ugly font... Almost everything that could be wrong is wrong.
- xwin 7y agoI came here to say the same thing. Looks like the author did not use a good authoring tool to produce good math output. I generally take notes like this with LaTeX and compile them to PDF but PDFs can be large and if committing to a Git repo can lead to large .git directories. The BasicTeX package for Mac (brew install basictex) has worked well for me: http://www.tug.org/mactex/morepackages.html http://www.tug.org/mactex/morepackages.html These days I also take math notes as plain HTML files containing Markdown and LaTeX, then render with the TeXme one-liner here: https://github.com/susam/texme https://github.com/susam/texme I guess what the OP has done here is take all the notes in Word or some other WYSIWYG document editor not specialized for mathematical typography and converted the whole document to PDF. This won't lead to good results. It is absolutely necessary to use tools specialized for mathematical typography to write and publish math. By the way, is there anyway to create high quality math distributables that are both self-contained and lightweight?
- mkl 7y agoWhy commit the output files? I generally put "*.pdf" in .gitignore.
- snazz 7y agoProbably so that someone can download it without compiling it? GitHub Releases or an equivalent would probably be better, though.
- xwin 7y agoThat's right. I would like others as well as myself to be easily able to download the PDF files without having to compile it. I tried out GitHub releases and it works okay but not great. I cannot track all the compiled PDFs I have at a single place or move them easily from one system to another like I could with GitHub repos. I am also trying to avoid getting locked into a specific service like GitHub releases.
- supernova87a 7y agoWow, I have to say I feel somewhat bad for the author who spent so much time (months?) compiling this semi-comprehensive reference work. There's so much information, but at the same time, so little useful information to any particular reader. It's so broad as to be a hindrance to using it in any sort of daily reference. Who would use this? Wouldn't you probably resort to a reference more specific to your field? Is this the product of someone's superficial fascination with mathematical equations combined with OCD to copy down everything ever read, gone awry? Or is this like a strange version of a Noah Webster?
- lotaezenwa 7y agoThis comment reminds me of the archetypal high-school student who asks "when are we ever going to use this stuff?" If you have to ask...
- doodpants 7y agoI'm hoping that this work might give me some valuable info on how to get started on various Project Euler[0] problems that I might otherwise have no idea how to approach, or that I wouldn't know what area of math to do research for. [0]https://projecteuler.net/ https://projecteuler.net/
- americanjetset 7y agoThis is exactly what I thought. In fact, when I got to the section that listed the right-truncatable primes, I immediately searched Euler because I knew there was a problem about them -- turns out I had already solved it though lol.
- asdfman123 7y agoWell, I find it extremely useful. This is my new go-to item when someone asks me, "What would you bring with you if you could go back in time to the year 1600?"
- lr4444lr 7y ago
- floatinthecloud 7y agoWhen I was studying mathematical physics, my classmates and I made similar quick reference notes in latex. Based on a cursory look, it seems to be missing some important complex analysis and abstract algebra/lie theory results (although I haven't read what the author studied).
- kd0amg 7y agoSearching for stuff I've used, this document is also quite light on combinatorics, complexity theory, and order theory (and of stuff I haven't used much, I don't see anything on category theory or topology). I don't think 330 pages is nearly enough to be truly all-in-one.
- throwawaymath 7y agoAgreed. This document is reasonably broad but it's missing quite a lot of undergrad mathematics, let alone graduate math. If you literally wrote down sequences of definition, theorem, proof, definition, theorem, proof, ... with no exposition or exercises whatsoever, I think you might be able to include most undergraduate math in about 1000 pages. That would include calculus, real analysis, complex analysis, linear algebra, abstract algebra, discrete math. Maybe elementary number theory, topology and probability theory as well. That would be...horrible to learn from, frankly. Imagine a ten volume set of Baby Rudins, with no exercises. If you really doubled down on the cheat sheet angle and didn't include any proofs - just the theorems, identities and inequalities - I think you could get through all undergrad math in a few hundred pages. But you wouldn't have any of the peripheral content the author included, like physics/economics.
- floatinthecloud 7y ago'Riley, Hobson and Bence' was a standard reference I used throughout my undergrad and graduate studies. Sure enough, it's about 1200 pages.
- thatsnotmepls 7y agoOut of topic, but why is your username green?
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- kejaed 7y agoMaking your own cheat sheet is half the battle when you are trying to learn the topic. I remember in my 4th year Stochastic Processes class [0] (back in 2005, wow) we could bring in a double sided page of notes. I wrote my sheet up in LaTeX [1] and shared it with the class, of course this made it better by having others contribute. Some didn’t understand why I would “help others out” by giving it away, but I never understood that, like a page of formulae are going to get you an A (also why not help others out?). Of course after spending so much time developing the formula sheet and working through the example problems (always the most important thing you can do), I think I looked at the sheet twice in 3 hours during the exam. Also, Dr. Glen Takahara, this class and your instruction are one of my fondest memories at Queen’s! [0] http://kje.ca/school/stat455/cheat2.pdf http://kje.ca/school/stat455/cheat2.pdf [1] https://mast.queensu.ca/~stat455/ https://mast.queensu.ca/~stat455/
- stevespang 7y agoHas anybody checked this for typos and mistakes ? PART 2: MATHEMTAICAL SYMBOLS 33
- deleted 7y ago[deleted]
- rando171717 7y agoSlightly off-topic: from a security perspective, how safe/not safe is it to be clicking open random pdf's? Wouldn't this be a possible avenue for malware?
- dual_basis 7y agoSure, but so is clicking open websites unless you have Javascript disabled, in which case half the web is broken for you.
- syn0byte 7y agohttps://github.com/osnr/horrifying-pdf-experiments https://github.com/osnr/horrifying-pdf-experiments https://www.alchemistowl.org/pocorgtfo/ https://www.alchemistowl.org/pocorgtfo/ Yes. Not only is it possible but historically already an avenue of attack.
- ranie93 7y agoAdd this to the list of items (or perhaps the only item?) you'd take if you'd time travel to the past
- fmajid 7y agoI've owned paper copies of Murray Spiegel's Schaum Outline of Mathematics, and even the government-funded Abramowitz-Stegun doorstop, this reminds me of those somewhat, but the title is misleading as it has as much physics and chemistry as mathematics.
- mpoteat 7y agoTo me this seems to be exclusively undergraduate mathematics that one might learn in an engineering program. No mention of topology or modern algebra.
- jlv2 7y agos/Cheat-sheet/Cheat-book/g
- phragg 7y agobet i could fit this on a 3.5in x 5in notecard...
- BlackFingolfin 7y agoOK, so, I also hate to be "that guy", but, despite the admirable effort put into creating this by the author, I am sad to say I don't see why some people are excited about this... Because unfortunately after just looking at a few pages, I saw lots and lots of error and misleading or plain confusing statements, basically on every single page I looked at closer, which makes me distrust it. Granted, these vary in their severity, but still... Examples: - p. 50, definition of a complex vector space, says " A complex vector space consists of the same set of axioms as the real case, but elements within the vector space are complex.". The vector space does not "consist" of the axiom, it adheres to them. And it makes no sense to say that the "elements" (vectors) are "complex". Rather, that scalars are allowed to be complex, not just real. - p. 50: definition of a subspace is a mess. To pick just one obvious problem with it: What even are "axioms (a) and (b)"? Perhaps the three unlabeled "axioms" at the top of the page are meant (being closed under addition, additive inverses, and scalar multiplication)? But certainly the third one (axion "(c)"?) needs to be verified, too (whereas the second, about additive inverses, is redundant). - p. 51 the examples at the top of the page end with mentioning C[a,b], the set of all continuous functions on an interval [a,b]. But then it claims that this is actually not an example, because "it has infinite dimensions". But really this is a perfectly fine vector space (also, we haven't even defined what a "dimension" is yet) - p. 51, definition of linear independence says "c_1=c_2=c_n=0" which is missing a "=..." before the "=c_n" - p. 52 the "general vector" given as a column vector doesn't make sense in a general vector space - p. 53: "Matricis" - p. 56 "Laprange's theorem" should be "Lagrange's theorem" - p. 126: "EXPONETIAL" - p. 167: "Matricies", "Prinicples", "opertaions", - p. 168: "Determinate"; the formulas for 2x2 and 3x3 matrices implicitly assume a labeling of the entries which is never given, rendering this semi-useless - one section is titled "MISELANIOUS" And on page 38, the fields of real and complex numbers, R and C, are introduced as being written with a "blackboard" font (\mathbb), while on page 51 this is not followed (instead, we get \mathcal{R} and plain C). Why even introduce these conventions if they are then not followed? Sure, many of these are minor and perhaps even "obvious" mistakes. But if you know the matter well enough to spot all of these, maybe you don't need this cheat sheet? Also, as a mathematician myself, my experience is that the number of spelling mistakes in a research paper (or in anything written and submitted by students) is a good first proxy for the quality of the text: if you can't be bothered to even run a spell checker on your text, should I really trust you to have verified all your computations and logical deductions carefully? (And no, I don't apply this to, say, posts here on HackerNews: I hate it when people shoot down a comment, or a twitter post, or whatever, just because it contains typo. But writing a book is a bit of a different affair, isn't it?). Hence my point that I wouldn't want to suggest this to anybody as a reference. :-(
- droithomme 7y agoIt's a very fine compendium of notable relations. At 212 pages long, it's certainly not a cheat-sheet. If it didn't have obvious spelling errors I might be more confident the rest has been transcribed accurately.
- lightedman 7y agoMissing the cheats for division (how to rapidly tell if a number is divisible by 3, 7, 2, 5, etc. for prime factorization.)
- kakaz 7y agoIt is interesting and fun! I have a loose suggestion - it could be published together with LaTeX codes for any formula present - so it would be great speed up for someone who wants to use various formula in his works. However the choice of various areas is strange for me ( partially lack of some engineering areas, partially lack of very basic physics things, partially lack of mathematics) A lot of things is missing: Maxwell-Clerk equations. Einstein equations. Schrödinger equation. Dirac equations. Notable: Laplace equation and Maxwell-Clerk equations, wave equation!!! Harmonic oscillator equation. Quantum physics, Heisenberg relation at least please! Hydrodynamic, notable no Navier-Stokes equations. Special functions: Bessel, Jacobi, Lagrange, Chevyshev polynomials, various equations related to it. No elliptic functions, no Weierstrass function mentioned. No various number theory objects: Mobius function, Minkowski function ?() not mentioned. Congruences nearly omitted ( Chinese remainder theorem maybe) Group theory, some simple results from category theory, Shannon theory completely missing. No universal algebra. No basic cryptography. Complete lack of various numbering systems ( binary, hex at least)
- tychonoff 7y agoNice work. But on page 43 "quadratic" is misspelled.
- amai 7y agoWhy does the author not use LaTeX?