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lainchan archive - /λ/ - 18037

File: 1471547763745.png (6.7 MB, 200x200, Graph Theory.pdf)


I know we've got a couple matheads up in here.

This thread is for discussing math, theoretical CS, crypto, and other mathemagical fun stuff.

Post books, papers, and blogs.

I've been working through this textbook, the first chapter is a really good intro to graph theory and how to reason about them IMO.


File: 1471551202005.png (3.7 MB, 200x200, kategori.pdf)

Finally some love for math.
Why do people seem to fear the subject at all?
Anyway, books!
This one is a great, well-paced introduction to category theory.


How do you use Math in CS anyways


some would say that CS is just a subset of math that deals with computation.

In a more concrete sense: you use graph and queue theory in networks, linear algebra in 3d graphics, information theory in compression, number theory in cryptography, category theory(I think) in programming language design(specifically for data types), statistical and high-level algebraic methods in AI... the list goes on and on.


type theory in programming languages too, the lambda calculus is also a set of math. CS itself is mathematics mostly: decidability and such. Vector analysis in 3D rendering n such shit.
But the bottom line is not so much the disciplines and how they map into computer subjects, but learning to think in such a way that you can dissect and solve a problem. The disciplines provide the technology for specific tasks, but the meat of mathematics is critical thinking, analysis, abstraction, finding the principles underlying things so you can come up with new methods, or weed out the unneeded data from a particular problem, see how the parts relate.
And foremost, it's fun as fuck. And beautiful.


File: 1471571003560.png (13.02 MB, 200x200, Knuth-SurrealNumbers.pdf)

correct, the most important reason to do math is because it's fun and beautiful. If you don't like those, just learn the parts that are important for what you do.

Another book and a video that explains it a little better(it's mostly John Conway going on tangents, but it all kinda clicked for me at the end, having read the book first). Surreal numbers are really fucking cool.



s/if you don't like those/if you don't think so


File: 1471635864938.png (177.16 KB, 200x159, math_girls__.jpg)

Since I started studying CS I realized how much I love mathematics.

Like >>18046 said it is true that the mathematics are the theoretical foundations for computations. But now I am nearly done and it seems that in reality you do not need "real" mathematics. It is good to be able to do some basic calculations but most people tell me that most of the time you do not need sophisticated knowledge of maths or algorithms. Hell, even some of my professors told me how rarely you need to do advanced calculations or mathematical modelling. (The professor who teaches 3D graphics even says you just need some simple matrix calculations, not "real" linear algebra.)

Fortunately I am too dumb for pure mathematics. Otherwise I would regret choosing CS instead of mathematics.

Now I am looking for fields of CS where you can play around at least a bit with some numbers and models and so on... Any ideas? Maybe scientific computing? Physical simulations? Signal processing? Computer vision?


File: 1471637813488.png (838.42 KB, 200x200, Algorithm and Complexity Lctn - Herbert S. Wilf.pdf)

all of those would be math-heavy, SP and simulations particularly. The mathiest part of CS would probably be algorithms, though.

related book


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Here is a lot of books for Lainon:

Graduate Texts in Mathematics: magnet:?xt=urn:btih:dc92c5df2c4d772a3d053a033a0201be9808b13c&dn=GTM
Group theory: magnet:?xt=urn:btih:978d5887ea41fc785b1265225b8842b34d44fded&dn=Books%20on%20Group%20Theory
Category theory: magnet:?xt=urn:btih:7a4b187243f978eda3960abd6e6a61cb569ba30f&dn=Category%20Theory
Complex analysis: magnet:?xt=urn:btih:0dc0b8717e0e80eb1474011009ae16d91dc31d77&dn=Complex%20analysis
Topology: magnet:?xt=urn:btih:7a6451e39da7a699279a5fa63c4e8c6977607740&dn=Topology
Combinatorics: magnet:?xt=urn:btih:6fdc51b49b0d3726b7c890684ce208d454dfe5d9&dn=Combinatorics%5Ball%5D
Differential geometry:
Set theory: magnet:?xt=urn:btih:2e59f32c79d142beba3e61c5d0448cb5e6d963ed&dn=Set%20Theory%20etc.%20textbook%20collection%20-%20CORRECTED
Differential equations: magnet:?xt=urn:btih:60b722a8f96939c86d658cc0e80361be89150d90&dn=Differential%20Equations%20Books
Algebra and trigonometry: magnet:?xt=urn:btih:121142a7970ef893ab7b72542d2eec7bc68f6ba6&dn=Algebra%20%26amp%3B%20Trigonometry


File: 1471673605230.png (7.68 MB, 200x200, Rosen_et_al_-_Handbook_of_Discrete_and_Combinatorial_Mathematics_2000.pdf)

The importance of discrete mathematics has increased dramatically within the last few years but until now, it has been difficult-if not impossible-to find a single reference book that effectively covers the subject. To fill that void, The Handbook of Discrete and Combinatorial Mathematics presents a comprehensive collection of ready reference material for all of the important areas of discrete mathematics, including those essential to its applications in computer science and engineering. Its topics include:
Logic and foundations
Number theory
Abstract and linear algebra
Graph theory
Networks and optimization
Cryptography and coding
Combinatorial designs
The author presents the material in a simple, uniform way, and emphasizes what is useful and practical. For easy reference, he incorporates into the text:
Many glossaries of important terms
Lists of important theorems and formulas
Numerous examples that illustrate terms and concepts
Helpful descriptions of algorithms
Summary tables
Citations of Web pages that supplement the text
If you have ever had to find information from discrete mathematics in your work-or just out of curiosity-you probably had to search through a variety of books to find it. Never again. The Handbook of Discrete Mathematics is now available and has virtually everything you need-everything important to both theory and practice.


File: 1471675780225.png (1.46 MB, 200x200, tumblr_oahrutBHMq1u2g2r8o1_500.gif)

Very interesting discussion about pure mathematics:


File: 1471676948157.png (1.97 MB, 200x200, tumblr_o9aof9UyN51txe8seo1_500.gif)

Pure mathematics is a simple way to happyness. All you need is a book, a piece of paper and a pen.


Honestly tho. Understanding a good proof is one of the most satisfying things.


some of these look like they aren't seeded, but I'll keep them up for a week.


Currently learning basic math (up to pre calculus) through Khan academy. Does anyone know if they leave anything important out?


Never been to Khan Academy. But the math curriculum up to calculus is actually very small.
Some basic algebra, polynomials, basic trigonometry (plane trig at that), analytic geometry, heavlily focused on conic relations... and that's about it.
If that's what they teach you, then I don't think you're missing anything *from the normal curriculum*. The actual techniques you'll need past that are a subset of what you're taught. You only need to understand the main ideas behind them.
Anyway I suggest you also take a very basic look at vectors, matrices, some elementary abstract algebra, elementary group theory, and a small bit of statistics.
While calculus is important, some sutff like statistics and matrices are more likely to show up in whatever career you pursue.


"Up to calculus" i meant "everything from highschool"
I believe they do teach everything you get in any school, it's quite an extensive curriculum but the concepts are simple, shouldn't take more than a week to finish it.

Here is what i'm doing right now:
Basic math
Statistics & probability

Then it's calculus, and i'll learn through MIT's open courseware. Thanks for your clarification though, i think i'll follow their method, since it's pretty quick and easy to learn.


I am constantly left with the feeling that I got shafted by high school maths, everything was taught as a list of things to remember not how it worked or why. I'm not even talking about anything in depth just simple things like why didn't they show us what a radian is or what sin/cos/tan are?


>why didn't they show us what a radian is or what sin/cos/tan are?
That subject belongs in a university maths course. I mean, nobody else "knows" maths except the ones studying all the works in say a university. Engineers and regular people only need to know when to apply what aspect of maths.


Surprisingly, they taught us radians, sin/cos/tan, deriatiives and integrals in school. I think these are basic topics, they should belong to school, not university.


File: 1471718733974.png (19.15 KB, 200x175, ClipboardImage.png)

I don't mean anything deep just show us an image like this.


I was miraculously saved. I started making gaems in GM when I was in high school, and reading about how to make the character in a top-down shooter look around I found out what sine/cosine is all about. Real easy, yet they manage to make it fucking dull at school.
Anyway, read Lockhart's lament, he touches deeply on that.
Basically, yes, school kills math. Instead of showing the fun and discovery of it, they tell you "bee squared plus square root of bee plus minus 4 aye see over four aye".
They never show you *why* would you want to do that, they just say "do this to pass the exam". If I tell you to do something like "echo 'HISTSIZE=1000' > .zshrc" to pass an exam, will you remember it? You'll most likely end up thinking that computers are a bunch of nonsense with no meaning whatsoever.
I think that's why a lot of people end up hating math or thinking it's hard. And also that's why students keep asking how it will apply in real life.
Makes me mad.


well, math is hard. People end up hating math because it is made to be incredibly boring. I didn't like math until I finished calc.


Here's a related thread:


Just on a side note, khan academy isn't really good. After 6 to 8 hours i gave up on it because the classes aren't really reliable. Some are good, others not so much. Also the curriculum isn't as straightforward as it looks.

I'm currently learning through Serje lang's basic mathematics. I'm enjoying, 2 hours in so far.


Wow, thats really cool! Thank you!

I really love to browse through such collections. At the moment I only know the basics of some of these topics. It may be interesting to see which of these sounds most interesting to start specializing in.


Are any of these seeded? I'm not sure if my client is acting up or they actually are not. I have a maniac obsession with accumulating maths books and sooner or later I will study em all


Badly seeded. I'm downloading and seeding what i can.


I guess my client is acting up. I use rtorrent and for no reason it's badly digesting magnets


File: 1471904658119.png (373.47 KB, 148x200, CzO7Exp.png)

God damn it, i was expecting to finish at least two chapters of this book today, it took me about 6 hours to do these exercises, they're like two pages from a single chapter. And i'm not considering the food/shower/procrastination, this shit took me my whole day basically.
Did you guys also have this problem in serje lang's basic mathematics? I feel dumb as a motherfucker. I'm not giving up on the book or anything, it's just a bit frustating, i expected to finish the whole book in 2 weeks.


you're doing too many exercizes. Focus on he ones that are actually interesting, only do a few of the busywork ones to get the hang of it.


it's important to grind out plenty of concrete problems at this level imo. gives you a good base of knowledge to abstract from.


>it's a bit frustrating
everything is frustrating at the start.
Also technical books, math books, that kind, don't just take two weeks to read.
I read technical books all the time and after a couple pages I feel drained so I have to put it down for a few minutes. Maybe it's just me, but technical books are still not light reading


I know, but i have a lot of free time and i'm really behind on math for comp sci courses. I always make sure i understand the concepts before moving to the next one.
It's just that there's a lot to learn and not that much time.


You do well in goig throuh the excercises, but don't sweat it. Here's a pro tip: you'll likely not use any algebra in compsci. Only the most elementary at best.
I hope your book has a chapter on boolean logic because that you're going to use.
Anyway the mahy stuff you'll learn will be somewhat self contained, that is to say the particular techniques you'll be able to figure them out doing them wihout much background knowledge.


Oh i just started learning because i got stuck in an exercise. I'm following MIT's open course online, in the second exercise they talk about derivatives, and i felt like i'd be missing out if i didn't fully understand what derivatives are and how to solve them.


>Here's a pro tip: you'll likely not use any algebra in compsci.
Uh, no offence, are you serious? You're gonna need algebra a lot, linear more so than abstract, but it really depends on what you're gonna do. If you work with graphics, space transformations, polynomials and numerical methods, you'll need a lot of linear algebra. If you do cryptography, numerical stuff, perhaps even languages, you will need abstract algebra to some extent.


well, he said compsci, and for what I know about compsci, is not so much specific applications such as 3d rendering and cryptography. Afaik "CompSci" is mostly decidability, reasoning about programs, lambda calculus, the turing machine, etc.

now if you're going to actually work through integrals then yeah, catch up


I really suck at math but desperately need to boost it on fundamental level of understanding in order to crunch out my masters in CS. I'm talking about "prove that this is valid" type of things. If you kind people could give me some layman book to really understand math I'd greatly appreciate it. Yes, I have solid fundamentals, but this kind of thing they require is mind bender stuff. I just can't adjust my mind to it and feel like a damn failure.


File: 1471995900838.png (6.73 MB, 200x200, [Serge_Lang]_Basic_Mathematics(BookZZ.org).pdf)

You can also check out 8chan's /comp/ for a great list of books to learn proofs.


File: 1472030973238.png (1.35 MB, x, Antonella Cupillari-The Nuts and Bolts of Proofs, 3rd Edition (An Introduction to Mathematical Proofs)-Academic Press (2005).djvu)

I'm in a similar position and really like this book so far.


For 4 months I've dedicated about 4~5 hours each day to that book, trying to do ALL of it.

Haven't read the last 2 chapters and still missing a few exercises here and there, but decided to put the book aside and move on to other math stuff - will come back to it if I need to refresh my memory or learn something I left behind.

Don't expect to go through that or any other math book like you go through some novel. It takes a lot of effort.

Like other suggested, go through what is actually of your interest.


I see, thanks, i'll skip the exercises earlier then.


Don't, unless you do them effortlessly. If you have any problem at all, you should practice.


File: 1472225653253.png (26.56 KB, 128x200, 41ZJauE46ZL._SX317_BO1,204,203,200_.jpg)

I have this book, is it worth going over or should i start with something else?


it's not a substitute for a textbook but for the material that it has and the level that it teaches at, it is definitely worth the read.

i'm a big fan of broad survey style texts (and papers) like this because the majority of mathematical material tends to be the opposite, tightly focused and lacking a global overview.

another book in a similar vein that is a more philopsophical and more algebraic is MacLane's "Mathematics: Form and Function"


For what I saw (I skimmed it just now) I can say that if you want to learn how to actually *do* mathematics, pick something else.
The book shows each area of mathematics as to how it was developed, what it is about, and the principles behind each discovery. It's pretty good for casual reading, that is, if you just want to know what the beauty of math is without actually engaging in it.
It leaves out the actual practice and procedure, and the actual discovery process.
Depending on what area of math you want to learn, I'd suggest either "Basic math" shared earlier in this thread, or, if you're ready for calculus, Spivak's Calculus.
I also suggeest Concrete Mathematics by Knuth et al. Particularly for those who want to learn math under the topic of programming and computer science


File: 1472254005838.png (20.72 MB, 200x200, Michael Spivak - Calculus.pdf)

Spivak's Calculus is a great book. Really rigorous but doesn't just pile things on like so many others. Plus the exercizes are 10/10.



Good post about precalculus, if anyone is interested.


I'd like to put up a few comments on the relevance of different mathematical concepts to tech. My background: I did a mathematics degree and now work as a dev.

Calculus / Differential Equations - You will never use this again unless you do computer graphics. I wish I could have taken back the 3 years of courses I did on this and instead learnt Japanese or Russian.

Linear Algebra - More useful than calculus, again useful in computer graphics. Haven't used in my work.

Any discrete mathematics or graph theory - Really useful and I've used concepts from this. Would highly recommend.

Algebra, Cryptogaphy - Enjoyed these courses. Haven't fully used the concepts but they help with my understand of security.


>Calculus / Differential Equations
Seriously? I'm studying pre calculus only to do these, since they're part of the MIT curriculum. I won't be doing 3 years but it will surely take me a month or two.

I'll take a look at the first classes and then decide, but haven't you used this knowledge even outside of computer science?


anything with physics is really heavy on calculus and diff eqs.


Yeah calculus is for physics and engineering. Those areas have co-opted the entire 1st year university mathematics curiculum which sucks. It would have been better to learn about proofs and abstract reasoning initially with discrete math taking a far bigger role.


>I wish I could have taken back the 3 years of courses I did on this and instead learnt Japanese or Russian.
Are you sure about that? Did you really learn nothing in these courses? It doesn't matter if (you think) you use what you learn, what matters is that you gain knowledge in the first place, which contributes to your mathematical maturity in general.


I wish I paid more attention in my Mathematical Logic course at university but damn that shit was boring at the time lol


>instead learnt Japanese or Russian.
Both of which are nearly useless unless you go to thse countries.


Well, you can catch MIT'S logic and logic 2 if you want.


Am i wrong in the assumption that calculus/differential equations are situational enough to be optional in computer science? Considering a self taught curriculum, of course.
From what i've gathered so far (and i'm still reviewing fundamentals of mathematics, so i can't actually go in and study calculus to create an opinion) it's in there mostly to give you the option to pursue computer vision/computer graphics route, correct?
Considering neither of those things interest me as a self taught student, i could just skip it entirely and not lose understanding of the field as a whole, and just learn it in the future if i ever need to. Right? For example, if i lean discrete math, i won't be at a loss if i didn't previously know calculus and differential equations.


Yes and no.
It has very, very few direct applications in CS, this is true. Computers are pretty much unable to reason analytically, outside of dedicated software for that purpose, they are inherently numerical.

However in Calulus you will learn a lot about symbol manipulation and proofs. These can be useful for every other math subject (not CS subject though).
Also consider that particularly advanced math is very interconnected: It is not rare to use the methods of calculus on problems of stochastics (Ito-calculus) or linear algebra.


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Very informative. I'm studying CS and made the same experience: Calculus and Differential Equations were taught a bit in the beginning but never used again. However, I really like these areas. Integrals and real numbers etc. are really cool. I think I will check out Computer Graphics and maybe CAD. Just have to work on my physics skills. (pic not releated, too basic)

I liked mathematical logic at university. Some topics were hard to grasp but really rewarding at the end. But I don't know if you really use some of the advanced concepts in CS… Maybe if you do formal software verification? Is this useful? At the moment is seems to me that basic knowledge in logic is sufficient.


Oh don't worry, i don't plan on never learning calculus. I'll just focus on basic mathematics, programming and then college mathematics.

Otherwise i'll be extremely frustated, if i go the usual route (fundamentals, calculus, physics, differential and only then some programming). Thanks a lot for your input though.


so apparently my uni has snuck a maths module on me, shouldn't be too bad I don't think. I'm just a downy networking student, so it will probably be dumbed-down enough for those of us who can only count to 255. But hey at least it isn't another web-dev / design.

only problem is I have done basically no maths since high school and I was a lazy shit back then. hopefully I can power through with my new found mildly obsessive work ethic.


a mildly obsessive work ethic is key for learning math. You'll be fine.


>Calculus / Differential Equations - You will never use this again unless you do computer graphics. I wish I could have taken back the 3 years of courses I did on this and instead learnt Japanese or Russian.
...but if you ever want to learn science you're going to need these.


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Thanks for the tip but I am well beyond the content of those courses.

>But I don't know if you really use some of the advanced concepts in CS
the upsurge of interest in functional programming and type theory over the past few years is built on logic from the 1930s and the consequences of Curry-Howard in the 70s/80s.

If anyone is interested in getting their logic up to scratch then Peter Smith's site http://www.logicmatters.net/ would be my goto.

Also picked up this old ass book from a secondhand sale.


APL is a beautiful language.
Sadly it's hard to use it at all, mostly because there is not much support for it. There is dyalog, which is closed source, and there is GNU APL but not many OSes port it (eg. none of the BSDs do afaik)
Anyway I did write an XCompose file if you want it, for getting the APL symbols directly from your keyboard (assuming you're using a us layout) just the way you'd do it in a normal APL keyboard, with the aid of a compose key.
If you want it I can gib


I'm finishing up on high school mathematics and i always have a problem with the way things are explained, for example, i learned about square roots and how to simplify and solve them, but the book/video/source didn't bother telling my why is that square roots exist, so i have to do a research that costs me a ton of time just to find out that they are used to measure the area of squares. Is there any resource that you guys know of where i can learn mathematics with a little more depth to each subject? Where not only the subject is explained, but the logical reason behind it is also given to you.

I apologize if i wasn't clear enough, english isn't my native language.



Dyalog is open source


I didn't really look into it, I thought by the licensing terms that it'd be closed source. Thanks for clarifying


I think they changed it recently (~6 months tops), but I only knew about it because it appeared on HN.



I don't think you will find a single resource that will give you those things, however, if you are a little more specific on what you want to learn, people might be able to give you some hints on what might be a good book or not.

That said, if you are learning those things on your own with no set schedule, take it easy and take whatever time you need - this is not a race.

And about square roots - I wouldn't say that they exist because we need them to compute whatever it is; it's just a number like any other, it does not have a reason of it's own to exists, it's just an abstraction created by people who study mathematics to focus on some interactions, e.g, given two sides of a right triangle, what is the length of the hypothenuse?


Check out The Princeton Companion to Mathematics. It's not a learning resource per se, but it contains pretty much all of mathematics with pointers to further resources.


Dyalog has allowed people to download free versions of the Dyalog APL software, which bothers you with reminders at random intervals and has other restrictions, but it hasn't been made Free Software.

I've made an APL thread so we don't consume the math thread: >>18314


How do you guys have time for programming and math? How should I spend more effective? I mean there is no much time after uni, how do you have time also for math?


im one week into studying math at cool leg
i feel dumb but i will do my best!


I allocate a couple hours to study math once every few days. I also frequent r/math, which is a pretty good resource.


well, how much time do you spend on programming every day?


barely any


File: 1473717807538.png (3.7 MB, 200x200, tmp_15806-kategori-1171074581.pdf)

Conceptual mathematics
It's about categories, very accesible


Are there any prerequisites to starting Spivak's Calculus?


Basic algebra and resilience


He says that anyone who knows how to operate numbers can read his book.
That aside, you really need resilience. It isn't easy, it asks you to think. That is, it is a good book.


Could somebody give some advice on knowing when you're correct in answering a problem?

The highest maths I've done is undergrad Calculus and Discrete, so very rudimentary. As a result, my self-confidence in my answers is practically 0.


File: 1473891643840.png (4.56 KB, 200x111, dumb.png)

i just posted this in /sci/ on 4chan, but maybe i think i'd probably have better luck asking here

-a sheep is eaten by any wolf that is closest to it
-if there are multiple wolves that are the same distance from a sheep, they do not eat the sheep

find an arrangement of infinitely many wolves in which there is no safe place for sheep

is there a certain name/principle that this puzzle is based off of? the only solutions i've been able to find used circles and i can't think of another way to go about it cleanly

i was trying to do something like pic related (which i remembered to post this time), but each time you eliminate one safe location like 30 more appear

let me know if anything about the question is ambiguous


hmmmm... it feels like the answer would be that there's no solution, but I think there are topological structures that fulfill those requirements. That's beyond my knowledge.

if you've done discrete you probably know how to do proofs and how to check them. Do that.


what about placing the wolves along y=0
Then a sheep's location is an ordered pair (a,b) and there is one wolf who is closer than every other wolf, namely the wolf at (0,b)


you should stipulate some maximum distance the wolves are lethal within (to bring out a metric/separation axiom argument), that there be countably many of them, and some sort of condition on wolves being on the same spot as a sheep. even then it's straightforward.


I suggest that you learn by reading good math books rather than Khan.
I used to see his lectures and they bore me out of my mind.
Besides the only way to really learn maths is to think maths, to wonder about the problems and try to solve them yourself. No hand holding.
For starters try Spivak's Calculus, it's dense but good. (also it covers the necessary prereqs)


Don't skip the exercises unless you're sure you can write them out. And even then..
You can try spaced repetition. i.e.
Leave some of the first exercises behind, but continue working through them after some time. This technique helps your brain remember stuff more easily.


>Calculus / Differential Equations - You will never use this again unless you do computer graphics.
Eh.. i'm iffy on this assertion. Machine learning uses some calculus.. sure, you don't need to understand the inner workings of calculus to derive a function..
but it's better if you do.



Yeah.. any linear arrangement of wolves makes for no safe spaces.
The projection of the sheep onto the line points out the wolf that will eat it.



Now that I think about it, there are infinite solutions, whether the wolves are uncountable or not. The assertion "if a and b are numbers and a > b, then (a-b)/2 is also a number" works for both the rationals and the reals, and (a-b)/2 is the only safe space between two wolves. From there you just need to fill space with the number line in whatever way you want and you've got a solution.

Also, I'm assuming

>-if there are multiple wolves that are the same distance from a sheep, they do not eat the sheep

really means

>-if there are multiple wolves that are the least distance from a sheep, they do not eat the sheep

because otherwise there would be no solutions, since there would be infinitely many wolves equidistant from each sheep.


There is no solution
Let's assume a solution where an infinite number of wolves are discretely scattered in the plane; take the least distance between two wolves on that plane, that is, take the two wolves that are closest to each other. Right in the mid point between both wolves a sheep would be 'safe' unless there is a third wolf that's closer (to the sheep) than the other two, while being further from each other wolf than they are from each other; if wolf 3 were to be closer to either of the wolves than they are from each other, wolves 1 and 2 wouldn't be the closest ones in the set.
Refer to pic related, the inner circle is the area where the third wolf should be to be close enough to eat the sheep, while the outer circle is the area where any other wolf would be closer to wolf 2 than wolf 1 is.

there's an infinite number of "safe sheep" in that scenario, namely, for any two points (0, b) and (0, b+1) where there are wolves, the line that satisfies (x, b+0.5) where x is any Real number.

Thanks for the challenge


File: 1473962888338.png (50.19 KB, 200x90, geogebra-export.png)

sorry, forgot the pic


Forgot to mention, one of the requirements is that there are infinitely many wolves.
If there could be a finite number of wolves, then there is a solution and it's trivial: there is only one wolf


This isn't correct
There's no reason to assume the wolves are discretely placed, you didn't prove there's no solution when they are continuous, such as on a line
To address your second point, all sheep on the line (x, b+.5) are not safe, because there is a unique wolf that is nearer than any other wolf, namely the wolf at (0,b+0.5)

This is based on the assumption that if there are 2 wolves that are the same distance from a sheep, but a unique wolf that is closer than the other two, the sheep will be eaten. The original question Is ambiguous in this sense


We have infinite wolves, so we can say "every midpoint between two wolves is also a wolf", which is true no matter what kind of infinity we're talking about(as shown in >>18736)


You also need calculus and differential equations in Economics, Finance and Statistics.

If you are trying to implement some non-standard model you are going to at the very least have a working knowledge of matrix calculus.


Right. For some reason I discarded continuum altogether. But if "wolves" can be placed continuously then there is an infinite number of solutions.
I totally overlooked this, nice one!


Woah chummer, a significant part of the Internet is in Russian, it's the biggest language after English. And a lot of quite interesting sites are in Russian.

Also, Russian is useful in most of the ex-USSR, not just Russia. Additionally, case languages are interesting and have interesting effects on thought-patterns.


Biggest language after english is mandarin, followed by hindu and spanish.



or maybe wolfman should read a topology text with some discussion on cardinal/transfinite numbers.


infinitesmals aren't real numbers, and I was *assuming* we're talking about the real plane. I mean, we could get all fancy and say we're talking about the hyperreal or the surreal plane, but that's outside the scope of the question.

The proof is simple enough in the real plane. Leave it at that.


get a load of this loser who doesn't learn stuff for fun


keep the flames to a minimum thanks


How about placing a wolf at every point on the plane? Then any sheep at (x,y) is eaten by the unique wolf at (x,y).


That's pretty much the answer.


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Hey there fellow lain-maths, university level math has finally ignited my interest in math, however I was one of the worst math students in school. Therefore my math fundamentals are almost nonexistent. I got problems when basic stuff like transposing/simplifying equations and such comes up since I lack the tools (and practice) to deal with them.

At which topics should I look? Can you recommend books that come with exercises AND solutions?
Also any tips on how I could combine the learning of math basics with programming? I'm glad for any help you can provide me.


This was similar for me two years ago. If you really lack practice I recommend Khanacademy. It isn't for learning proofs, sure. It isn't for deeper understanding of concepts either. But there are a lot of interactive problems to practice. It's nice for refreshing the fundamentals.

I did this a few weeks until I had a sound grasp of the basics.

Then I concentrated on the problems from university. (Also bought Spivak's Calculus but still haven't finished it because our curriculum is quite rigorous.)

Personally I would not to combine maths with programming at first. It's too easy to get distracted from the problem at hand and to play around with computational instead of mathematical problems. What I did sometimes was to plot some functions or I let the computer do some symbolic integrals. But later the problems got too abstract and trying to understand the bare definitions and proofs was more beneficial for me.


here's what you do, every day you should take 2hrs in the evening and crunch through the chapters and exercises in either a 1st year calculus text or a 1st year discrete math text.

Any text that has solutions is fine.

Just remember, the only thing that you need to do is focus



Thanks already for the tips, practicing through Khan Academy right now.

Any tips on the "workflow" while self studying math? Especially while working with a textbook.


What I did for Spivak is, I'd read the chapter fully(taking notes usually), then do the first few problems which are generally repetition-based practice, then I would skip down to the last few problems which are generally harder and more broad. I'd work through a chapter in about 3-4 days that way.


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Can someone lain help me? I was doing lang's book, and all of a sudden in 3 chapter he gave this problem, and now I am stuck.


I'll give you the answer for the first part.

a == b (mod 5)     <==>     EXISTS j. (a - b) = 5j          by definition of congruence.
x == y (mod 5) <==> EXISTS k. (x - y) = 5k by definition of congruence.

Now on with the proof:

a + x == b + y (mod 5)     <==>     EXISTS n. (a + x - b - y) = 5n          by definition of congruence.

So that statement is true if and only if there actually is such an n. Let's rearrange it a little:

EXISTS n. (a + x - b - y) = 5n
EXISTS n. (a - b) + (x - y) = 5n

But wait! We already know what those two things are!

EXISTS n. (a - b) + x - y) = 5n
EXISTS n. 5j + 5k = 5n
EXISTS n. j + k = n

The sum of two integers definitely exists, so n exists. QED.


Okay I'm not going to give you the solution. (btw can you give me the title and author of book? looks good), I'll just throw a hint.
Some notation: a|b means 'a divides b', so 5 | a-b would mean '5 divides a minus b' or 'a-b is divisible by 5'.
The hint: revise the next theorem: if a|k and b|k then a+b|k. Look at the proof for it


fuarrrk a second too late


Just a nitpick, your first two equivalences should be like
a == b (mod 5) <==> 5 | a - b              by def. of ==
<==> exists j. a - b = 5j by def. of |


Ok, seems like I did the proof.
# We got a == b mod 5;
# As far as I know, we can represent a as a 5q1+r1, where r1 is b, and if we substract b from a, we got something divisible by 5*q1, where q1 is positive integer such as "n>=1"
# same with x==y mod 5, x --> 5q2+r2 // r2 is y
# if we take our problem, we and substitution,
we got (5q1+r1) + (5q2+r2) == (r1+r2) mod 5
# know if we are substracting first from one, we
should got something divisible by 5, without remainder.
# (5q1+r1)+(5q2+r2)-(r1+r2) = 5q1+r1+5q1+r2-r1-r2 = 5q1+5q2 = 5 * (q1 + q2), or we can say 5 * k, where k is (q1+q2), and this one should be divisible by 5, 'coz we multiple integer by 5.
Is my proof true?

>can you give me the title and author of book?

sure, http://w1r3.net/QjZgHM.pdf


Ya you got it.
However a proof is a rhetoric argument and should be more readable, maybe on paper it is easier to follow, just s/r1/b/ and s/r2/y/ no need for extra symbols to obscure he meaning; it is right though.

I didn't know that book had Number Theory, that is neat!


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Hey /lam/,
Not sure if this belongs here, but whatever
We have a slack group that mainly talks about math, though chemistry, philosophy, japanese and programming are discussed from time to time. Anything academic is welcome however. Past projects include Logic I & II and Galois Theory.
If you're interested, then leave your email here (making a fake one is recommended, needed only for an activation) and and invite will be sent.
>inb4 slack
discord is gay




sent :')



sent :')


>cognitive science in the same channel as programming and cs
i like math tho, i'll give your slack a shot




Biology/medicine included?


It's allowed, since pretty much anything goes.
Don't expect much discussion though, since I don't think we have anyone specialized in bio.


It's cool. I'm into technology and programming too. I don't really consider myself good at math but I like being around those who are and talking about it.



That sounds fun, I'd love to join.



Any pdfs on the mathematics/mechanics behind cryptography?
I don't entirely understand how it works.


File: 1475675616402.png (12.84 MB, 200x200, W. Chen - Discrete Mathematics.pdf)

sent :')
chapter 12 in pdf related


Any PDFs that teach how to compose a mathematical proof?

I want to modify/extend an algorithm from some computer science paper but I don't know where to start.


File: 1475684507814.png (1.35 MB, 200x200, BookOfProof.pdf)


fuarrrkin' eh, why not


no thanks


sent :')


I'd like to get in on some of that action.


can I join up



I allowed this to stay, but now it's consuming too much of this thread, so now stop.


will do, is it alright if we made our own thread?



make one in >>>/cult/ or >>>/q/ link it in this thread imo


or >>>/sci/ for that matter, where this thread really should be now.




OP here. I fully agree.




I'm actually seeding >>18089


Thank you for this post I really enjoyed this book!


I graduated CS and did well in my math courses, but I don't think I really paid attention or cared enough and I feel like I don't remember anything except for the linear algebra I use in graphics programming.

Can I re-teach myself math from the beginning by working through books/textbooks and solving exercises? Is this realistic? I would also like to go past where my university curriculum ended off, which was basically Calc III.


1. Why, if you already learned it and forgot it, do you want to learn it again only to forget it, again?
If it is because you somehow think you'll use it even though you haven't at all used it... well there's your answer.
2. Learning it all over again can be very tedious, elementary math books are long, and filled with drill excercises and explanations on all kinds of stuff you already know. I've tried re-learning again starting from calculus and I get tired of reading what's a function, what's a graph of a function, what's a polynomial, what's a linear transformation, etc. Imagine learning a new (programming) langauge and again reading "what's a variable, what's a routine, what's source code, the difference between compiled and interpreted languages".
What I mean is you need not learn what you already know. You just need only skim and remember what's useful to you. Moreover, if you re-read calculus but you have no use for it, then you'll not only forget about it again, but you won't be motivated to read through it in the first place.
3. The current math curriculum is very strange: it is aimed towards physics and engineering majors for the most part. Calculus is mostly useful just for that, particularly the "how to compute integrals for such and such" aspect of it, so highly emphasized. However, there are a lot of branches to math that are worthwhile, especially now that you already know the semantics of calculus.
There are all sorts of branches of interest, and it is not a linear path where you strictly learn one subject after the next. Look at Number Theory, Graph Theory (if you haven't already), Group/Ring/Module/Lattice theory, Real/Complex analysis, Topology (it is a natural progression to Analysis but also to Graph theory and Group theory), Number theory, Category Theory...
I believe they are all worthwhile and very interesting subjects and you need not waste your time going over the details of basic boilerplate to appreciate them in their beauty.
If I may suggest good books on the foundations of mathematics: Enderton's Elements of Set Theory, and Spivak's Calculus.


Then again, if you really want to go all over the basics again, starting from basic single variable algebra, >>18163



1. I feel like there's areas of my work where the knowledge would be very useful. Right now I just usually find workarounds to my lack of math knowledge.

2. You're right, and if I read something that I already know then I will just skim over it and refresh my memory. I'm more interested in going back for the things that I really truly completely forget.

3. Yeah, I don't see how calculus would be extremely useful for me. I would be interested in discrete mathematics and the areas you have listed here.

Thanks for your posts! Really useful.


IMO graph theory(and by extension, topology) is something that all CS people should have at least a passing knowledge of. It can be applicable in surprising situations.


don't bother it isn't worth the time. (re-)learn it as you need it. if you really want a solid base then discrete mathematics (as you saw it in college) along with whatever you picked up in your algorithms course(s) will do in almost all cases.

please don't make posts telling CS grads to gain an undergraduate mathematics education that they will likely never make use of.


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have to a basic maths module at uni. People still trying to have "why do we need working" arguments with the lecturer. I assumed people would have got the fuarrrking message at this point but apparently not.

Also people were struggling with basic linear equation rearranging and we have to do a group work without getting to pick the groups so this has the potential to be ... fun.


>Calculus / Differential Equations - You will never use this again unless you do computer graphics. I wish I could have taken back the 3 years of courses I did on this and instead learnt Japanese or Russian.

Really? Seems to me that if you're trying to make anything that actually applies to reality, these things tend to come up quite often. Even making a simple motion controller, or playing around with PWM servos, it really helps to understand that velocity is the derivative of position, and what that means, conceptually.


>it has been difficult-if not impossible-to find a single reference book that effectively covers the subject.

Best catch-all book I found is 'Discrete Mathematics' 4th ed, Ross & Wright. It covers most concepts one would find on an undergraduate course in satisfactory detail. It is pretty weak on graph theory, mind.


It'll depend on your country, but here in the UK most universities have to have policies by which you can ask to be marked individually following group work. Ensure everything you contribute is recorded somewhere as being your addition to the project, and if soykaf hits the fan play the individual marking card.

I had 3 African migrants in my group for an intro to program design class. We had to create flow diagrams for different aspects of an automatic road barrier. They did nothing, I kept a record of what I did, asked to be marked individually, instant B+ and they got Ds.

Group work can really fuarrrk over your degree if you don't stand up for your own contributions. Good luck.


UK and I wasn't aware of that, thanks for the tip friend.


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Does anyone have any good resources on multi-path routing?

I have a decent understanding of graph theory and basic routing algorithms, but I'd like to expand specifically into multi-path for post-graduate research.