/sci/ - Science & Math

>>12312643
What does the image have to do with the text?

>>12312643
Are you perchance a fifth grader?

>>12312903
And if yes, are you male or female

>>12312643
kek modular arithmetic can hardly be considered CS only. FLT is pure math.

>>12312643
[Everyone liked that]

This one of those times where 4chan fucks up and switches images, right?

>>12312643
are you talking about the cursive L in FLT?
that's actually genius. OP is tarded

>>12312643
jokes on you dude, computer scientists literally use the same notation as mathematicians, especially theoretical computer scientists

>>12312911
It doesnt matter, the holes are tight

>>12312643
OP's pic is a bad example. pic related is a simpler example of math language going full retard: If Q=0 then it can't be a function of x.

>>12315026
Their style of writing is very different. It's more practical. (even theoretical computer scientists)

>>12315039
...no, it isn't, by in large it's the same.
http://www.dcs.ed.ac.uk/home/mrj/ETHbook/chap6.ps
You're telling me this is "more practical" as far as exposition?

>>12312643
>>12315039
My favorite thing in the world is when people say computer scientists study strictly more practical things, or that they don't believe in <continuous math> because <my favorite crank said it was bad and it's not real>. Neither of these things are true.
Even in something like this:
http://web.cs.elte.hu/~lovasz/bookxx/hombook-almost.final.pdf

You find that as CS has matured, there's been a multitude of interesting math from all subfields, and in particular, physics and CS's *theoretical* intersection has been studied extensively in the last decade.

>>12312643
The joke is that programming languages are transparent, consistent, and deliberate in a way that mathematical notation never will be.

>>12315073
>by in large it's the same
that's just a round-about way of admitting that they are different. No I'm not opening your postscript file.

>>12315090
wat
language design is a great topic, but math is hardly uniformly poorly written. the de facto most popular entry level language python, is written around the idea of minimal translation between mathematics and code

>>12315094
>they're the same almost everywhere
>>that's just a round-about way of admitting that they are different.
are you fucking dumb? If you read anything from algebraic complexity, graph isomorphism, the latest algorithms papers from STOC and FOCS, etc etc., you will find that the notation of the papers is almost exactly as you would find in a mathematics and physics paper. The only exceptions are systems and applications researchers, both of which may have dramatically less math and more empirical data in their papers, and what math they do have is nonstandard notation.

>>12315085
>people say computer scientists study strictly more practical things
Who said this?

Also the example you posted supports my point. Most equivalent math texts have far fewer diagrams, usually none at all. The author clearly knows the fastest route to helping the reader understand what he's explaining. It isn't just 100 pages of symbol manipulation.

>>12315099
I said they are more practical. You purposefully misinterpreted that as meaning they are always more practical, so that you could sperg out apparently.

>>12315095
You're talking out your ass. Python was not "written around the idea of minimal translation between mathematics and code". That sounds like an advertising blurb for Fortran. The phrase "de facto most popular" is completely meaningless.

>>12315107
>I said they are more practical.
They are not necessarily more practical LMAO.
>>12315110
the fuck are you on about? Why do you think python sells itself as one of the most popular number crunching and scientific computation tools out there? Why do you think there's been so many research into mathematical methods with python? The only use Matlab has as such a tool is simulink for engineering, but python is generally made
1) it's easy to translate between the calculations and theory into code
2) it's easy for beginners to do anything without having to know anything about how computer code actually works, aside from a few organizational
tools.
>"de facto most popular" is completely meaningless.
would you like me to say "literally the most popular intro language, among the most widely used aside from java in industry?"

>>12315103
> Most equivalent math texts have far fewer diagrams, usually none at all.
The fuck are you on about? Yeah, if you're reading baby Rudin, this is true, but every topology text worth its salt, every graph theory book worth its salt, etc., has a multitude of diagrams. There are so many graduate level textbooks in math and papers that use diagrams. Fucking category theory was made so people could do mathematics on diagrams
>t isn't just 100 pages of symbol manipulation.
Ah, the classic "I've never read a paper in math in my life"
Cry more, especially when there are literal 100 page papers in CS about symbol manipulation.

>>12315137
Listen retard, the point is that the notational rigor of mathematics is considerably less than software. The fact that a popular language can be used for math doesn't suddenly make this less true. The ease that math can be expressed in the programming language doesn't matter. Your hallucinated Python history wouldn't matter even if it was true.

>>12315154
>Listen retard, the point is that the notational rigor of mathematics is considerably less than software.
This doesn't mean anything. I agree that there's generally less abuse of notation, but if you've done any serious mathematics, you know that being "heavy" on notation doesn't mean that your notation is bad.
>The fact that a popular language can be used for math doesn't suddenly make this less true.
*a popular language made its entire evaluation scheme and syntax structure around mathematical application
It's not even about the ease that math can be expressed in programming languages. It's that these languages are made to express specific classes of ideas in specific ways, which is where you get different paradigms. On the other hand, math is a collection of topics with different notation, and it's largely fine but inconsistent between authors - but any good authors take pains to define all terms clearly.

Here, you are trying to differentiate between programming languages and mathematical language, but these aren't objects with meaningful comparison by their very nature. You're honestly protesting the author's quality here - it's entirely possible to make unreadable code with a good language, and unreadable mathematics with a good notation.

>>12315170
>You're honestly protesting the author's quality here - it's entirely possible to make unreadable code with a good language, and unreadable mathematics with a good notation.
No, I'm not protesting the author's quality because readability is not the issue here. In a programming language with a formal specification you can know if your code is internally consistent or not. There is no equivalent for math notation. This is why tools like Coq exist: to provide the rigor of programming languages to math notation.

>>12315137
>Why do you think python sells itself as one of the most popular number crunching and scientific computation tools out there? Why do you think there's been so many research into mathematical methods with python?
Because Python has a bunch of libraries, is free, and is easy.

>>12315190
>There is no equivalent for math notation. This is why tools like Coq exist: to provide the rigor of programming languages to math notation.
There is a need for such an implementation, but as far as math that is internally consistent, this is why homotopy type theory was created. This was literally the intent behind it.
Compilers are good, I'm not contesting that. I'm contesting this claim that programming languages are immediately clearer or that they have better notation. Because, as I'm sure you're aware, the reason why Coq and HoTT exist is to make judgements on the semantic value of a proof - the syntactic value is something that's up to taste and clarity, and it's the subject of this discussion.

>>12315209
>programming languages are immediately clearer or that they have better notation
Mathematical notation is often clearer than source code, but the former can be arbitrary as long as the reader understands. This is not rigor.

>Because, as I'm sure you're aware, the reason why Coq and HoTT exist is to make judgements on the semantic value of a proof - the syntactic value is something that's up to taste and clarity, and it's the subject of this discussion.
There's a difference between self-consistent semantics and self-consistent syntax. Modern mathematics succeeds at the former but fails at the latter. Coq can only make judgements on semantics because the syntax is well defined. The disconnect between formal semantics and formal syntax is extremely ironic.

>>12315209
>Coq and HoTT exist is to make judgements on the semantic value of a proof
Are you aware of Pollack inconsistency, comrade?

>>12315035

> assumes that x isn't a constant

>>12315209

> this is why homotopy type theory was created

Homotopy type theory is an application of type theory which has more to do with topology than mathematical logic. Coq really has nothing to do with homotopy type theory, and the book "Homotopy type theory" which is basically the most important text in the subject explicitly explains this.

>>12314923
>>12312893
>>12313725
OP here. It’s the F little l T smooth brains.

>>12315029

>>12312643
FlT

>>12315362
4chins converted my SCRIPT SMALL L (U+2113) to and ordinary l.

>>12315137
Using javascript to comment about python is pathatic.

>>12312643
wait a minute...
that beer's going to get warm
and OP doesn't make any sense anyway

>>12315308
>Homotopy type theory is an application of type theory which has more to do with topology than mathematical logic.
This isn't exactly true. Voevodsky's push to start studying HoTT started from his paper that was accepted into Annals despite there being a serious mistake that only he detected years later.
>has more to do with topology
I mean, that's what the 'homotopy' is there for, but if you've actually read the damn book, you'd know it's a complete foundations, and calls itself that for a reason.
>Coq has nothing to do with it
correct

>>12315291
It clearly isn't, but this elucidates the ambiguity. Q(x)=0 could be the formula for Q as a function of x, meaning Q is always 0 and the x is redundant, or it could be referring to those values of x at which Q is 0. Mathematicians make room for such ambiguity just so they can prune it. It's much more pleasant to read mathematics papers from 100 years ago because the way people thought was less constrained by all the formality that is necessary today. e.g. they immediately take for granted that they can step over trivial cases without having to point them out at every turn like insufferable faggots.

Can someone explain to me the difference between these things? I came across them while reading and kept a list of them because they all seemed to be more or less in the same family of ideas, possibly different fields using different jargon for the same thing.
>smooth transformation
>diffeomorphism
>h-cobordism
>homotopy
>mapping

Thank you in advance.

>>12316039
[math]

\delta \, \epsilon \left ( 0,1 \right ) \\
\displaystyle
\prod_{k=0}^{n} \left ( 1 + \delta ^{2^{k}} \right )
= (1+ \delta)(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
(1- \delta) \prod_{k=0}^{n} \left ( 1+ \delta ^{2^{k}} \right )
= (1- \delta)(1+ \delta)(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
= (1- \delta ^{2})(1+ \delta ^{2})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}}) \\
= (1- \delta ^{4})(1+ \delta ^{4}) \cdots (1+ \delta ^{2^{n-1}})(1+ \delta ^{2^{n}})
= (1- \delta ^{2^{n}})(1+ \delta ^{2^{n}}) = 1- \delta ^{2^{n+1}} \\
\\
\boxed{(\delta ^{2^n})^2 = \delta ^{2 \cdot 2^n}=\delta^{2^{n+1}}}
\\
\displaystyle
\prod_{k=0}^{n} \left ( 1+ \delta ^{2^{k}} \right )
= \dfrac{1- \delta^{2^{n+1}}}{1- \delta} \\
\displaystyle
\lim_{n \to \infty} \prod_{k=0}^{n} \left (1+ \delta ^{2^{k}} \right )
= \lim_{n \to \infty} \dfrac{1- \delta^{2^{n+1}}}{1- \delta} = \dfrac{1}{1- \delta}
[/math]

>>12315085
please kill yourself or go back and then kill yourself you absolute lunatic. This is a troll thread, how you can’t discern that these are CSniggers and undergrad mathfags flaming each other could only be explained by being extremely new or unbelievably gay and incompatible with image board culture you fucking faggot.

>>12316118
Neat trick there.

>>12316130
So report the thread then. Either way fuck off sperg

>>12316051

they are not even close to the same things.

>>12316221
Okay. Then prove you aren't just a larping retard and tell me how they are similar?

>>12315035
Sure it can
For every x input, output 0

>>12315197
>>12315137
Python is popular because it's easy and fast (to write) with heaps of good libraries. Honestly everyone should be using Python as a general-purpose tool that is trivial to learn. You don't need to know how to program. It's useful for everyone and anything.

>>12315035
You sound like you stopped at pre calc.

>>12312643
The problem here is not the notation.

>>12316130
>reeeeee stop ruining the fun I'm having being obtuse on purpose!
kill yourself

>>12312643
>computer scientists have better notation
>computer science isn't as complicated when it comes to notation
yeah try telling that to actual computer scientists