/sci/ - Science & Math

>mfw

>my sides when OP doesn't know what a differential form is

>Mfw I do this all the time in Kinetics.
>divide by differential
>solve ODE by forcibly integrating

>mfw I have no face

>>6068920
My ODEs TA does it and it drives me crazy

>my sides when a math graduate is surprised to discover he knows more about maths than somebody who is not a maths graduate

>>6068907
>physicists start grabbing differential terms and throwing dx around like a fucking multiplicative term
>mathematicians get all angry
>b-but you can't do that it doesn't work that way
>all math done with it works
>solves equations and provides advances and models
>years later mathematicians find out a proof of why it works
>complain anyway

how dare people use a stick to build a fence when they don't understand the internal structure of wood xylem!!!! I'm so much better than them!

>>6068923

>implying you need to be a math graduate to know those things

Why do so many people object to differential forms?
It seems like "hurr you can't separate dy and dx" is fundamentally no different from "hurr you can't take square roots of a negative number".

>>6068934
because they're insecure fucks that desperately search for ways they can attempt to be elitist

>my brain cells when a new wave of /r9k/ green text shitposting threads

>>6068929
>claiming I implied that
>when in fact I never even implied it in the first place
>constanza dot jay peg

>>6068934

I don't think people do really. Differential forms are amazing and should be taught instead of vector calculus. People complain about them being used without further explanation than "well, this you aren't really supposed to do this, but multiply by it anyways"

>implying the basis of OP's argument about differentials is not also the basis for the solution of separable PDEs that we all fucking learn in basic math class
>implying its not the basis of the solution of the most basic form of ODE that exists.


how is this thread still receiving replies? oh wait....

>>6068934
It's totally fine if you actually understand what you're doing. The vast majority of physics undergrads don't.

>>6068944
They're taught? I just walked into class one day and dy/dx was being rearranged as if it were regular division.

So you're telling me I should only solve differential equations by Laplace or Fourier transforms?

>>6068948
>differential equations
>real math
oh god my sides
algebraic number theory master race reporting in

>>6068946

>2013
>not using greentext properly

>>6068951

It's not usual, but many universities (hopefully?) should have some undergrad classes that teaches them.

>>6068949
lol, i'm a pseudoscience undergrad (econ) and we're learning differentials now.

>>6068951
> I just walked into class one day and dy/dx was being rearranged as if it were regular division.
sorry we don't do the extra steps every fucking time.

When we first learn dy/dx or when we re-learn it in an actual math class we do it properly.
At least I kinda remember getting slapped in one of my upper level engineering courses.

>>6068907
> implying that taking short cuts in math makes it so it's not math anymore.

>>6068964
My school obviously teaches this in an upper year differential forms class for math majors but I seriously doubt that more than 15 or so people take it every year.

I still to this day do not know what the fuck dy/dx is supposed to mean. When doing applied math I pretend they are numbers and do not think more. When doing pure math I never fucking touch that shit.

>>6068965
>my sides when you think it's not watered down to babby-level symbol-pushing

>>6068973

I learned about them on my freshman year and never really took a multivariable calc class.
That being said it was one of those so called super-freshmen courses and only math majors took it; not mentioning over half the class dropped in the first week.

mfw I took linear algebra at a CC in one semester then transferred to a university where they have it taught across three semesters from a textbook with less content.

I'm a first year math student. Even my family doesn't want to here about my work. I just want to share the joy. So lonely.

>>6068987
you get a hug for being honest, anon

you're a good person

>>6068987
Graduate or undergrad? If it's the latter, just wait. It only gets worse from here.

>>6068995
Undergrad.

>>6068996
Thanks Anon.

>>6068995
>>6068987
Although I should add, even though almost nobody understands what you do it isn't any less rewarding than if they did. You just have more stupid questions to put up with.

>>6068975
I don't think he said that you insecure math major.
Are you sad that no one respects you or your shit major?

>not doing quantum algebra

step it up /sci/

>>6069005
>implying I'm not working on a paper on locally compact quantum groups

>>6068987

>first year undergad

Really? A first year undergrad usually doesn't do anything most science/engineering majors could understand/need.

>>6069006
Yeah, a little. Thanks for understanding :)

>>6069005
>quantum algebra
>not string algebra
embarassing

>>6069007

wait...this is actually a thing? I was just making a joke.

>look it up
>https://en.wikipedia.org/wiki/Quantum_algebra
>mfw

Hello!

You calculus kiddies don't know shit about math.

Best!

>>6069025
I thought you were cool Best! man.
You are an elitist faggot too?

>>6069039
Hello!

Any faggot can copy his signature, you don't even need to guess a password to do it.

Also there's not a single interesting math thread on /sci/ so there's no reason he'd be here.

Best!

Recently just finished the finals in Basic Calculus.
Great Success

>>6069039
He has a couple imposters these days.

>>6068920
>>6068921
w-what are you meant to do?

>>6068907
>>my sides when an upper year engineering undergrad can't demonstrate that the sum of two continuous functions is continuous

they should care why?

>>my sides when a physics major treats dy/dx as a fraction without understanding the difference between real numbers and the extended real numbers

>Not know the difference between extended real numbers and nonstandard reals
>Not knowing the transfer principle makes them the same for doing math

>>my sides when they think they know anything about math

>Pre-babies first real analysis
>knowing shit about math

yeah your math knowledge is so impress

>>6069007
>not working on quantum lattices
>2013

>responding to this painfully obvious bait

>>6068907
>tells you you can't treat dy/dx as a fraction
>solves simple ODE's using separation of variables
>life

>>6069049
But his signature is so gay, I didn't think anyone would be autistic enough to copy it.

>>6068907
>1
To what degree? It's intuitively obvious that that statement is true. If the sum of two reals is always a real (unless I'm wrong about this, but two defined numbers being added should always result in another defined number), then the sum of two functions that have a real solution for all inputs would likewise be real since there would be a real sum for each respective x. How rigorously are you expecting some one to prove it?

>2
Why can't I do this? Where does it break down?

>3
>mwf they aren't math majors and use it as a tool instead of a dogma

>My sides when you type in lowercase

Stay pleb OP

>>6069192
>>6068907
At least neither of you are one of those pretentious fucks that put periods at the end of every greentext

>>6068907
1. why does it even need proving?
2. the dy/dx separation is a bit retarded, but works in some cases
3. Grow up

>>6069222
>1. why does it even need proving?
0/10 try harder next time

>>6068907
>use method of increments
>get the derivative as a fraction represented by delta x over delta y
hur dur

>>6069324
>What is infinity.
>What is division by 0.

If you grab any old calculus book like piskunov, goursat, rey pastor, etc. they all give a rigorous treatment of differentials. Of course you need the function to be differentiable, condition which is meet by hypothesis in most physics like mechanics. Fuck off you aspie, it's you who doesn't know maths.

>>6069333
Irrelevant.

>>6069342
Approximation leads to mathematical coincidence. It is the bane of mathematical progress and rigor.

>>6068955

> Differential equations
> not real math

Analyst here: you're retarded.

>>6069006

> Implying nobody respects Gauss, Hilbert, Banach, etc.

You must be some sort of uneducated pleb.

>>6069179

You don't even understand what continuity is. Holy shit, what a dumbass.

>>6069366
> implying I said anything about your hero worship

>>6069370
I'm not him, but I agree with him.
You can intuitively think about math instead of being stupidly rigorous.
Adding continuous functions makes perfect intuitive sense.
Multiplying not so much.
Division is right out.

>Complaining about numbers
>Perpetuating the decimal system.
>Being on /sci/ while not using this time to prove the superiority of the duodecimal system.

What a shitty math major you are. The one thing you faggots could provide for humanity and you're blowing it.

>>6069396

>stupidly rigurous

People who don't know about math shouldn't be talking about it.

>>6069405
or you could just stop being an elitist prick?

guess what. I'm an engineer. I use math. Surprised?
Proofs (in math at least) are a complete bore fest.
Continue to tell me all the ways that I don't use math.
I find it hilarious

Yep, /sci/ is the worst fucking board of all.

>>6069412

I'm not saying it out of "elitism". If we didn't care about "stupid rigour", we wouldn't have gotten very far. In fact many math revolutions have come just from people applying rigour to "intuitive" things (Weierstrass for example).
Or do you really think we would have gotten very far with an "intuitive" definition of continuity?

You're free to find it boring, I certainly find boring what engineers do, but I do find it useful. As you should feel about rigour.

>>6069429
you just figured it out? a board filled with angry, pretentious, dense, empiricist shit-heads?

>>6069441

That's not what makes /sci/ bad, many boards have worse people in them. The problem is that /sci/'s population is very small, at least on the other boards there are many more topics to choose from.

>>6069443
other boards have a greater variety of people, too
other small boards usually arent as shit as well.

>>6069439
I didn't say WE and neither did he.
People in this thread are complaining that engineers don't know how to do rigorous proofs.
Why the hell should they? Rigor is your department, not ours.

> In fact many math revolutions have come just from people applying rigour to "intuitive" things (Weierstrass for example).
This is exactly what I mean.
Why should engineers be the ones to start mathematical revolutions?
Do you seriously think your major is that useless that you need engineers to check your work?
I certainly don't. I'm perfectly happy letting others contradict my intuition while I'm building rocket ships. That's why are majors exist. It's because they are different.

>>6069445

Nobody asked them to. But at the very least, they should know the basis of the tools they use. Rigour in analysis was established a long time, I'm pretty sure they can handle the little extra effort and which will help them not depend on "intuition", which tends to fail horribly the minute you take it out of its repetitive setting.

>>6069441
>empiricist shit-heads

Back to /x/

>>6069449
You have no idea about engineering.

>>6069449
>Rigour in analysis

>doesn't realize that analysis is a seriously flawed field of mathematics, as explained by the great mathematician Norman Wildberger:

http://www.youtube.com/watch?v=Nnp4qZX9H1U

>>6069451

What is it that I don't know? Enlighten me.

Btw, so far I've only said that depending on intuition for math and rejecting stupid rigour is terrible. I'm pretty sure you wouldn't depend on "intuition" when designing something, would you?. Never did I say engineers should come with their own proofs or know as much math as I do.

>>6069455

Oh god, this again, I'm seriously not going to be turning this into such a thread, go troll people by making a new one. I might join if bored enough.

>>6069449
> they should know the basis of the tools they use.
we tend to do this in college.
Then we never use it again, so we completely forget.
I remember being told you couldn't just move the dy/dx around in calc 3. I have a vague idea on why this is true, but it works in the variety of differential equations that show up in dynamic situations.
I'm pretty sure it stops working when having multiple independent variables and I might have a vague idea on how to expand it in that case, but I'd always check a book instead of just assuming I had it properly memorized.
But should I know set theory? should I be able to construct all real numbers that I've been using since I was five?
No this isn't useful to us.

> the little extra effort
it's not exactly little you know?
memorizing all the little methods to get from nothing to useful equations is pretty difficult.
I'm happy enough knowing I can go from vague ideas about energy levels to an uncomplicated computer. But now I have to know how to construct a domain to talk about the number of charge carriers in some dope silicon?
I know the domain and range are positive because that just "makes sense" intuitively.

>>6069447
Visited the board twice in my life. You illustrate my point vividly.

>>6069460

Except you don't, most engineers I know (and I know plenty) take calc I-III, lin alg, diff eq, perhaps some random stuff like discrete math or if they need to use fourier series, complex variable.
I have been TA for calc I-II, diff eq and lin alg for engineers; you don't actually see much of what makes stuff work.

It is little extra effort, idk where you get this stuff about memorizing, it's not. Memorizing is what you do in all calcs. I can't understand how you manage to memorize all those methods of numerical and algebraic integration of idk how many special cases, or the div, curl, etc...

I seriously think some real analysis and set theory would help you. Not even constructing the real line. But knowing an actual definition of continuity and being able to construct a proof for the sum of continuous functions? Is that too much to ask?

>>6068907
>number of shits given that an engineering undergrad can't demonstrate that the sum of two continuous functions is continuous
... is it:
(a) none
(b) one
(c) two
(d) more than two

I just want to point out to all of you, that when you do anything but help each other further your understanding of science and mathematics, as well as the understanding OTHERS have of science and mathematics, you are only damaging and deterring the progress that can be made.

In other words:
Don't feed the fucking trolls.

>>6069472
> memorize all those methods of numerical and algebraic integration
You mean the ones we learned in our baby's first calc in high school?
I don't have them exactly memorized, I can just derive them from geometry. Rectangle areas are really easy to calculate.
All the other methods I already programmed three years ago. I will never go that low level again because I don't need to and if I did I'd just look at a book, not memorize it.
Div, curl, etc. I just treat as vector multiplication. Another thing that makes math majors butt clench.

> But knowing an actual definition of continuity
High school taught it well enough. There were three conditions, none of them difficult to comprehend.
As far as constructing the proof...I probably could, but I might get stuck somewhere.
I don't have discontinuous functions very often.
If my function was discontinuous I would know it way before I started looking at the actual function. It would show up in the physical modelling.

> Is that too much to ask?
Are you willing to learn how to design products for your customer base? To learn about aesthetics? To learn how to steal ideas from nature?
This isn't my job. This is what I did in school.
I have more important things to prove that rely on physical laws not mathematical ones.

>>6069472
I'll tell you what.
Sell me on learning set theory.
Show me a useful problem that can be solved your way.

My next math step was going to rape graph theory until I could optimize some pipe systems.
Sell me on the reason to do things the right way instead of just finding methods to optimize graphs.

>>6069370
I'm well aware of the definitions of continuity they teach you early on in calculus. I haven't taken any analysis courses, so I haven't broken it down past that point. I also didn't define what continuity was, I did generalize by saying that it was pretty much a function that is defined for all values on a given domain. In this case, it would be reals. Sure, the definition I provided wasn't correct to some asspained math major, but I really don't think that I need to specify the nuances unless I'm dealing with weird as fuck functions that have no bearing on real world application.

Please show me a continuous function that is not defined for all reals in the given domain. Also, please show me a function that is defined for all reals that is not continuous. That's what it takes to prove my statement wrong. Actually, in retrospect, the second one may exist. I'd imagine you'd give me a peace-wise function with a gap that you fill in with an arbitrary number. Or a step function like [x]. I should have specified that the two sided limit has to exist, but it's a fairly rare circumstance to encounter in reality.

>>6069495
Yeah, those, among other things like trig substitution for calc; or all divergence, Greene, Stokes for vector. You even said it's not an effort, which make my point stronger, what I'm telling you to learn requires less effort than that.

High school doesn't teach it well. Actually, a bit of real analysis and a bit of set theory and you actually have a much easier definition than anything used in calc for example.

I won't even answer your last point. You're the one using all this math without understanding it really. I'm telling you it's not hard to understand, it doesn't take much work, and it truly helps you. Idk why you keep trying to defend yourself.

I'm aware that I abused that word in this context by saying that all continuous functions had to be on the real line. So don't try to be clever and give me some weird ass function defined for some other set.

>>6069499

Let's not go to far, as I tell that other anon, or (maybe it's you too?). The definition using set theory simplifies things so much and opens very powerful but easy to use theorems.
Also, take probability, it's all about sets too.

And it's not getting very far into set theory that you can reap some pretty neat things. That's why I'm saying engineers could learn some without sacrifising time into stuff they do want.

>>6069502
> trig substitution
I hate integrating and have always hated integrating because of the memorization.
You have a way to just automatically know how to integrate all functions?
> Greene
I either have to look this up or I haven't covered it yet (can't remember if it was part of my next mathematics course)
> Stokes
Stokes did stuff besides screw over fluids?!?
Yeah I have no idea what this is.

> you actually have a much easier definition
but...I don't define mathematical things...ever.
It's only that OP was whining that we can't do proofs with continuity. We can. It's just not going to be rigorous because that's your job.

> You're the one using all this math without understanding it really
And you are defining it without knowing what it's used for.

If it's so easy, why isn't taught that way?

> Idk why you keep trying to defend yourself.
Am I?
I was under the impression I was trying to be convinced to sacrifice my time to learn something I will probably never use again.
If it was so easy, there'd be a simple way that doesn't just involve reading a textbook cover to cover. I have about 50 books already that I want to do that for. It's not easy getting motivated to do it.

>>6068986
Was it a university for people who see only curves?

>>6069509
> The definition using set theory simplifies things so much and opens very powerful but easy to use theorems.
Show me.

> take probability, it's all about sets too.
not the way I do probability

>>6069514

Those are all theorems for integrals in vector calculus. You definitely will learn them at some point.

I know it's not usual, but it's not impossible to find situation that doesn't fit the rigid standards of what you know, is it? People taking the standard approach would not be able to do anything, while someone with the basis could actually work it out. But if it's that strange as to not be useful... then I guess I was giving engineering too much credit.

Either way, I give up, all I'm saying is that the benefit is worth the little effort to learn this things.

>>6069518

On topological spaces (which R or R^n or many otehrs you don't work with are), a function is continuous iff the inverse image of an open set is open for every open set in the codomain. Much simpler than dealing with epsilons and deltas.

And yes it should appear in probability, even basic theorems are stated in terms of sets, aren't they?

>>6069520
(I was a graduate student in ME btw)

> People taking the standard approach would not be able to do anything, while someone with the basis could actually work it out
show meeeeee.
you were doing so well too.

> But if it's that strange as to not be useful... then I guess I was giving engineering too much credit
It's not that your definition won't be useful, it's that there's billions of other stuff more useful like graph theory, sturm-louiville, variations...the list is endless.
I have not encountered a problem (yet), where I would go, man I wish I knew some set theory.
pretty sure this more because I have little idea of what you do with set theory besides the dick waggery that goes around /sci/.

>>6069524

As I said, I give up. I'm too tired to keep this up, it's 5 am here and I don't care enough about this subject to keep it up at this time. If you don't want to put a little more effort into clearing up things you're using and will use that's your choice.

>>6069525
> put a little more effort
this is the problem I'm seeing
This isn't a little more effort.
If it is, show me how it's only a little more effort
From your definition in >>6069523 I have to look at definitions inside definitions.

>>6069523
I have no doubt that they appear.
but I do not use basic theorems when I'm doing probability.

I get you though on the sleepy thing. I have no idea why I'm still conscious. Sleep well helpful anon.

>>6068955

Hello!

What type of number theory? :)

Best!

>>6069499

Hello!

So, I actually had an extended discussion with a set theorist who passed their oral qualifying exam today (a giant hurdle towards getting their PhD). They tried to explain to me what the broad-strokes ideas of what set theory PhDs do. I have to admit, that while extremely interesting (the empirical observation that most extensions of axioms should come from some large cardinal axiom--and the existence of large cardinals is still conjectural) I didn't really see how it affected me. I would even go so far as to say that the research a modern PhD in set theorist would do is completely irrelevant to the vast majority of the questions that I'd ever consider/care about--even though it is undeniably, awesomely beautiful.

That's my two cents!

Best!

>>6069531

Last post and actually going to bed. The definition I gave just requires you to know what an open set is, you don't even need to conern yourself with the topology part (which isn't particularly hard, it's just a set where so called open and closed sets exist. Of course you will need to read those definitions and some properties of sets. I didn't claim it was effortless, but I did claim it is easy, and it in fact it. Check them out in wiki, the set theory part of the proof could be taught to middle schoolers without much trouble.

As for probability, you haven't even used stuff like P(A U B) = P(A) + P(B)? (if the events are mutually exclusive or something) There's set theory there.

But if you really want to know if it will be at least somewhat useful, we can do a little experiment:

Learn the set-theoretic definition of continuity and a couple of properties (union, intersection, empty set). Then try to prove OP's first point: Show that the sum of two continuous functions is continuous. Show it with the definition you know from calc and then show it with the new one. You'll see the difference (and that's without mentioning that the new proof will hold for any topological spaces, the old one only for R and with some tweaking R^n, but not more.)

Night.

>>6069552

Hello!

More technically, the sum of continuous functions is continuous holds when f,g:X-->A where X is a topological space, (A,+) is a topological group, and f,g are continuous functions.

Of course, this is more just a remark since I'm sure you meant continuous functions f,g:X--->R^n for some topological space X :)

Best!

My sides when 90% of genius "pure math" majors end up teaching community collage and are barely paying rent.

>>6069552
>inverse image
this is the part I'm stuck on so far.
open sets were pretty easy to pick up on wiki so far. I think I've had these definitions stuck in my head that last time I started down this path. coming back slowly.

the more I think about it, the definitions of the functions I used required it... well played anon.
no unions though. Measuring and moving states. Bayseian something...
It's another textbook I was planning on reading.

still thanks for convincing me.

>>6069501
>Please show me a continuous function that is not defined for all reals in the given domain.
that doesn't even make any sense.The domain of a function is by definition the points, where it is defined on
>Also, please show me a function that is defined for all reals that is not continuous
are you for real?

seriously you are the exact kind of person OP is talking about

>my sides when a scientist uses excel

>>6068907
why should I care about knowing the technicalities of math
if I'm en engineer, I want to do engineering, as long as my bridges don't collapse I don't care
explain why this is a problem

ITT engineering/physics students trying to show they really understand the math they're using.


>my sides

>>6069669
Math is a tool, what use is it to a mechanic to understand how the screwdriver he uses was modeled ?

>my sides when arrogant maths students take physics classes because they think they're going to be super easy
>my sides when some maths student in a workshop tries immediately to blaze through the problem with maths without thinking what he's doing and does loads of unnecessary work figuring out something that's obviously 0 by symmetry

>my sides when the top 3 scoring students on the maths department relativity class were all Physics students, as shown to me by the guy who runs the class because maths students are so autistic they can't apply their maths to anything real

>>6068924
pretty much this.

>>6069669
>ITT engineering/physics students trying to show they really understand the math they're using.

We don't need to understand it.

You don't need to understand Computer Science to write a computer program.

We're not interested in pure maths or computer science, we're interested in doing physics with it.

It's not physically possible to learn maths CS and physics. It takes a lifetime of study just to be a pure maths expert let alone all 3.

>implying you have to understand the tools you use
I like learning about why it works, many don't. You don't need to know either, doesn't matter how simple it is.

Had a lecturer who was a physics PhD on top of a maths PhD, illustrated the distinction quite well sometimes
>All right here's an integral, in mathematics we would argue this doesn't exist.
>But look, it's right there on the blackboard and it leads us to the right answer

1/0 isn't infinity, but if you get 1/0 in physics it bloody damn is a lot of the time (think optics)

>>6069682
>mfw the stuff OP is talking about takes a semester of studying mathematics
>mfw learning math cs and physics on babby level takes you a lifetime

a*ds=v*dv

errry day.

Fuck you, autist mathfags.

>>6069153

>Doubting the autism of sci

HAHA WOW

>maths students even bothering to breathe when they don't know how cells work and the reaction pathways for respiration

lmao, forever babby tier

>>6069445
>>6069460
Engineer here.
You disgust me.

You're typically the kind of lazy dumbass who will apply some explicite finite difference method in his code without worrying one second if it's legitimate, because he has no idea what he is doing, and come up with complete bullshit.

Then I have to clean your shit behind you.

You're not a good engineer if you don't have a very good understanding and an ease in manipulating basic math. You're a technician at most.

>tfw you will probably never do anything to do with differential forms and hence understand why people talk about how you can apparently divide them by each other

>>6069761
>butrfrustrated biology major detected
don't you have some soft science to do?

>>6069501
>that second paragraph
The worst part is you don't even seem to be shitposting.

>mfw me and my physics friends laugh at engineering majors who can't derive all of their equations from newton's 3 laws and the laws of thermodynamics

How old are you all guys?

I doubt any of you are older than 21-22.

>>6069767
>You're a technician at most
Good thing /sci/ is here to say that you actually cannot do your job despite doing it.

>HAHA NORMIES, aren't as educated as I am. Means they're no good even if they didn't have the resources I did

Please leave.

>>6069783
>mfw me and my pure math friends laugh at physics majors who can't derive any of their equations from some set of axioms.

>>6069819
Just because your company gave you a fancy title doesn't mean you're an engineer mate.

>>6069823
Oh, you know it for certain, m8!

>>6069826
Yes I do know for certain.
If your boss decided to change your job title into "king of the world", that wouldn't mean you're actually king of the world, ya dig?

>>6069682

Physicist here: of course you need to understand the fucking math. Otherwise you are just symbol pushing and you don't understand the limitations of physical models. Every physicist should at least know real and complex analysis and functional analysis at a pure math level.

>>6069824
>mfw me and my mathematical logician friends etc...

>>6068907
a woman in my physics class said she had to tell one of her students the formula for the volume of a sphere. he was a senior. in college.

>>6069820
>Means they're no good even if they didn't have the resources I did
but they have.

>>6068924
no, that's not the point. the point is that sometimes it doesn't work, and then you fuck it up and get the wrong answer

>>6069898
>a woman in my physics class said she had to tell one of her students the formula for the volume of a sphere. he was a senior. in college.

Why is that bad? I'd rather have a student that knew his shit and had to look up formulae than some kid that remembered the formula for every geometric shape under the sun but didn't understand what the fuck he was donig.

>>6069911
Bragging about memorization is quite often a way for people to feel smug. Since it works for geography, history, and many other subjects, they think its valid for mathematics as well.

>>6069682
Learning what the OP is reffering to certainly does not require a lifetime.

>>6068907

>mfw we have computers to solve calculus

>mfw people think that shit is relevant outside of non-applied math

>mfw people not in math bother with that shit

>>6069996
>implying people too dumb to understand this shit get a numerical solver running sufficiently

>>6069961

learning that shit may only take a minute

however, you neglected to mention that there are trillions of turds out there just like that shit

what's important, and what isn't? that's for this nigger to judge, not for you.

>>6069998

copying and pasting something into alpha, matlab, WX, sage, or whateverthefuck is not rocket science, buoy.

>>6070000
>however, you neglected to mention that there are trillions of turds out there just like that shit
I'm not sure what you're talking about.
I'm not reffering to specifically the two examples OP mentioned, I'm reffering to the whole math level they belong to, i.e. math undegrad.

Learning undergrad math doesn't take a lifetime.

>>6070005
but it is kind of.
how would you for example chose an ode solver for a given problem? matlab has like 20 of them for all kinds of different situations.

>>6069501
http://mathworld.wolfram.com/DirichletFunction.html
Nowhere continuous function.
Defined on R.
You are retarded, please study math more seriously.

>>6069898

>expecting her to derive it using triple integrals in spherical coordinates

seriously?

>>6069501
HAHAHAHHAHAHHAHAHHAHAHHAHAHAHHAHAHHAHAHAHAHAHAHHAHAHHAHAHHAHAHHAHAHAHHAHAHHAHAHAHAHAHAHHAHAHHAHAHHAHAHHAHAHAHHAHAHHAHAHAHAHAHAHHAHAHHAHAHHAHAHHAHAHAHHAHAHHAHAHAHAHAHAHHAHAHHAHAHHAHAHHAHAHAHHAHAHHAHAHAHAHAHAHHAHAHHAHAHHAHAHHAHAHAHHAHAHHAHAHA

>>6069501

I'm not even a math major, actually I'm a chem E major and I have come across all kinds of weird functions like error function, exponential integral, gamma function, etc. It would actually be really useful to force STEM people to take a real analysis course.

>>6070012
>"oh this problem looks like x"
>"so I run this corresponding y routine"
Unless you keep no notes on what you've done before, you should have no trouble.

>>6070037
>no trouble
>with lazy algorithms
I'm just too tired to laugh at you.

>>6069501

Physicist here: you have no clue what the fuck continuity is. Take a fucking analysis course, dumb ass.

>>6070007
but why stop at undergrad math?
why not just learn your whole fucking major so you can stop whining that we don't all of your fucking shit?
oh wait then you wouldn't matter...ever

>>6070012
how would you for example chose an ode solver for a given problem?
lol. ode45 until it stops working

>>6069501
lol. so by your definition, a step function that is also defined on all points in its domain is continuous. full. retard.

>>6069803
protip: none of them are actually engineers or mathematicians or what not. they are all undergrad students. some of them are even in highschool, still.

>>6069767
> in manipulating basic math
who said I couldn't manipulate it?
I just said I couldn't explain it to a rigor level equal to a math major because I don't give a shit.
I can manipulate the shit out of math and make it my bitch without listening to every little whiny shit she has to say.

>>6069803
> 23
hence why I can't remember any of this low-level bullshit.
My matrix equations are working fine, despite me not being able to describe their continuity.
I can tell when my model breaks and I have a pretty good idea physically why it stopped working.
I don't need to look to see if it's continuous, I already knew it was continuous because I'm working with a real physical system.

>>6069501
>I also didn't define what continuity was, I did generalize by saying that it was pretty much a function that is defined for all values on a given domain

Ok, I'm pretty poor at calc, but even I have to question that.

I might be wrong, but I always assumed that "continuity" means that f(a) has to be real and also equal to lim x->a f(x) on both sides.

From what you said, I could have some bizarre function like "f(x) = 0 if x is rational and f(x) = 1 if x is irrational", but you claim it would be "continuous"?

>>6070414
Technically speaking, if we let the domain of the function f have the discrete topology, then any function from it (to another topological space) will be continuous.

mathfag out.

>>6070397
>protip: none of them are actually engineers or mathematicians or what not. they are all undergrad students. some of them are even in highschool, still.

You know, the more I read this board, the more I'm convinced of that.

And I'm no math expert here -- I'm just basing this on all the inconsistencies I see here. (And I'm relatively new to /sci/.)

Like for example, I've seen some people rage with autistic fury that 0^0 is always undefined in all cases, and others rage with equally-intense autistic fury that 0^0 = 1 in all cases. (And, you know, maybe one of them is right -- I can't say for sure because I'm not an expert.) But when you see that kind of inconsistency presented in such a frantic head-banging way, you gotta wonder if maybe you're not dealing with experienced math professors here.

And the funny thing is that just a half-hour of googling will usually set you fairly straight on a lot of this stuff, explained in a way that even a high-schooler could understand. It kinda makes you wonder if there are any passengers left anymore on the give-a-fuck boat.

And even when posters are right about the math, they sometimes write about it with an arrogant, unprofessional attitude that just makes the whole board feel "off kilter" to me. It's like people have absolutely zero-fuck-all patience with newfriends who participate on this board to help them learn the concepts better. I find it hard to believe that a seasoned math professional would normally have that kind of attitude. Or if they did, then why the hell would they even waste their time posting this board?

>>6070494

Dude, it's still 4chan, full of trolls. Even the people who do know about stuff do whatever the fuck they want here.
If I want to genuinly help people I go to stackexchange (and posters with genuine doubts in math should go there too), if I have a research question I'd go to overload or just ask people in the math department. I come here to piss off newfags by acting like an ass.

>>6070420
>Technically speaking, if we let the domain of the function f have the discrete topology, then any function from it (to another topological space) will be continuous.

Can you recommend a web page that talks about this in more detail?

It sounds like you're using the term "continuous" in a way that I didn't encounter in my calc course. We didn't talk about functions from one topological space to another. And also, it seems to me like you might be talking about two different functions here -- #1: f(x) and #2: this other function that maps f into another topological space -- and so I might be getting confused about which one you are saying is "continuous". I was really more interested in how to tell if f(x) itself is continuous, since I'm only at the first-year calc level.

>>6070531

Saying "f(x)" i continuous is wrong, f(x) is a number, f is function (just claryfing it for you).

The topological definition is just more general compared to the one you learn in calc. R is a topological space with the usual topology and both definitions of continuity are equivalent in that setting.

As for how to tell if a gven f is continuous. You can work from the definition you have, or use theorems which apply (the sum of continuous functions being continuous would help in some cases for example)

>>6070531
http://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf is the easiest set I could find from 5 minutes of googling -- and it has the advantage of addressing continuity right from the beginning. (>>6069523 has the complete explanation: a function <span class="math">f:(R,\:T_R)\mapsto(S,\:T_S)[/spoiler] is continuous if and only if <span class="math">V\in T_S\Rightarrow f^{-1}(V)\in T_R[/spoiler] where the T_i are 'topological spaces'.

I was referring to the same function f, but I admit to being kind of sneaky there -- we can't talk about functions being 'continuous' without equipping the domain and codomain with something called a topology (or 'topological space'). When you start learning analysis it's always implicitly assumed that the real numbers <span class="math">\mathbb{R}[/spoiler] are equipped with the 'standard topology', which is a set whose elements are precisely all open intervals in <span class="math">\mathbb{R}[/spoiler]. (With this topology, it's often called a 'Euclidean space'. See the PDF for more detail.)

I did the equivalent of challenging someone who says 'if a * b = 0 then either a = 0 or b = 0' by replying 'not in mod 4 arithmetic!'--using a nonstandard but not incorrect definition.

Topology is a dense subject, but it does tend to produce gems like these. It seems to feature pretty heavily in Analysis too.

>>6070543
>Saying "f(x)" i continuous is wrong, f(x) is a number, f is function (just claryfing it for you).

Sorry. I meant to talk about f being continuous at a particular value of x, but I wrote f(x) which was a bit sloppy.

Please correct me if I'm wrong, but it seems like the word "continuous" is being used in two different ways here, and I'm not seeing the connection.

My understanding is that if f is R->R and is continuous at a, then f(a) must be a well-defined real value that's also equal to lim x->a f(x) from either side.

It seems to me like the "f(a) = lim x->a f(x)" requirement is critically important to make "continuity" useful and meaningful for f: R->R functions. But (unless I'm reading it wrong) the concept of the limit seems to be missing entirely from the topological definition of "continuity". So how can the topological sense of "continuity" be helpful or relevant to the "f(a) = lim x->a f(x)" sense of "continuity"? It seems to me like they're using the same term for two different things, and I'm not seeing a particularly meaningful connection between the two uses of the term.

>>6070572

Thanks for the link, I appreciate the time you took to track that for me.

>>6070572

Looks good. I always like getting recommendations for good instructor's course notes, and this one looks good at first glance. Thanks again.

>>6070601
It's embedded in the notion of a topology, actually. The entire idea of a 'limit' is contained by the topological space.

In plain English, the 'analysis' definition is: "Choose an open interval U containing f(a), no matter how small. Then you can find an interval around a that maps into U". The 'topology' definition is: "Choose any neighbourhood U of f(a). Then you can find a neighbourhood of a that maps into U."

So the topological definition generalizes the usual analysis one.

>>6070614

Ok, I think I got it. They key for me is when you said:

>the real numbers R are equipped with the 'standard topology', which is a set whose elements are precisely all open intervals in R .

I had been thinking of f as having the domain R -- when in fact the domain you're talking about appears to be the set of all open intervals in R.

> In plain English, the 'analysis' definition is: "Choose an open interval U containing f(a), no matter how small. Then you can find an interval around a that maps into U". The 'topology' definition is: "Choose any neighbourhood U of f(a). Then you can find a neighbourhood of a that maps into U."

Very helpful, thanks.

>>6070636
Given a function <span class="math">f: X \to Y[/spoiler], you can view <span class="math">f[/spoiler] as being a function on (arbitrary) subsets of <span class="math">X[/spoiler] by looking at the image of subsets: for any subset <span class="math">A \subseteq X[/spoiler], we have <span class="math">f(A) = \{f(x): x \in A\}[/spoiler].

>>6070651

Thanks. As a newbie who knows nothing about topology, it would be helpful if they could make a sharp distinction between:

"a function that maps X to Y"

...versus...

"a function that maps {the set of all subsets of X} to {the set of all subsets of Y}".

For me, it was quite confusing for the same name "f" to be used for both of those functions.

I know it's possible to tell the difference by the type of the argument ("f(A)" versus "f(x)"), but still, using "f" for both functions seems to be one of those things that would just trip up newbies like myself.

(My background is software engineering, where using the same name for two different things is just begging for software bugs to happen, so we try to avoid it whenever possible.)

>>6070651
True, but not what I'm talking about here: as a function, f doesn't "act" on the topology at all, it still "acts" on <span class="math">\mathbb{R}[/spoiler] only, bringing it to elements on <span class="math">\mathbb{R}[/spoiler].
The topology is just additional 'information' that tells you what happens when you do stuff to the function.

>>6070671
>I know it's possible to tell the difference by the type of the argument ("f(A)" versus "f(x)")
That's how I think about it. That way of talking about functions is pretty universal in modern mathematical notation, so you often won't see the distinction made.

Also, note that the same sort of thing is done with the *inverse* image: if <span class="math">f: X \to Y[/spoiler] is a function and <span class="math">B \subseteq Y[/spoiler] is a subset of the codomain, then
<span class="math">f^{-1}(B) := \{x \in X: f(x) \in B\}[/spoiler]
If <span class="math">B = \{y\}[/spoiler] is a singleton set, then we often use the shorthand <span class="math">f^{-1}(y) := f^{-1}({y})[/spoiler].

>>6070692
Correction: the shorthand <span class="math">f^{-1}(y) := f^{-1}(\{y\})[/spoiler].

>>6070683
I'm not sure what you mean, then. Weren't you implicitly using the same idea when talking about "an interval that maps into" something?

>>6070697
If you're referring to my statement here >>6070572
then yeah, you're right. I thought that you were suggesting that f assigns each open interval in X to exactly one open interval in Y, and wanted to clarify that I didn't mean that.
(I.e. the domain of f is X, and not <span class="math">T_X[/spoiler]. The post here >>6070636
>the domain you're talking about appears to be the set of all open intervals in R.
seemed to reinforce the error, so I decided to throw in a word of clarification.
Sorry about that.

>>6070692
>That way of talking about functions is pretty universal in modern mathematical notation, so you often won't see the distinction made.

Well, I think it depends on the branch of math. Maybe they're loose about that in topology, but in other branches of math it could be a disaster.

For example, in set theory, a clean distinction needs to be made f(a) and f({a}). The function f could easily be defined in such a way such that the first one makes sense and the second one makes no sense, or vice-versa. So using the same function name "f" for both functions within the same example has far too much potential for confusion.

>>6070706
All I was doing was making explicit the often implicit use of the "image of a subset" functor <span class="math">\mathrm{Hom}(X, Y) \to \mathrm{Hom}(2^X, 2^Y)[/spoiler]. The issue of how this plays with the topology didn't enter into it at all.

Also, in case there's confusion about which posts are mine, I posted these: >>6070651 >>6070692 >>6070697

>>6069848
Ah yeah, I can imagine how crucial the three cornerstone Banach theorems are to a physicists daily work.

>>6069007
>Not categorifying further than level 1

>>6069907
Meanwhile, mathematicians don't get an answer at all. How is that better?

>>6070394
that would be the engineer's approach
have fun with stiff problems broski

>>6071025
> until it stops working
did all of /sci/ fail basic reading comprehension?

>>6069907
> sometimes it doesn't work
if it doesn't work and you get the wrong answer that's your fault for not remembering when it stops working.
The thing mathmagicians don't seem to get is that we are doing the same math problem over and over again.
It's the physics problem that changes, not the math.

>>6071029
obviously ode45 would still work. but it would do a shitty job and take a fuckload of time.
and remember:
thats just one step in your algorithm and you have no fucking clue, that this is the step that causes a problem

>>6071051
ah.
My only experience with "stiff" problems was when ode45 was just breaking, so I went to my professor.
He told me my problem was stiff and to talk to a different professor.
I later found that my symbolic math in matlab was just breaking and deciding to arbitrarily cut off certain terms, so my ode function wasn't meeting up with the other ode function.

Stiffness wasn't covered in our low level computational mechanics class. Maybe it was covered in the aero one though.

How long is a fuckload of time? Because I've definitely let MATLAB run a whole day for an optimization problem.

>>6071070
>How long is a fuckload of time?
if you're interested, you can look at this article
http://blogs.mathworks.com/seth/2012/07/03/why-do-we-need-stiff-ode-solvers/
>ode45 required 3046 steps to solve the problem, while ode23s required only 91 steps!

>>6071103
why is this called "stiffness"?
http://en.wikipedia.org/wiki/Stiff_equation
I guess we did study this. We said the solver was unstable though, not that the equation was stiff.
Something about Euler's method not working.
So how do you know it's stiff before you run the solver?

>>6071126
I guess they are called stiff, when the solution to your ode quickly evolves into a steady state and stays there.
Like the kind of behaviour, exp(at) for a<0 and growing t shows.
So when you know, that for example a chemical reaction happens really quickly and afterwards nothing much is happening, you should better use an implicit solver even if the single steps take more time than with an explicit one.
A good example for that are most reaction diffusion systems.

>>6070494
It also doesn't help that in the sciences people perceive math differently than mathematicians do and this pisses off mathematicians to no end (even the way science people pose their questions pisses off mathematicians).

>We have to know so much math in physics/comp-sci/etc..
>Are mathematics a science?
>Mathematics depend on the laws of matter/biology/nature/etc..
>Why don't mathematicians only study useful things?
>What are some real world applications for x branch of mathematics?

Also, math people argue against math people on points of little consequence. Including the example you posted (in the real world people would just say "it depends").

>Is multiplication just sophisticated addition?
>Does the set of natural numbers contain 0?
>Are mathematics invented or discovered?
>Does the set of real numbers even exist?
>etc..

You never actually see mathematicians arguing about actual math.

>>6071284
>>We have to know so much math in physics/comp-sci/etc..
>>Are mathematics a science?
>>Mathematics depend on the laws of matter/biology/nature/etc..
>>Why don't mathematicians only study useful things?
>>What are some real world applications for x branch of mathematics?
You've been hanging around high school idiots far too long.

>>6071284
smbc comics are always gold haha

>>6071291
No, these are all threads made by sciencefags on /sci/. I've seen even grad level physicists confounded by the idea that mathematics doesn't rely on the laws of physics (in other words, if you were to change them then mathematics would still be the same).

>>6069783
>not including Maxwell's equations

>>6069783
> newton's 3 laws
What are you a freshman in physics?

Newton's first law would be cool if it was Newton who discovered it and not Galileo.
Newton's second law can be derived from conservation of energy.
Newton's third law is a particular shitty case of conservation of momentum.

> mfw I'm an engineer laughing at you freshman

>>6071143
> happens really quickly and afterwards nothing much is happening
I like this definition.
Still don't know exactly why the use the word stiff.
I haven't had too many problems that get anywhere in a reasonable amount of time.
I'll try to remember this, when they do.

>>6068958
>2013
>not calling it arrow-texting

P.S. while math majors are cooking at Mickey D's to pay for grad school so they can get a $60k job, I'm racking up $100k straight out of undergrad.

>>6069773
That one actually was a shitpost. It's really the only reliable way to get information from /sci/.

>>6071394
>major in pure mathematics
>$300k any job I want

>I'm racking up $100k straight out of undergrad.
In debt maybe.

>>6071405
>300k any job I want
Assuming that you don't want to be anything other than the chair of the federal reserve.

>>6070414
I actually mentioned that the two sided limit has to exist in the last sentence of the post.