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Ted Shifrin
Ted Shifrin
00:01
NO.
robjohn
robjohn
00:22
@geocalc33 we can see that you have typed, however.
leslie townes
leslie townes
geocalc: except for me, i can't see even that.
geocalc33
geocalc33
is $\log^2 x +\log^2 y =1$ a surface of revolution?
Ajay
Ajay
So for my previous question, was the conclusion I drew correct.
If I compute the curl of a vector field and see that the vector field is not conservative, would that mean that I can't use the fundamental theorem of line integrals to evaluate a line integral?
robjohn
robjohn
@Mohammed I leave a trail of bread crumbs.
geocalc33
geocalc33
you can favorite the room I think
robjohn
robjohn
00:27
I am taking a fussy dog to the park. BBL.
Ajay
Ajay
Where $A$ is the line segment from (1,0,-1) to (3,4,2)
Take the following line integral for example $$\int_{A}^{} xydx + y^{2}dy + yzdz$$
Ted Shifrin
Ted Shifrin
00:55
@Ajay There is no fundamental theorem except when you have a gradient field. The work is path-dependent.
Ted Shifrin
Ted Shifrin
01:40
@robjohn These are what fell out of your soufflé mold?
Mohammed
Mohammed
02:12
I have a formula that I want to test on large numbers
If, p: prime number and p+2: prime number
P^2 - [(p+1)×5]=E
E: prime number
I want the largest possible number "p" that achieves this formula
Ted Shifrin
Ted Shifrin
So write computer programs.
Mohammed
Mohammed
I don't know, unfortunately. I hope someone can help me. What do I know exactly?
Ted Shifrin
Ted Shifrin
Well, learn.
Mohammed
Mohammed
Learn*
Ted Shifrin
Ted Shifrin
Seriously. If you want to experiment with mathematics, do it, but don't expect us to do it for you.
Mohammed
Mohammed
02:21
I mean, which language is better to learn programming that will help me with exams like this
Ted Shifrin
Ted Shifrin
I am not a programming expert.
Mohammed
Mohammed
When I ask questions in the forum about formula tests, the answer is always this is an easy program to do
Ok
@TedShifrin
I read your CV on the site, I have a question for you, if you will allow me
Ajay
Ajay
If you want something for exams you should learn pseudocode
There are a number of languages you can use: Python, Matlab, Java, C++ etc
Though it's full of bugs, you can't even do arithmetic with brackets
Here is a github repo that lets you run the pseudocode: github.com/virchau13/pcse
Mohammed
Mohammed
No, not for exams
Ajay
Ajay
SO I recommend that you should try eccentricorange.github.io/CAIE-Computer-Science/… if you are having too much dificulty with the above one(This is for windows only, the above can be used on all OSs)
Linux, mac, windows etc
Mohammed
Mohammed
02:31
Nice
But how write in it
Ajay
Ajay
Here is the syntax alongside.us/pseudocode/0478_pseudocode_guide.pdf
Mohammed
Mohammed
I want something easy and not complicated. I just want to take tests, not do other things
Now i go to syntax
Ajay
Ajay
You need a software like VScode and whenever you want to program in it you need to put .pcse at the end.
Here is an example use DECLARE x: INTEGER
DECLARE y: REAL
DECLARE z: REAL

x <- 5
y <- 5.2
z <- x * y

OUTPUT z
Mohammed
Mohammed
I have vs
Ajay
Ajay
you can save this file as mess.pcse
Mohammed
Mohammed
02:36
Learn simple things in Python such as types of statistical variables, arithmetic operations
Learned
Ajay
Ajay
just search pcse
Mohammed
Mohammed
Link
Ajay
Ajay
If you use the pcse extension one you need to install it from the marketplace
github.com/virchau13/pcse
Mohammed
Mohammed
I find different things in google
Ajay
Ajay
the one who developed the extension
U know this guy used to go to my school
see ya
gotta go no
Mohammed
Mohammed
02:41
I will installe it
Is vs
In*
Do you recommend I learn Java?
Bye
user10478
user10478
What is the meaning of the input to a Heaviside function? Solving PDEs via Laplace Transform produces Heaviside functions like $H(t - 2x)$. Plot3D'ing these in Mathematica seems to reveal that $H(t - 2x)$ is identical to $H(2t - 4x)$, so it seems scaling doesn't matter, only the span, but when I scale by a negative number the jump flips.
leslie townes
leslie townes
heaviside only cares about the sign of the input, so yeah, scaling by positive numbers shouldn't matter.
user10478
user10478
Is that just a definition thing or is there some reasoning behind it?
leslie townes
leslie townes
well, the reasoning behind it is the definition. H(bleh) is 1 if bleh is positive and 0 if bleh is negative. different books might disagree about what H(0) is.
so to find where H(bleh) is 1, you look where bleh > 0 (or >= 0, depending on your definition). which is the same as looking where 2*bleh > 0, or c * bleh > 0 for positive c.
Ted Shifrin
Ted Shifrin
02:56
Step functions rule.
leslie townes
leslie townes
for any c > 0 and any nonzero t one has H(ct) = H(t) because the sign of ct is the same as the sign of t.
they really do rule.
user10478
user10478
Okay yeah, that makes perfect sense. I just wasn't used to seeing it with 2D input.
leslie townes
leslie townes
yeah, it could get complicated if you're stuffing some multivariable function inside of H, because multivariable functions can change sign in more interesting ways. you got off easy with t - 2x.
my daughter's shouting nonsense syllables and blaming it on her imaginary friend when we tell her to stop.
Ted Shifrin
Ted Shifrin
Of course. That’s why she has imaginary friends.
leslie townes
leslie townes
sometimes she hits herself on her forehead (not hard) and says that her imaginary friend is hitting her. she uses this to get attention.
Ted Shifrin
Ted Shifrin
03:01
I don’t have any idea what a multivariable Heaviside function is.
user10478
user10478
I don't think what I described is a true multivariable Heaviside function.
In Mathematica, HeavisideTheta[] allows multiple, separate inputs, and returns $1$ iff all inputs are positive.
I was just using a single function input but it was an expression in two variables.
geocalc33
geocalc33
this is still considered an integral transform if written this way? $h(s)=\int_0^\infty f(s,x)g(s,x)~dx$
woah the inverse Mellin Transform of 1/z is the heavside step function
I wonder why that is
Ajay
Ajay
03:51
Alternatively you could learn Jython
@Mohammed I recommend you find an easier language like python. When I tried to start with Java I was completely lost, but after 2 years of python it is a lot easier now.
love_sodam
love_sodam
04:27
@LeakyNun Existence of $g$? That's because $\tilde{f}$ is defined on a simply connected domain and $\tilde{f}(z)\neq 0$ for any $z$ on its domain. My question is if this fact implies the existence of square root of holomorphic function between annulus. And as you said, this is a contradiction because identity function doesn't have a square root.
Ted Shifrin
Ted Shifrin
04:43
Annuli aren’t simply connected, obviously!
love_sodam
love_sodam
But unit disk is simply connected.
Ted Shifrin
Ted Shifrin
So what?
love_sodam
love_sodam
So a square root $g$ exists.
Ted Shifrin
Ted Shifrin
Square root of what?
love_sodam
love_sodam
$\tilde{f}$
Ted Shifrin
Ted Shifrin
04:55
What specific function?
love_sodam
love_sodam
16 hours ago, by love_sodam
Show that there is no injective conformal map from the punctured disk $\{z:0<|z|<1\}$ onto the annulus $\{z:1<|z|<2\}$. To show this, suppose there is a conformal map $f$ between them. Then $f$ is bounded near $0$, we can extend it to holomorphic map $\tilde{f}$ on open disk. Now, $\tilde{f}$ is a nonzero holomorphic map on a simply connected domain so it has square root $g^2 = \tilde{f}$. Does this imply any holomorphic function between annulus has square root? (so that it makes a contradiction
Specific question is this.
Ted Shifrin
Ted Shifrin
Your final question makes no sense.
Between annulus?
You mean annulus to itself?
love_sodam
love_sodam
Yes. $\{z:1<|z|<2\}$. I wonder if the existence of $g$ guarantees that.
Ted Shifrin
Ted Shifrin
No.
Riemann extension works for a missing point, not a missing disk.
love_sodam
love_sodam
user image
Maybe I didn't understand the solution.
Ted Shifrin
Ted Shifrin
05:04
You compose the function with the inverse of your injective conformal map (which you suppose exists). The resulting contradiction shows no such conformal map exists.
Sorry, not inverse. You use the inverse with the supposed square root.
user10478
user10478
One more question, say I'm doing a Laplace Transform or Fourier Transform with respect to $t$, and I have boundary conditions like $u_t(a, t) = f(t)$ and $u_x(c, t) = g(t)$. Can I just translate these as $U_t(a, s) = F(s)$, etc., or do I have to apply the same transform of derivative formulas used in the PDE to the LHS of the boundary condition equations?
love_sodam
love_sodam
05:26
@TedShifrin You mean $g:\Bbb D\setminus\{0\}\to \{z:1<|z|<\sqrt{2}\}$?
 
1 hour later…
yearning4pi
yearning4pi
06:32
@AkivaWeinberger A provocative statement lol
 
1 hour later…
Mohammed
Mohammed
07:40
There is a 7-hour video explaining algebra in Channel "freecodecamp" Is this video enough for me to know an important amount of algebra?
copper.hat
copper.hat
08:02
i don't know, i have never watched a 7 hour video.
Ajay
Ajay
08:23
@Mohammed I watched it. I can wholeheartedly say that it does not cover what is important. Me and my dad watched it together and agreed the video is just a long waste of time.
I wouldn't say that they don't cover what is important, just the way they teach it is neither rigorous nor intuitive. It is very monotone and boring.
Mohammed
Mohammed
08:45
@Ajay, Can you suggest me a better one?
Ajay
Ajay
Not a video, but a textbook. An IB AA HL textbook. I will send link shortly. The textbook covers all the algebra and more. Calculus, stats and prob etc included.
 
3 hours later…
Koro
Koro
12:04
Can anyone please verify my answer to a group theory question here? Thanks.
 
2 hours later…
yearning4pi
yearning4pi
13:37
@Koro Have you shown that "V" is closed under inverses? Later on you have expanded $gu_i^k_1g^{-1}$. What if $k_1$ is negative?
yearning4pi
yearning4pi
13:51
Correction: $gu_i^{k_1}g^{-1}$
Koro
Koro
14:06
Thanks for reviewing :). Yes, I have shown that V is closed under inverses but skipped the details in the post. Should they be incorporated?
About that $gu_i^{k_i}g^{-1}$, I did think about $k_i$'s being negative but that's not a problem because $gu_i^{-1}g^{-1}=(gu_ig^{-1})^{-1}$
I think that one more problem is with the way V was defined.
V gives a vibe that G is countable.
which is doesn't have to be.
I'm deleting that answer.
yearning4pi
yearning4pi
Hm. That works for uncountable $G$ and $U$ if I recall your choice of $V$ correctly.
Koro
Koro
14:33
Here it is (deleted now):
Let's define $V=\{u_1^{k_1}u_2^{k_2}...u_n^{k_n}:n \in \mathbb N,k_i\in \mathbb Z, u_i\in U\},u_i$'s need not be distinct.

**Showing that $V$ is the 'smallest' subgroup that contains $U$:**

By choosing $n=1$, it follows that $V$ contains $U$.

$V$ is clearly closed under group operation.

For any $u\in U,$ choosing $n=1$ and $k_1=-1$, it follows that $u^{-1}\in V$. So $V$ is closed under inverses.

$V$ contains identity of the group. It follows that $V$ is a subgroup.
I feel that V should have been written differently. But I'm not sure yet.
anak
anak
15:03
Effectively all you want to say is $V := \langle U\rangle$. So you can either use the definition by intersections of subgroups (I would prefer this, personally), or you can do it using finite products.
love_sodam
love_sodam
15:33
Is a matrix ring $M_n(F)$ a PID? where $F$ is a field.
anak
anak
This depends on n, too.
@love_sodam what's some easy properties of PIDs?
love_sodam
love_sodam
Every ideal is principal ideal?
anak
anak
That's certainly the "PI" part. What about the "D" part?
love_sodam
love_sodam
domain
Ah I see.
anak
anak
Seems you see what I see? :)
love_sodam
love_sodam
15:40
it's not even a domain
anak
anak
Unless what?
 
1 hour later…
Jakobian
Jakobian
16:55
Unless n = 1
anak
anak
@Jakobian that was low hanging fruit not meant for you. :(
 
1 hour later…
Mohammed
Mohammed
18:00
If i want learning Algeria by YouTube, what is the best chanel?
Because any video i can translate it, but books it require to be very good in English
Algebra
Algebra which i learned in high school, is it helpful?
leslie townes
leslie townes
mohammed it may help to be more specific about what you want to learn. 'algebra' can be something taught in high school, or in university, or in graduate school. the topics covered vary a lot. i don't know of any good youtube resources, but with more specificity, maybe someone else can help.
Mohammed
Mohammed
First, it must be taken into account that I am an amateur, not an academic
Jakobian
Jakobian
18:17
@anak I guess heaven needs to banish me now
Mohammed
Mohammed
I watch videos about numbers, read their types, and sometimes I watch videos to solve algebraic equations.
Xander Henderson
Xander Henderson
19:07
@Mohammed That didn't really answer the question. "Algebra" in middle school or high school is largely about symbol manipulation (given that this is equal to that, solve for those). "Algebra" in undergraduate is typically about the study of structure (how do you abstractly factor things? do things have "prime" decompositions? how is a polynomial like an integer?). "Algebra" in graduate school tends to be category theory, which is like the study of structure on steroids.
What, specifically, do you want to know?
At what level are you hoping to study?
(The fact that you are an amateur and not an academic is largely irrelevant---indeed, the fact that you are asking for recommendations on YouTube automatically made me assume that you are not an academic, as most academics would ask for book recommendations).
Lukas Heger
Lukas Heger
19:23
@XanderHenderson I don't agree that algebra in graduate school tends to be category theory. There's also graduate level commutative algebra, noncommutative algebra, representation theory, homological algebra. Category theory is part of it, but it's not the whole thing
Xander Henderson
Xander Henderson
@LukasHeger I was (a) being somewhat facetious and (2) trying to fit a lot into a single comment.
The original version of the comment was "'Algebra' in graduate school tends to be a bunch of diagram chasing", if that makes you feel any better. :P
anak
anak
Speaking of which, I wonder how categorification is going these days.
The last I looked into it in representation theory was about the q-Fock space.
Jakobian
Jakobian
20:23
When can you call someone an academic?
I guess students don't count this way.
robjohn
robjohn
I think grad students might count
But any level of postdoc or professor
geocalc33
geocalc33
what's the first step in showing $R_{ab}=0$ is satisfied by some metric
Educ
Educ
0
Q: Compute the gradient of Function Defined by Integral

EducI would like to know how to compute the gradient of Function Defined by Integral For example, Let $\displaystyle f(x,y,t)=\int_{0}^{k}g(x,y,t)\rm{d}t$ be function and $t\in\mathbb{R}^{+}$ and $(x,y)\in\mathbb{R}^{2}$ $$\nabla f(x,y,t)=?$$ How can I compute the gradient of that function with respe...

real-analysis partial-differential-equations vector-analysis gradient-descent gradient-flows
leslie townes
leslie townes
something's a little goofy there in t being both a variable in f and a dummy variable in the integral
Ted Shifrin
Ted Shifrin
Worse than a little goofy.
amWhy
amWhy
20:43
@robjohn I'd say so, as well, especially those in a PhD program.
@Jakobian That could be a could question on Academia.se, as well.
Xander Henderson
Xander Henderson
@Jakobian I would say that graduate students are "baby academics", but that "read" academics are those who are paid to be in academia, with an emphasis on those with some research requirements---some graduate students, university and college faculty, postdocs, etc.
amWhy
amWhy
@XanderHenderson Too many analysis people here, @Xander! ;P
Xander Henderson
Xander Henderson
Most adjunct faculty probably don't fall into this category, but the boundaries of "academic" and "non-academic" are fuzzy.
@amWhy You can never have too many people interested in analysis.
amWhy
amWhy
@XanderHenderson Absolutely! Well, then, let me say we need more logicians and more Algebra here!! There is no limit to the number of people interested in logic, set theory, or algebra. I'll invade this room with other specialists, or you can admit, I have a point ;P
Educ
Educ
@leslietownes I fixed now check please
@TedShifrin Please, check now
0
Q: Compute the gradient of Function Defined by Integral

EducI would like to know how to compute the gradient of Function Defined by Integral For example, Let $\displaystyle f(x(t),y(t))=\int_{0}^{k}g(x(t),y(t))\rm{d}t$ be function and $t\in\mathbb{R}^{+}$ $$\nabla f(x(t),y(t))=?$$ How can I compute the gradient of that function with respect to $t$.

real-analysis partial-differential-equations vector-analysis gradient-descent gradient-flows
Xander Henderson
Xander Henderson
20:50
@amWhy Nah... one logician is plenty, and any algebraist is too many algebraists. :P
amWhy
amWhy
@XanderHenderson :P :D
Ted Shifrin
Ted Shifrin
21:09
Three analysts that I count.
@Educ So you’re doing calculus of variations?
This is calculus in the space of functions.
Educ
Educ
21:27
is this what we called Functional analysis
Ted Shifrin
Ted Shifrin
21:44
Not really.
But you need to understand that a "direction vector" is a pair of functions. You'd better be sure you have the question precisely correct. If so, I will answer it when I come back later.
 
1 hour later…
geocalc33
geocalc33
23:08
$g=du~dv$ how would you write this (pseudo) metric in matrix form? Since the differentials are multiplied I don't know how to do this... on the other hand the Euclidean metric can be written easily as $g=\left( \begin{matrix}1 & 0\\ 0 & 1\end{matrix} \right)$

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