ahmet

On 7/19/2020 at 11:06 PM, HallsofIvy said:

If I remember correctly, a region in $R^2$ is "regular" if its boundary is a simple closed curve.  (And a curve is "simple" if it does not cross itself.)  Yes, the rectangular region $a\le x\le b$, $c\le y \le d$ is a "regular region".  As to the integral, $\int_{u(x)}^{v(x)} f(x,y)dy$, Assuming that f is an "integrable" function of y, then $\int_{u(x)}^{v(x)} f(x,y)dy$ is a function of x, F(x).    I might think of the "x" as a "parameter" in the integral but as a variable in f(x,y) and in F(x).

hi, can we conclude/say that all of elementary functions (that consisted of just one term) were simple curve

elementary functions : 

*trygonometric (cannot consist of more than one term)

*logaritmic (cannot contain more than one term)

* polynomic (this category can consist of just one term and can be divided to two subcategories : 1) with odd number degree 2) even number degree  (e.g. [math] f(x)= x^{3}, g(x)=x^{4} [/math] ))

* inverse trygonometric functions (cannot be more than one term)

* exponential functions (should contain just one term)

All these functions should be simple curve ,could you confirm this information please?

clarification: the criterion given in the paranthesis are in fact ,all equivalent and means this 

for instance : trygonometric functions cannot be defined like this one: [math]f(x)= cos(x) + cos(tx) [/math] t ∈  R constant number) or this one [math]f(x)=sin(x)+cos(x)[/math]

for exponential functions for instance none of these are acceptable [math] f(x)=e^{x}+e^{5x} , g(x)= e^{x}+5^{x}[/math] and so on. futhermore just one type of these functions are claimed not the mixture of them (e.g. this is not an issue: [math]f(x)= cos(x)+x^{4} [/math] )

oh my gosh! 

I am full with energy!

is this caused by eating walnuts , hahahahaahaha  

oh natural , natural, natural  

,

one another nice musics even if I do not know what "chameleon" means.

it seems like a POPular  wind is blowing from russia.

I listen only POPular musics    

full energy!    

oh my gosh! I can't move to anywhere   

it is because of covid - 19. 

may I ask something more while trying to make my boring times go away 

1) does youtube pay fee just regarding the count of watching (assume please ads turned on)?

2) what happens if the language option is changable (in fact this is the same question with previous one) 

A notation: I have detected many music videos ,that seem like some unqualified productions, however, they are watched too many times. 

music , music , music    

15 hours ago, studiot said:

You can often get examples from google by selecting the  'images tab for example

Fourier series

https://www.google.co.uk/search?q=Fourier+series&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjQ-IDVo4zrAhVWiFwKHSePAjIQ_AUoAnoECBIQBA&biw=1366&bih=646

 

This should keep you busy.

thnak you for suggestion,I had better read the books you provided here and similar books. Because I hope I shall see the proofs of claims (e.g. if this is regular continuous then ...(it will show me)) 

17 hours ago, studiot said:

Not sure what you are trying to achieve here, seems like a very tall order to me.

Have you looked in standard texts such as Titchmarsh "theory of functions" or Knopp "Infinite series and Sequences"  ?

16 hours ago, studiot said:

Again not sure what you seek here.

The best book I know for understanding is Ahlfors "Complex  Analysis"

A wide ranging use of complex analysis is Churchill's "Complex Variables and Applications"

Also lots of detailed worked examples in Alan Jeffrey's "Complex Analysis and Applications"

thank you very much for your suggestions. I do not deal with theoretical explanations anymore or they are not so much important to me.

generally books in mathematics are following these scheme:

theorem 

proof

lemma 

proof

corollary

but here examples are very important to me. I try to analyze them. mmm, some samples of books would be very good if those books include graphs of such functions. (e.g. a differentiable function f(x,y)= x.y , this is just one example for differentiable function 

or [math] g(x,y)=\frac {e^{x^2-y^2}}{1+sin^4(x^2+3xy+y^2)} [/math] is continuous at everywhere. but I need many many examples. Graphs would be very nice (if exists))

16 hours ago, Strange said:

!

Moderator Note

Similar threads merged.

I would recommend a library or bookshop (online or physical)

 

sorry for the occasion if I am doing a mistake but I just thought that complex analysis and basic analysis would be very different branches of maths.

(normally these examples (if we divide into two categories) will never appear in same book or any else literature imo. )

but you might be right because the expression of wishes seem similar. 

pahaha : low reliability in the video but still laughing...:)   hahaha hahaha 

that examplify with broad view of:

** simple functions (exponential, trygonometric, hyperbolic, logaritmic, inversed trygonometric and hyperbolic)

** riemann surfaces

**  differentiable functions

** Laurent series (all types)

**C-R equations

** conform transformations 

Note: preferred language is English but  (if it is not againts the rules of this website) sources in russian ,arabic and turkish and are also welcome.

(theoretical explanations such as lemmas,theorems,corollaries are not needed (should not be emphasized or concentrated on.))

Thanks

Dear maths lovers

I need sources that classify functions/sequences or functional sequences (in broad view (wide count of examples)) ,such as;

*** convergent functions / sequences

*** divergent functions / sequences 

*** differentiable functions (>1 variables)

*** differentiable functions (>2 variables)

*** regular continous functions

*** continuous functions

*** integrable functions

*** lipschitz criterion satisfied functions

*** cantor theorem satisfied functions

*** regular convergence (functional sequences)

(note: thesis and/or books are preferred ,because the soruce(s) I look for should provide broad view)

Thanks in advance

I recommend  thinking via "approximately multidimensional approach"  ....to respond this query

what does this mean?

in fact, the demonstration belongs to me (i.e.: there is no such thing,but I demonstrate it,follow---->>)

multidimensional is a core keyword here: means some obtained functions (e.g.: having knowledge about more than three languages (e.g. german,english,spanish,chinese) and having knowledge about more than three disciplines (e.g: maths physics chemistry biology)

I know that all these are difficult but not impossible. I used approximately ,because in fact there should be no limit regarding both disciplines and languages.

.....

17 minutes ago, Strange said:

So, the question is: Is education being reinvented / restructured [because of the pandemic]?

Probably. But as with so much of the "the world has changed" hype, I suspect that it will only be a short term change. Before long, everything will be back exactly as it was before.

no,not thoroughly. 

Because there are some contexts in science of education (but I can't provide sources in english before making a research,most of sources that I know are in turkish relevant to this issue ) 

but succintly : covid 19 is only a trigger or an indirect tool for this. 

the contexts that I imply on this issue claim that some more realistic and more modern usages should be available (this system presumably/probably is called as "constructive/contemporary education system" in english)

4 minutes ago, Strange said:

Does The Doctor learn something from each of his new incarnations?

  ok. I provide one observed report to ensure you understand more clearly. 

Once coronavirus deteceted and it had been a pandemic issue many countries announced that the some educational processes would not go on as in its normal system.

although turkey intented to continue in its normal process after a significant amount of time,the system has not started or continued normally

but one thing continued: "distance learning."

now,I am not sure whether everything would be same even if the cure or the vaccine of this disease be found after an undefined/unknown time period. 

meanwhile, there is no effective result in the current case to say that  disease has been eradicated.

I also believe if the pandemic is not a planned action, its cure or vaccine might take very much amount of time to be found,this is the reason why the humanity could not find the cure or vaccine for HIV. anyway, this is another disccussion here, as the time for cure or accine to be found is unpredictable, can we really say that everything would be same  (specifically for education)? 

what do you think about this issue?

39 minutes ago, mathematic said:

Graduate school is always a good idea.  You need to factor personal needs, such as money, your age.

I disagree to this idea.

1 hour ago, Ravenclau said:

While still in college, how should one prepare for the best chance at a statistics job? Is going on to graduate school recommended in the field?

generally if you are hardworking one,then you will eventually find your way, but nevertheless if you work at a theoretical area, then to me, your chance is smaller.

I think computer science is more advantageous. 

if you have suitability to be a contemporary educator or scientist ,then you will already have option to learn by yourself.(i.e.: you will be able to continue (independently) in mathematics)

but in general ,the applied sciences are more advantegous to earn money than theoretic sciences.

one more addition: statistics is known as "applied mathematics" in some universities, applied mathematics cannot be limited with statistics though.

ow,I think I found or I can find many   just being relevant and responsible one is sufficient  

this therad can be closed or deleted. 

hi,

I feel myself at some stages still new. but Although all articles that I scanned contain "results" section with numeric analyses (e.g. manova's or other spss analyses), I do not know  whether such types of analyses are mandatory or numeric or graphic representations. I mean only for theoretical articles. 

hımm yes,at a time I remember one article at a known journal presumably with no discussion and results (in fact the tongue was wholly speculative) but still unsure whether such telling methods can be acceptable by good journals.(here by "good" I mean wide IF and indexed databases, as much as possible)

could someone show me articles with no numeric/analytic results in social science and /or arts and humanity sciences?

thanks

thank you for this post. I really appreciate if the content is cared at any school.

here in turkey the program is generally too much theoretic.

Just now, joigus said:

Also, by "normal" (in this context) I understand:

 

gHg−1⊆H

 

Not "perpendicular". Any more questions?

no (more) questions ,I just tried to understand what you meant 

I think almost all parts of mathematics have intersections (even topology and functional analysis with algebra)

....

21 minutes ago, joigus said:

Take a guess.

I can guess many things really such as Algebraic closure, closure in topology and analysis , and functional analysis...

16 hours ago, joigus said:

 

Edit: You also need Abelian character for showing closure

in mathematics, closure can correspond many things.may I ask:  which type of closure do you meantion here?

11 hours ago, TreueEckhardt2 said:

Thank you for your response.  When you say, "This thread can be analyzed under algebra and number theory," Do you mean that I should post this topic on a different website that deals with algebra and number theory?  Or maybe I should post to the general forum instead of this subforum?

hi,

no, both this website and subforum are correct location for discussion but I meant two things:

i. I recommended that you check algebra (general) and number theory contexts (i.e. books, aricles or notations) 

ii. other approaches would potentially be off topic.

some other mathematicians' ideas would be good here, because I might have forgotten some theorems or maybe I do not remember all of them.

to me,I have not seen  rational contexts for these explanations. but not sure. maybe some other mathematicians' idea might be suitable to make more clear explanation.

for a general redirectory or recommendation: I suggest that you follow general algebraic contexts(this means that this thread can be analyzed under algebra  and number theory)