[QUOTE=JohnnyMo1;40315918]Can't get over this:
[url]http://thatsmathematics.com/mathgen/[/url][/QUOTE]
Thats gold hahahaha
XKCD providing useful tips as always
[img]http://imgs.xkcd.com/comics/integration_by_parts.png[/img]
[QUOTE=JohnnyMo1;40334028]Man, I'm finding certain proofs legitimately fun. I just did one for my topology midterm that involved appealing to the fact that finite products of connected spaces and compact spaces are connected and compact respectively, and then appealing to the generalized version of the extreme value theorem, and then the generalized intermediate value theorem. Slick.[/QUOTE]
I don't really know what any of that is, but it sounds awesome.
Is anyone here taking a bachelor in mathematics? I'm thinking about reading it alongside my engineering program, but I wonder if it's rewarding enough. Is there a noticeable difference in thoroughness when you compare the two (mathematics wise)?
[editline]21st April 2013[/editline]
And what's a typical job in which one can apply these mathematics?
I'm currently a sophemore dualing in Mathematics and Physics. Unfortunately at my CC, there's not enough Physics courses, so at the moment I'm about a year behind on the physics degree, and in turn, getting three years (about) of mathematics finished.
For me, career paths range from highschool teaching to theoretical physics, as well as general engineering and specific areas of choice in the physics field. I haven't done a lot of research with the math degree, being as for our school the math and physics degrees are only five (if I remember correctly) classes different, that I felt like I was shorting myself if I chose not to pursue both.
[QUOTE=Anglor;40360166]Is anyone here taking a bachelor in mathematics? I'm thinking about reading it alongside my engineering program, but I wonder if it's rewarding enough. Is there a noticeable difference in thoroughness when you compare the two (mathematics wise)?
[editline]21st April 2013[/editline]
And what's a typical job in which one can apply these mathematics?[/QUOTE]
Math math is going to be waaaaay more thorough than engineering math. My physics math is more through than engineering math and my math math is far more through than that.
[QUOTE=Anglor;40360166]Is anyone here taking a bachelor in mathematics? I'm thinking about reading it alongside my engineering program, but I wonder if it's rewarding enough. Is there a noticeable difference in thoroughness when you compare the two (mathematics wise)?
[editline]21st April 2013[/editline]
And what's a typical job in which one can apply these mathematics?[/QUOTE]
As Johnny says, maths will be (or at least should be) a lot more thorough in the details than engineering!
Typical applications for maths here are things like software development, banking (quantitative analyst), teaching and even some [url=http://en.wikipedia.org/wiki/Government_Communications_Headquarters]civil service positions[/url]. Of course you can also stay in academia for a research position or do something totally different - I think a maths degree is generally fairly highly regarded in a broad range of careers.
As with most non-vocational degrees it's hard to find a real job that really uses what you learn directly but the general approach and problem-solving type skills are definitely transferrable.
[QUOTE=JohnnyMo1;40361851]Math math is going to be waaaaay more thorough than engineering math. My physics math is more through than engineering math and my math math is far more through than that.[/QUOTE]
this is why im minoring in math along with a software engineering major
even though software engineering is probably the department with the most math involved, its still not enough for me
does anyone know how i would get the constant which you add to -x/arcsin x to make the ends touch with x/arcsin x
[QUOTE=Eltro102;40371067]does anyone know how i would get the constant which you add to -x/arcsin x to make the ends touch with x/arcsin x[/QUOTE]
Well you want it to meet at x=1 (and -1) right? So see what the values of the two functions are at x=1 and then find the difference...
doh! how could i miss that, although I thought it would be some funky math constant like pi or e
[editline]21st April 2013[/editline]
its, 1.27323954212 if anyone cares
[QUOTE=Eltro102;40371529]doh! how could i miss that, although I thought it would be some funky math constant like pi or e
[editline]21st April 2013[/editline]
its, 1.27323954212 if anyone cares[/QUOTE]
(otherwise known as 4/pi)
Thanks for the input guys!
Hey, I'm just starting to learn first order differential equations and I got no clue how to solve this one
[url]https://www.dropbox.com/s/89rqm9j020xrsrx/IMAG0019.jpg[/url]
(sorry for the crap phone pic)
I might be wrong, but it seems to me that y(x)=ln(2exp(2x)/(1-exp(2x))) is a solution to that.
[editline]22nd April 2013[/editline]
Hold on a minute, I'll explain a bit.
[editline]22nd April 2013[/editline]
[img]http://uppix.net/6/b/2/b82dcaba70d259b4184ecccef5a90.png[/img]
Then you integrate all that:
[img]http://uppix.net/8/3/3/79a7a780112734545809e8951b648.png[/img]
Then do an integration by substitution with u=exp(y) as a substitute.
We have u=exp(y) => y=lnu => dy=du/u
[img]http://uppix.net/a/a/d/ad37f0ca040ff4ad52a2b88c60223.png[/img]
[QUOTE=_Axel;40378621]
Man, I really should learn LaTeX, this looks horrible.[/QUOTE]
Microsoft Words equation editor
[QUOTE=Drakehawke;40378797]Microsoft Words equation editor[/QUOTE]
is terribad
[QUOTE=Drakehawke;40378797]Microsoft Words equation editor[/QUOTE]
I can't believe you just said that, I'm almost crying.
[editline]22nd April 2013[/editline]
I mean
[IMG]http://quicklatex.com/cache3/ql_867a67a0c7e75edc661b42bb91e9db6c_l3.png[/IMG]
[QUOTE=_Axel;40378621]I might be wrong, but it seems to me that y(x)=ln(2exp(2x)/(1-exp(2x))) is a solution to that.
[editline]22nd April 2013[/editline]
Hold on a minute, I'll explain a bit.
[editline]22nd April 2013[/editline]
[img]http://uppix.net/6/b/2/b82dcaba70d259b4184ecccef5a90.png[/img]
Then you integrate all that:
[img]http://uppix.net/8/3/3/79a7a780112734545809e8951b648.png[/img]
Then do an integration by substitution with u=exp(y) as a substitute.
We have u=exp(y) => y=lnu => dy=du/u
[img]http://uppix.net/a/a/d/ad37f0ca040ff4ad52a2b88c60223.png[/img][/QUOTE]
thanks <3
Aw man, I lost track of time and missed the first hour (out of an hour and fifteen minutes) of my topology lecture today, and my professor said he'd Xerox me his lecture notes for the day.
What a cool guy.
[QUOTE=Drakehawke;40378797]Microsoft Words equation editor[/QUOTE]
Codecogs ftw over MS Word!
[url]http://www.codecogs.com/products/eqneditor/editor.php?mode=NEW[/url]
Also; tangentially related. How would I evaluate this integral? It was on my test today, and I'm not 100% certain I did it correctly. I got either -1 or -4; I can't remember which.
[img]http://latex.codecogs.com/gif.latex?\int_{1}^{\infty%20}%20\frac{ln(x))}{x^2}[/img]
[editline]22nd April 2013[/editline]
That integral is also dx, btw. For some reason I forgot to include that on accident.
[QUOTE=mastoner20;40381904]Codecogs ftw over MS Word!
[url]http://www.codecogs.com/products/eqneditor/editor.php?mode=NEW[/url]
Also; tangentially related. How would I evaluate this integral? It was on my test today, and I'm not 100% certain I did it correctly. I got either -1 or -4; I can't remember which.
[img]http://latex.codecogs.com/gif.latex?\int_{1}^{\infty%20}%20\frac{ln(x))}{x^2}[/img]
[editline]22nd April 2013[/editline]
That integral is also dx, btw. For some reason I forgot to include that on accident.[/QUOTE]
I used integration by parts with f(x) = lnx and g'(x) = 1/x[sup]2[/sup].
After a single round I got -(lnx + 1)/x for the antiderivative, and for the improper integral I got 1 since the antiderivative approaches 0 as x gets large, and equals -1 at x = 1. 0 - -1 = 1.
It's definitely really easy to get a sign mismatch, and I don't know for certain that I'm right, but I think I kept track of my signs well.
Okay, then hopefully I'm not too far off, although after using integration by parts I got:
[img]http://latex.codecogs.com/gif.latex?\int_{1}^{\infty%20}%20\frac{ln(x)}{x^2}dx%20=%20\lim_{t\rightarrow%20\infty}\int_{1}^{t%20}%20ln(x)\frac{1}{x^2}dx%20=%20\lim_{t\rightarrow%20\infty}xln(x)\cdot%20ln\left%20|%20x^2%20\right%20|%20-%20\int_{1}^{t}%20ln\left%20|%20x^2%20\right%20|\cdot%20\frac{1}{x}dx[/img]
and
[img]http://latex.codecogs.com/gif.latex?=%20\lim_{t\rightarrow%20\infty}%20xln(x)\cdot%20ln\left%20|%20x^2%20\right%20|%20-%20x^2ln\left%20|%20x^2%20\right%20|%20\cdot%20ln\left%20|%20x%20\right%20|%20+%20\int_{1}^{t}%20ln\left%20|%20x%20\right%20|\cdot%20\frac{2x}{x^2}dx[/img]
I went further and did some sort of weird e*ln(stuff) mumbo-jumbo and got -1 on the test, is all I remember. That derivation is going from memory, as well, though.
[QUOTE=mastoner20;40382535]Okay, then hopefully I'm not too far off, although after using integration by parts I got:
[img]http://latex.codecogs.com/gif.latex?\int_{1}^{\infty%20}%20\frac{ln(x)}{x^2}dx%20=%20\lim_{t\rightarrow%20\infty}\int_{1}^{t%20}%20ln(x)\frac{1}{x^2}dx%20=%20\lim_{t\rightarrow%20\infty}xln(x)\cdot%20ln\left%20|%20x^2%20\right%20|%20-%20\int_{1}^{t}%20ln\left%20|%20x^2%20\right%20|\cdot%20\frac{1}{x}dx[/img]
and
[img]http://latex.codecogs.com/gif.latex?=%20\lim_{t\rightarrow%20\infty}%20xln(x)\cdot%20ln\left%20|%20x^2%20\right%20|%20-%20x^2ln\left%20|%20x^2%20\right%20|%20\cdot%20ln\left%20|%20x%20\right%20|%20+%20\int_{1}^{t}%20ln\left%20|%20x%20\right%20|\cdot%20\frac{2x}{x^2}dx[/img]
I went further and did some sort of weird e*ln(stuff) mumbo-jumbo and got -1 on the test, is all I remember. That derivation is going from memory, as well, though.[/QUOTE]
woah that's some funky integration by parts you've got going there...
Letting u=ln(x) and dv/dx = 1/x[sup]2[/sup] you should end up with something very easy to integrate, since then du/dx = 1/x and v = -1/x
The answer [i]is[/i] -1, so that's good, but the only place you should need to do funky stuff with ln is to calculate ln(x)/x for x-> infinity, but that's (clearly?) 0.
Oh, I see what it was I was doing wrong! Thanks! For some reason I was thinking int(1/x²) was ln x², which, you're right, it isn't. Thanks for clearing it up! Now I can hope I get about 1/2 a point on my 10pt problem for getting the right numerical answer! Haha.
[quote][url=http://facepunch.com/showthread.php?t=1186816&p=40393649&viewfull=1#post40393649][B]Do you know, said the youth, that the eyes in this body of yours are now bound and closed,[/B][/url][/quote]
If the metric space the eyes are in has the Heine-Borel property, then they're compact.
[editline]23rd April 2013[/editline]
I wanted to make that joke in the thread but it was both irrelevant, and I doubt any of the stoners would have gotten it.
I tried to prove for myself that incoming light rays parallel to the axis of a parabolic mirror always converge to the focus
6 pages of calculus and no solution later I looked it up and it's provable with a small diagram and a single trivial derivative :suicide:
[QUOTE=JohnnyMo1;40380922]Aw man, I lost track of time and missed the first hour (out of an hour and fifteen minutes) of my topology lecture today, and my professor said he'd Xerox me his lecture notes for the day.
What a cool guy.[/QUOTE]
What kind of stuff are you doing in topology? We've just gotten up to the notion of being compact in a topological space. I really need to find some examples of finite subcovers for various compact sets to help me see what's going on. And I missed how this definition of being compact implies closed and bounded in a metric space.
[QUOTE=DainBramageStudios;40400779]I tried to prove for myself that incoming light rays parallel to the axis of a parabolic mirror always converge to the focus
6 pages of calculus and no solution later I looked it up and it's provable with a small diagram and a single trivial derivative :suicide:[/QUOTE]
Yup... We pretty much stream-lined that entire section of our book (3 chapters) into a single day's lecture in Physics, and boiled it down to three equations to always know and use. Just in time for our exam Monday... -.-
[QUOTE=ThisIsTheOne;40403198]What kind of stuff are you doing in topology? We've just gotten up to the notion of being compact in a topological space. [/QUOTE]
We've just started a bit of algebraic topology. We did homotopies and path homotopies, covering spaces, and now we're working up to the fundamental group of S[sup]1[/sup].
[QUOTE=ThisIsTheOne;40403198]I really need to find some examples of finite subcovers for various compact sets to help me see what's going on. [/QUOTE]
I like the example of X = {1/n : n is a natural number} union {0} in the subspace topology from R. It's compact. To see it, imagine an infinite open cover A of X. Some element of A must contain 0. (assume the element is a basis element, just for simplicity's sake, you don't lose generality) That element is going to look like (a,b) intersect X for some a < 0 and b > 0. The only points of A left uncovered are points of X greater than or equal to a, and it should be easy to see that there are only finitely many such points, so they can be covered by a finite subcollection of A.
I can think of some other examples if you'd like.
[QUOTE=ThisIsTheOne;40403198]And I missed how this definition of being compact implies closed and bounded in a metric space.[/QUOTE]
It doesn't imply that for general metric spaces. Spaces in what that does hold are sometimes called Heine-Borel spaces or said to have the Heine-Borel property.
[editline]24th April 2013[/editline]
Really, finding a single finite subcover for a compact set doesn't help, since for compactness you need to show that EVERY open cover has a finite subcover.
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