Search found 156 matches

by Farabor
Mon Nov 18, 2013 6:24 pm UTC
Forum: Mathematics
Topic: Polynomial roots in a generic field
Replies: 2
Views: 1110

Re: Polynomial roots in a generic field

Followup, having found a formula in the book then searched online.....This seems to be Vieta's formulas, with the ring extensions. ( http://en.wikipedia.org/wiki/Vieta%27s_formulas So...the formula definitely holds, is the result back in the original integral domain/field though? Pretty sure...
by Farabor
Mon Nov 18, 2013 6:08 pm UTC
Forum: Mathematics
Topic: Polynomial roots in a generic field
Replies: 2
Views: 1110

Polynomial roots in a generic field

So, in the course of a semi-unrelated problem, the following question came up. In the real numbers, polynomials factor into linear terms and irreducable quadratics, who's roots are complex congugates in the complex numbers. This means that if you take the complex numbers as algebraic complete field ...
by Farabor
Mon Nov 18, 2013 6:20 am UTC
Forum: Mathematics
Topic: Cantor set problem from Pugh
Replies: 8
Views: 2518

Re: Cantor set problem from Pugh

Neat discussion, thanks for the thoughts! Of course, we're not even touching cantor sets in my class until next semester...silly professor doesn't use the textbook at all.
by Farabor
Wed Nov 13, 2013 7:30 pm UTC
Forum: Mathematics
Topic: Cantor set problem from Pugh
Replies: 8
Views: 2518

Cantor set problem from Pugh

So I'm taking my first graduate level Analysis course, and the textbook has a three star problem in it: One that the author doesn't know the answer to. The book is Real Mathematical Analysis, by Charles Pugh. I thought I'd pose the problem here to see if anyone either knows the answer or would like ...
by Farabor
Mon Oct 21, 2013 12:32 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1280: "Mystery News"
Replies: 42
Views: 11213

Re: 1280: "Mystery News"

Oh, and my quick fix to this problem is to mute my volume.
by Farabor
Mon Oct 21, 2013 5:41 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1280: "Mystery News"
Replies: 42
Views: 11213

Re: 1280: "Mystery News"

BlitzGirl wrote:Or it might be a large computer-ish object known as your television. Try that.

What is this strange magic you speak of?
by Farabor
Thu Oct 17, 2013 3:38 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1278: "Giraffes"
Replies: 67
Views: 21357

Re: 1278: "Giraffes"

My hobby: Enumerating Randall's hobbies.

(Not actually going to enumerate them, I'm lazy and have a linear algebra midterm I should be working on!)
by Farabor
Thu Oct 17, 2013 2:14 am UTC
Forum: Mathematics
Topic: Order of magnitude of mathematical knowledge?
Replies: 3
Views: 2153

Order of magnitude of mathematical knowledge?

So, I was chatting with my fellow (first year) graduate students today and the question came up of "What percent of mathematical knowledge would one possess at the average new Ph.D of mathematics?" Obviously this is a question of order of magnitude, and it's somewhere pretty danged low. .0...
by Farabor
Tue Oct 08, 2013 4:43 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1274: Open Letter
Replies: 162
Views: 39638

Re: 1274: Open Letter

dp2 wrote:Where's the Shadow Government when you need it?

http://www.youtube.com/watch?v=OI6Qdoq679I


Just ask Shadowfacts, duh!
by Farabor
Fri Oct 04, 2013 3:26 pm UTC
Forum: Mathematics
Topic: Fields of characteristic 2?
Replies: 7
Views: 7468

Re: Fields of characteristic 2?

It does, quite a bit! Although I really need to bone down on my factor groups and ring ideals (We're doing factor groups now in Herstein's classic book, probably won't get to ring ideals until next semester at this pace)
by Farabor
Fri Oct 04, 2013 4:08 am UTC
Forum: Mathematics
Topic: Fields of characteristic 2?
Replies: 7
Views: 7468

Fields of characteristic 2?

So, I'm a first semester grad student in mathematics, and in the course of my linear algebra class the professor messed up in the notes by not including the restriction that a bunch of the theorems for a vector space V over an arbitrary field F only held if the characteristic of the field is not 2. ...
by Farabor
Thu Oct 03, 2013 5:25 am UTC
Forum: Mathematics
Topic: Linear functionals in an infinite dimension vector space
Replies: 11
Views: 3002

Re: Linear functionals in an infinite dimension vector space

An infinite-dimensional vector space doesn’t even necessarily have a basis…unless you assume the axiom of choice. Yeah, we've gone over that in class, that that's one of the many "Equivalents of the axiom of choices". Amusingly, when I turned in my homework I enumerated my bases for ease ...
by Farabor
Wed Oct 02, 2013 12:42 am UTC
Forum: School
Topic: Plea from a first year Mathematics TA.
Replies: 8
Views: 5083

Plea from a first year Mathematics TA.

/rant on Dear prospective students preparing to enter a math class, Please read the prerequisites listed in the course catalog. These aren't there just to make you spend more money or more time. Contrary to popular opinion, mathematics actually does build upon itself. Among other things, this means ...
by Farabor
Mon Sep 30, 2013 2:38 am UTC
Forum: School
Topic: PhD salary
Replies: 14
Views: 11372

Re: PhD salary

Florida state school here, math department, $20000+ tuition.
by Farabor
Sun Sep 22, 2013 3:00 am UTC
Forum: Mathematics
Topic: Linear functionals in an infinite dimension vector space
Replies: 11
Views: 3002

Linear functionals in an infinite dimension vector space

So, I'm working on a problem in Halmos's Finite Dimensional Vector spaces book to show that there's an isomorphism between (V/M)' and M^0 (functionals on the quotient space and the annihilators space). As part of my proof of the one to one and onto correspondence, I used the fact that functionals ar...
by Farabor
Fri Sep 20, 2013 8:43 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1267: "Mess"
Replies: 110
Views: 21074

Re: 1267: "Mess"

So, I'd just like to point out some basic things here in an attempt to restore sanity: Argument by repeated assertion usually means there's no actual argument/debate going on, just people talking AT each other. Arguing with someone you deem to be an idiot on the internet (Whether or not they actuall...
by Farabor
Wed Sep 18, 2013 12:57 am UTC
Forum: Mathematics
Topic: examples of linear/multilnear functionals?
Replies: 3
Views: 1492

Re: examples of linear/multilnear functionals?

Got it now, thanks!
by Farabor
Wed Sep 18, 2013 12:31 am UTC
Forum: Mathematics
Topic: examples of linear/multilnear functionals?
Replies: 3
Views: 1492

examples of linear/multilnear functionals?

So I'm taking my first graduate level class in Linear Algebra, and we've just covered introduced linear functionals/multilinear functionals/dual spaces. I feel like I understand the abstraction level, that we're learning it at.....the problem is, I'm not able to see concrete examples. So, going to s...
by Farabor
Wed Sep 11, 2013 1:44 am UTC
Forum: Mathematics
Topic: Normal way to show Q(cube root of 2) is a subfield of R?
Replies: 7
Views: 4034

Re: Normal way to show Q(cube root of 2) is a subfield of R?

Thank you all for the replies, I'm (mostly) following where this goes....sadly, I kind of hazed over my polynomial ring ideals part of my undergrad abstract algebra class. Hopefully the grad level 1 will get me up to speed on this. (I was just kind of puzzled to find this problem in my _linear_ alge...
by Farabor
Tue Sep 10, 2013 10:02 am UTC
Forum: Mathematics
Topic: Normal way to show Q(cube root of 2) is a subfield of R?
Replies: 7
Views: 4034

Normal way to show Q(cube root of 2) is a subfield of R?

So, I just had an assignment in my first graduate level class to show that the set consisting of a+b*(cube root of 2)+c*(cube root of 4), where a,b, and c are rational numbers is a subfield of R. The way I showed the only nontrivial part (Multiplicative inverses was) I mapped the multiplication of t...
by Farabor
Tue Sep 10, 2013 9:53 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1262: "Unquote"
Replies: 100
Views: 19803

Re: 1262: "Unquote"

And yet, sadly, noone in my Spanish class in college had seen Rocky.
by Farabor
Fri Sep 06, 2013 11:19 pm UTC
Forum: Mathematics
Topic: Partitioning a group by cosets-axiom of choice?
Replies: 2
Views: 1518

Partitioning a group by cosets-axiom of choice?

So, we were proving Lagrange's theorem in class today (about the order of a subgroup dividing the order of a group). In proving the step that the union of all left cosets of H partitions G, the professor wanted to limit it to finite groups for fear of invoking the axiom of choice. I am 99% confident...
by Farabor
Fri Aug 30, 2013 10:23 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1258: First
Replies: 72
Views: 21760

Re: 1258: First

1258th!

(couldn't resist)
by Farabor
Fri Aug 30, 2013 7:03 pm UTC
Forum: Mathematics
Topic: Any usefulness of this metric?
Replies: 6
Views: 4328

Re: Any usefulness of this metric?

Nicias wrote:Sure. If you have a metric space where you want to preserve the topology but you want to make it bounded in diameter this could be useful since any two points always have d*(x,y)<1.


True, and neat. Thanks! (So glad to finally have made it into grad school. @whee!)
by Farabor
Fri Aug 30, 2013 6:48 pm UTC
Forum: Mathematics
Topic: LaTeX advice?
Replies: 37
Views: 9589

Re: Latec advice?

Err, yes. Windows 8
by Farabor
Fri Aug 30, 2013 6:48 pm UTC
Forum: Mathematics
Topic: Any usefulness of this metric?
Replies: 6
Views: 4328

Any usefulness of this metric?

So, I'm encountering metric spaces for the first time and my professor posed this homework question (Which I've solved btw, no help needed there): Let (E,d) be a metric space. Define a new d* function such that d*(x,y)=d(x,y)/(1+d(x,y)). Show that d* is also a metric on E. Other than an interesting ...
by Farabor
Fri Aug 30, 2013 6:44 pm UTC
Forum: Mathematics
Topic: LaTeX advice?
Replies: 37
Views: 9589

LaTeX advice?

So, I've just started grad school, and I've never used any form of software for LaTeX...any advice on which I should use/where I can go to learn how to type up my math homework/papers?
by Farabor
Mon Aug 12, 2013 6:24 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1250: "Old Accounts"
Replies: 54
Views: 50562

Re: 1250: "Old Accounts"

Post by TimeLurker
I'd be careful which online community you leave. I’ve heard of places where, if they suspect you might be leaving, they tie you up in their basement and force you too stay. :wink:


There are places you have to pay extra for that service!
by Farabor
Fri Jun 28, 2013 7:04 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1231: "Habitable Zone"
Replies: 51
Views: 13701

Re: 1231: "Habitable Zone"

PiZZaMartijn wrote:Sounds like you need a edgeless safety cube


The earth actually has 4 24 hour days per day.....
by Farabor
Fri Jun 28, 2013 6:50 pm UTC
Forum: Mathematics
Topic: Clever High School Math Problems
Replies: 31
Views: 13814

Re: Clever High School Math Problems

My favorite problem was posed to me after 5th grade as part of an entrance exam to an advanced math program Find a 10 digit number such that the first digit tells how many 0s there are in the number, the second digit tells how many 1s there are in the number, the third how many 2's, all the way up t...
by Farabor
Tue May 28, 2013 5:33 am UTC
Forum: Mathematics
Topic: Origin of e as group identity?
Replies: 7
Views: 2543

Re: Origin of e as group identity?

Yeah, due to confusions and changing on requirements on me from my first to last years of finally getting my bachelor's degree, I ended up needing to get 2 semesters of a language in in spring/summer, and the only way I could guarantee that down here was to take Spanish. Le sigh. Hell, I'd have pref...
by Farabor
Mon May 27, 2013 9:11 pm UTC
Forum: Mathematics
Topic: Origin of e as group identity?
Replies: 7
Views: 2543

Re: Origin of e as group identity?

Thanks...I knew there was a reason I wanted to take german, as opposed to the Spanish I found myself being made to take for scheduling reasons....
by Farabor
Mon May 27, 2013 3:50 pm UTC
Forum: Mathematics
Topic: Origin of e as group identity?
Replies: 7
Views: 2543

Origin of e as group identity?

Out of idle curiosity for any history of math buffs, anyone know (or have a reasonable sounding theory) on the traditional use of the lower case e for the identity element of a group? (re)taking a modern algebra class now and it's been bugging me for no apparent reason.
by Farabor
Sun Apr 21, 2013 5:17 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1201: "Integration by parts"
Replies: 81
Views: 25617

Re: 1201: "Integration by parts"

So, I'm a bit confused at all the comments about it not being easy to teach people what, generally, they should use/identify for this technique. When I teach it, especially for beginning calculus problems, there are pretty much exactly two cases you'll use it. In both cases, its freaking obvious wha...
by Farabor
Fri Mar 29, 2013 6:58 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1192: "Humming"
Replies: 53
Views: 10980

Re: 1192: "Humming"

I just came here to say....you guys rock. We have the best geeks of all kinds gathered in one place, and this and Time and factoring graham's number+1 is what we do....

Cancer can wait!
by Farabor
Wed Mar 27, 2013 10:56 pm UTC
Forum: Mathematics
Topic: Speed limit for series convergance/divergence?
Replies: 4
Views: 1309

Re: Speed limit for series convergance/divergence?

No, Rudin has some good exercises that contribute to an argument that no such sequence exists http://math.stackexchange.com/questions/20378/which-series-converges-the-most-slowly Thanks for the link, followed it and the followups....not fully up to some of the theorems mentioned in the mathoverflow...
by Farabor
Wed Mar 27, 2013 5:49 pm UTC
Forum: Mathematics
Topic: Speed limit for series convergance/divergence?
Replies: 4
Views: 1309

Speed limit for series convergance/divergence?

So, in the math lab we were talking about the idea of using the comparison tests as a "speed limit" for how fast a sequence needs to go to 0 in order for its series to converge. IE 1/x diverges, goes too slow. 1/(xlnx) goes a bit faster to 0, but is still too slow. 1/e^x is fast enough for...
by Farabor
Tue Mar 26, 2013 2:48 am UTC
Forum: School
Topic: Awesome Teacher Quotes
Replies: 1764
Views: 394306

Re: Awesome Teacher Quotes

My Spanish teacher, on giving an explanation on the proper uses of one two different words for "to know"

"Conoces the Muffin Man?"
by Farabor
Fri Mar 22, 2013 7:22 pm UTC
Forum: Mathematics
Topic: (Semi homework) Recursive polynomial functions
Replies: 5
Views: 2091

(Semi homework) Recursive polynomial functions

So, I have a homework problem that we worked out how to solve, but it required one thing that's been asserted to be true, but I'm not sure why. The asserted fact is: If a function f(n) fits the form f(n+1)=f(n)+p(n), where p(n) is a known polynomial of degree k, then f(n) itself is a polynomial of d...
by Farabor
Tue Mar 12, 2013 8:05 am UTC
Forum: Mathematics
Topic: Direction to study for Lambert W function?
Replies: 8
Views: 3859

Re: Direction to study for Lambert W function?

Ahh, I see. Thanks....the book I was reading from didn't make it clear that that was the origin of the W function and that it was the inverse of xe^x. So I was just staring at this odd piecewise defined function with power series/log series and was like "What is this?"

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