Search found 156 matches

by Farabor
Mon Jun 23, 2014 3:50 am UTC
Forum: Mathematics
Topic: The Most Important Math
Replies: 48
Views: 19495

Re: The Most Important Math

The answer is clearly logic. Proof: Every argument in this thread uses logic to justify its truth. Thus logic is the essential underpinning of everything :) I'm with Farabor. Math is based on the idea that logic is... well, logical. E.g. axioms in any field of mathematics are statements that are co...
by Farabor
Sat Jun 21, 2014 12:39 am UTC
Forum: Mathematics
Topic: The Most Important Math
Replies: 48
Views: 19495

Re: The Most Important Math

The answer is clearly logic. Proof: Every argument in this thread uses logic to justify its truth. Thus logic is the essential underpinning of everything :)
by Farabor
Fri Jun 13, 2014 10:24 pm UTC
Forum: School
Topic: Title for grad student teaching a class?
Replies: 16
Views: 16197

Title for grad student teaching a class?

Well, I'm a Graduate Teaching Assistant in mathematics at my local university. Starting in the fall I'll be teaching a course full time. I'm caught debating what to have the students call me. Mr.? Professor? First name?
by Farabor
Wed May 28, 2014 10:50 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1374: "Urn"
Replies: 91
Views: 17501

Re: 1374: "Urn"

orthogon wrote:What's an imaginary urn?


A real urn times i, of course.
by Farabor
Fri May 16, 2014 9:52 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1369: TMI
Replies: 51
Views: 17781

Re: 1369: TMI

Just remember, TMI is a TLI, not a TLA.
(Just like TLA is actually a TLI, not a TLA. Pedants FTW!)
by Farabor
Sat May 10, 2014 3:16 am UTC
Forum: Mathematics
Topic: Second order differential equations - why doesn't this work?
Replies: 5
Views: 2344

Re: Second order differential equations - why doesn't this w

As a minor note: c 1 e ax +c 2 e ax = b 1 cosh(ax) + b 2 sinh(ax) As long as a is real. You can convert from to the other just using algebra. If a is imaginary, you get sin/cos instead. As an alternate approach, you can write y'' - y = 0 as an equation of the form (D^2 - 1)y = 0, where D = d/dx to ...
by Farabor
Sat May 10, 2014 3:10 am UTC
Forum: Mathematics
Topic: How to augment mathematical education?
Replies: 7
Views: 3352

Re: How to augment mathematical education?

Since you have time on your hands, I'd recommend reading "Gödel, Escher, Bach: An Eternal Golden Braid". It's an amazing work that, among other things, will walk you through parts of the foundational crisis in mathematics and Gödel's incompleteness theorem. (On a side note, I love that the...
by Farabor
Tue May 06, 2014 12:19 am UTC
Forum: Mathematics
Topic: Text advice requested: Multivariable Analysis
Replies: 3
Views: 2182

Re: Text advice requested: Multivariable Analysis

I just looked at that link, and it looks very inappropriate....it seems to presume that I know material that I don't actually know. I'm thinking about that Spivak book, as I liked his "Calculus" that I had in undergraduate analysis.
by Farabor
Mon May 05, 2014 5:45 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1364 - "Like I'm Five"
Replies: 59
Views: 21597

Re: 1364 - "Like I'm Five"

How much math is in a ton of math? If it's stored on 64GB MicroSD cards weighing 2g each... it's somewhere in the order of "all the math". You should say "all known math", as I'm quite sure we have not yet been able to measure how much math we have yet to discover. I think it ma...
by Farabor
Mon May 05, 2014 5:32 pm UTC
Forum: Mathematics
Topic: Text advice requested: Multivariable Analysis
Replies: 3
Views: 2182

Text advice requested: Multivariable Analysis

I recently finished a first year graduate course in multivariable analysis using the book "Analysis on Manifolds" by James R Munkres. Unfortunately, due to several factors (The teacher using completely different definitions of a manifold than the text, the pacing of the class, etc.), I lef...
by Farabor
Mon Apr 07, 2014 9:47 am UTC
Forum: Mathematics
Topic: Fields of characteristic 2?
Replies: 7
Views: 7469

Re: Fields of characteristic 2?

So, I've progressed in my studies into the beginnings of multivariable analysis/linear algebra. I'm now curious as to how things like determinants act when the underlying field is of characteristic 2. Normally the determinant being 0 of a matrix if and only if the vectors are linearly independent co...
by Farabor
Tue Mar 11, 2014 9:38 pm UTC
Forum: Mathematics
Topic: algebraic degree of sin(1 degree)
Replies: 4
Views: 2728

algebraic degree of sin(1 degree)

So, I've just finished showing that sin (1 degree) is algebraic for my homework problem. I used the method of Euler's equation, with e^(i*90 degrees), which lead me to a 180 degree polynomial in sin(1 degree) (Danged overloaded term, degree!). Thus, I've got it's algebraic of degree no more than 180...
by Farabor
Wed Feb 26, 2014 5:57 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1335: "Now"
Replies: 131
Views: 62214

Re: 1335: "Now"

When will it be now?
Soon.
by Farabor
Sun Feb 16, 2014 7:36 am UTC
Forum: Mathematics
Topic: expressing finite amount of sets with notation
Replies: 7
Views: 2586

Re: expressing finite amount of sets with notation

If you really wanted to do this, this should work: ∀ A ,∃ n ∈ N # A = n ⇒( A ⊂ T ⇒∩ a ∈ A a ∈ T ) This'd read, unless sleep dep is messing with me: For all nonempty subsets of T with finite cardinality, the intersection of all of the elements of that subset is also in T, which is I believe w...
by Farabor
Sat Feb 15, 2014 3:44 am UTC
Forum: Mathematics
Topic: Meta fundamental theorem.
Replies: 7
Views: 3106

Meta fundamental theorem.

So, I was tutoring some kids in an intro to abstract algebra class, and they could not seem to get the importance of actually knowing/understanding the Fundemental Theorem of Arithmetic for their assignment. This led to the following new formulation that went well amongst my fellow TAs, so I thought...
by Farabor
Tue Feb 11, 2014 1:59 am UTC
Forum: Mathematics
Topic: A probability(?) problem
Replies: 13
Views: 4119

Re: A probability(?) problem

sgfw wrote:[b]
My friend believes that there is not enough information to make a practical conclusion.


You're both right. There's an infinitesimally tiny higher probability of a 2. Practically speaking, that's nothing. All depends on how you look at it.
by Farabor
Tue Feb 11, 2014 1:57 am UTC
Forum: Mathematics
Topic: mini-rant on convolution integrals
Replies: 6
Views: 2965

Re: mini-rant on convolution integrals

mark999 wrote:I don't have a problem with people using t and tau. They're clearly different.


Some of us have horrible handwriting, and not much better eyesight....
by Farabor
Sat Feb 08, 2014 4:06 am UTC
Forum: Mathematics
Topic: Axiomatic mathematics has no foundation
Replies: 158
Views: 35071

Re: Axiomatic mathematics has no foundation

Nothing has an absolute foundation when it comes to anything which requires communication. How do you define a word? By reference to other words. Circular logic. It just so happens that as social animals our brains have the ability to construct shared meaning. Even grunting/pointing/other forms of c...
by Farabor
Fri Feb 07, 2014 3:42 am UTC
Forum: Mathematics
Topic: mini-rant on convolution integrals
Replies: 6
Views: 2965

mini-rant on convolution integrals

So, teaching people convolution integrals (which I've only done a few of myself in my undergrad), I'm constantly reminded of how annoyed I am at the variable choice that seems to be in all the textbooks I see. Why, for the love of (insert deity/platonic ideal here)'s name would you use a lower case ...
by Farabor
Tue Feb 04, 2014 10:15 pm UTC
Forum: Mathematics
Topic: (Solved) Series/sequence convergance
Replies: 5
Views: 2108

Re: (homework) Series/sequence convergance

So, according to my calculations, a closed form of the n'th term of hte sequence is ((4^n)*n!*n!)/(2n+1)! . Taking logs gives me n*log4+2*log(n!)-log((2n+1)!). I'm seeing that if I want this to go to 0, the log is going to have to go to -infinity, not 100% sure on the derivitive or how log grows in...
by Farabor
Tue Feb 04, 2014 4:06 am UTC
Forum: Mathematics
Topic: (Solved) Series/sequence convergance
Replies: 5
Views: 2108

Re: (homework) Series/sequence convergance

So, according to my calculations, a closed form of the n'th term of hte sequence is ((4^n)*n!*n!)/(2n+1)! . Taking logs gives me n*log4+2*log(n!)-log((2n+1)!). I'm seeing that if I want this to go to 0, the log is going to have to go to -infinity, not 100% sure on the derivitive or how log grows in ...
by Farabor
Tue Feb 04, 2014 12:39 am UTC
Forum: Mathematics
Topic: Did I discover smth old or new? (prime related)
Replies: 6
Views: 2114

Re: Did I discover smth old or new? (prime related)

Now, the strange thing is that if you add up Prim and NonP, you get the current number. I ask you kindly, what is the name of this property? It is called the fundamental theorem of equivalence relations . But I think the more important question here is, “How was the user name ‘untitled’ not registe...
by Farabor
Tue Feb 04, 2014 12:35 am UTC
Forum: Mathematics
Topic: Need help understanding the usual topology on R
Replies: 23
Views: 5612

Re: Need help understanding the usual topology on R

Xenomortis wrote:Measure Theory?
(Undergrad mathematics)


Well, we're getting to measure theory later on in this semester (Which is my second semester of grad school, in the Analysis track). I'll ask the professor if we'll get to that.
by Farabor
Tue Feb 04, 2014 12:34 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1325: "Rejection"
Replies: 515
Views: 113977

Re: 1325: "Rejection"

Amusingly enough, I AM the proverbial universally regarded nice guy who's (almost) always been alone/out of a relationship...and frequently am the one who's shoulder is cried upon. The niceness part comes from feedback I get from others....and I can tell you this, there is NOTHING more frustrating t...
by Farabor
Tue Feb 04, 2014 12:14 am UTC
Forum: Mathematics
Topic: (Solved) Series/sequence convergance
Replies: 5
Views: 2108

(Solved) Series/sequence convergance

So, I'm working on a problem on whether or not the alternating series of numbers of the form (2*4*6*....n)/(3*5*7*...(2n+1)) converges or not (Basically 2/3 * 4/5 * 5/6, etc). Thus, using ye old alternating series test, I need to check for if the sequence is decreasing and going to 0. That it's decr...
by Farabor
Tue Feb 04, 2014 12:09 am UTC
Forum: Mathematics
Topic: Need help understanding the usual topology on R
Replies: 23
Views: 5612

Re: Need help understanding the usual topology on R

Normalization is totally legit, not a hack at all! So says a "physicist". You probably call the Dirac delta a function non-ironically as well. So, I've dealt with the Dirac delta in differential equations, where it's mentioned that it's not a function, and defines it in terms of its prope...
by Farabor
Sat Feb 01, 2014 1:57 am UTC
Forum: Mathematics
Topic: Need help understanding the usual topology on R
Replies: 23
Views: 5612

Re: Need help understanding the usual topology on R

Cool beans, we're just about to get into integration in R^n right now in my multivariable class, manifolds come later in the semester. Then a summer of prepping for my qualifiers! :)
by Farabor
Fri Jan 31, 2014 4:34 pm UTC
Forum: Mathematics
Topic: (homework) x^3-9 mod 31 irreducible.
Replies: 6
Views: 2640

Re: (homework) x^3-9 mod 31 irreducible.

Yeah, I realized that right before I turned my homework in that the cyclic nature was unnecessary. What was especially silly was because we hadn't gotten to that proof in class, I went ahead and noted that the multiplicative group of Z mod 31 was cyclic for yet another reason (The finite abelian gro...
by Farabor
Thu Jan 30, 2014 10:00 am UTC
Forum: Mathematics
Topic: (homework) x^3-9 mod 31 irreducible.
Replies: 6
Views: 2640

Re: (homework) x^3-9 mod 31 irreducible.

Ahh, got it. That (not so) hidden use of Lagrange's theorem to get that 3*10=30 as the order of the group was the key step I missed. Thanks!
by Farabor
Thu Jan 30, 2014 4:10 am UTC
Forum: Mathematics
Topic: (homework) x^3-9 mod 31 irreducible.
Replies: 6
Views: 2640

(homework) x^3-9 mod 31 irreducible.

So, I'm taking a course on abstract algebra and we've just introduced polynomial rings. One of the exercises is to show that x^3-9 is irreducible in the integers mod 31. First, I note that I can of course brute force a solution by the fact that if there's a way to factor this, at least one term must...
by Farabor
Thu Jan 30, 2014 3:36 am UTC
Forum: Mathematics
Topic: Need help understanding the usual topology on R
Replies: 23
Views: 5612

Re: Need help understanding the usual topology on R

A topology is a collection of sets declared to be “open”. The standard topology on ℝ consists of the open subsets of ℝ, by the usual definition of “open”. Check, so going from metric spaces to topology (Since I've only worked in the former), just means we need a different definition of open sets th...
by Farabor
Thu Jan 30, 2014 3:18 am UTC
Forum: Mathematics
Topic: [Solved] Linear algebra/multivariable calc question
Replies: 11
Views: 3178

Re: [Solved] Linear algebra/multivariable calc question

Strange, I'm in my second semester of grad school, and we did Linear Algebra first followed by Multivariable Analysis (Which I'm currently in). So, just had the joy of a week in class on proving the implicit function theorem without really understanding what the bleep it was. I finally broke down an...
by Farabor
Fri Jan 17, 2014 5:23 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1318: "Actually"
Replies: 76
Views: 15963

Re: 1318: "Actually"

Actually, there's a homeomorphism between all of them, so they're the same, really!

(Okay, so I'm just learning topology now, so sue me....)
by Farabor
Mon Dec 30, 2013 6:07 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1310: Goldbach Conjectures
Replies: 65
Views: 15537

Re: 1310: Goldbach Conjectures

I find the comic mildly amusing, but a logical fail, since the logical chain is "stronger being true automatically implies weaker being true". Actually I think it does if you allow the blasphemy of counting 1 as prime... ok, let's give the comic a bit of leeway there, otherwise I wouldn't...
by Farabor
Mon Dec 30, 2013 6:55 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1310: Goldbach Conjectures
Replies: 65
Views: 15537

Re: 1310: Goldbach Conjectures

I find the comic mildly amusing, but a logical fail, since the logical chain is "stronger being true automatically implies weaker being true".
by Farabor
Wed Dec 11, 2013 12:57 am UTC
Forum: Mathematics
Topic: Equivalent norms question
Replies: 2
Views: 1379

Re: Equivalent norms question

Doh! Finals are frying my brains. Thanks!
(now off to show that |A|=|A*| using the operator norm, instead of the norm I wanted to use....
by Farabor
Tue Dec 10, 2013 10:51 pm UTC
Forum: Mathematics
Topic: Equivalent norms question
Replies: 2
Views: 1379

Equivalent norms question

So, I'm working in a finite dimensional vector space, so I already know all norms are equivalent. I _think_ the following should be trivially true, but I wanted a double check: Is equality in one norm if and only if equality in the other norm? I.e. two vectors have the same length in norm 1 means th...
by Farabor
Wed Nov 27, 2013 10:40 am UTC
Forum: Mathematics
Topic: Thanks for the help!
Replies: 0
Views: 1082

Thanks for the help!

So, I was in the middle of typing up a question for a subpart of my proof of the Cauchy-Binet theorem. (Well, not really _my_ proof, actually mostly stolen from Pugh, but who's counting?) when the process of formulating the question so it'd be understandable to readers prompted me to figure out the ...
by Farabor
Tue Nov 26, 2013 1:05 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1295: New Study
Replies: 50
Views: 10310

Re: 1295: New Study

Klear wrote:
cellocgw wrote:Real statistic: 100% of the time that I want chocolate, I want chocolate.


And 100% members of the tautology club are members of the tautology club.


Let us not forget, The first rule of tautology club is the first rule of tautology club.
by Farabor
Fri Nov 22, 2013 6:33 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1294: "Telescope Names"
Replies: 89
Views: 22880

Re: 1294: "Telescope Names"

This reminds me of a lecture I attended recently on Large cardinals. This particular chain from the huge cardinal wikipedia page comes to mind:


almost n-huge
super almost n-huge
n-huge
super n-huge
almost n+1-huge

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