Search found 47 matches

by Something Awesome
Fri Oct 04, 2013 11:24 am UTC
Forum: Mathematics
Topic: Fields of characteristic 2?
Replies: 7
Views: 7528

Re: Fields of characteristic 2?

Every finite field of characteristic 2 looks like a direct sum of copies of Z/2Z. The field of rational functions over Z/2Z turns out to be an infinite field of characteristic 2. Usually, somewhere in the proof of a theorem, you'll get something like "2x = 0, so x = 0 (and then conclude somethi...
by Something Awesome
Mon Sep 02, 2013 4:05 pm UTC
Forum: Mathematics
Topic: Measuring sphere area
Replies: 10
Views: 3110

Re: Measuring sphere area

And the second would be: what's the correct approach? (cone slices, I presume?) You can also modify your approach to something that works. Instead of varying over dz, you want to hug the sphere as close as you can, with an arclength term ds. With the equation of the sphere R^2+z^2 = r^2, we have r ...
by Something Awesome
Sat Jul 14, 2012 7:51 pm UTC
Forum: Mathematics
Topic: How can I tell if Im good at "Real Math"? + Emphasis anxiety
Replies: 11
Views: 4839

Re: How can I tell if Im good at "Real Math"? + Emphasis anx

Hello forums. I've finished my time at community college where I've finished the calculus line, differential equations, and an intro to logic class. I aced them all, and was chosen to be a math tutor for the school. In the fall, I'm transferring to a university, where I'll be taking a 300 level sta...
by Something Awesome
Sun Apr 08, 2012 4:42 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 489384

Re: Favorite math jokes

At a conference, two mathematicians are debating a recent result in topology. They disagree on its implications, and it soon escalates to personal attacks. "Your momma's so fat, she can't be embedded in R^3!" "Well, your momma's so fat, she's a counterexample to the Whitney Embedding ...
by Something Awesome
Fri Feb 25, 2011 12:37 am UTC
Forum: Mathematics
Topic: What is the best university for mathematical logic
Replies: 12
Views: 4515

Re: What is the best university for mathematical logic

Yeah, logic is extremely tiny nowadays. In the US at least, I've heard good things about University of Michigan, UC Berkeley, University of Illinois at Urbana, and Carnegie Mellon University. Most schools are lucky to have any sort of program for math foundations.
by Something Awesome
Tue Oct 19, 2010 1:25 pm UTC
Forum: Mathematics
Topic: Grade 12 math problems
Replies: 9
Views: 1545

Re: Grade 12 math problems

My teacher's been making a huge deal out of the difference between reciprocal and inverse. Honestly I can't tell the difference. I know that inverse is when x and y are switched, and reciprocal is when you do 1/x and 1/y, but I have no idea when it means which one. And the wording is a little diffe...
by Something Awesome
Mon Oct 18, 2010 3:40 pm UTC
Forum: Mathematics
Topic: RIP Benoit Mandelbrot
Replies: 7
Views: 1674

Re: RIP Benoit Mandelbrot

Even I'll miss him. His work and other work on fractals helped inspire me to work more in mathematics. I think this is his most notable accomplishment: getting more young people excited about math and its beauty. Sure, fractal geometry has all sorts of useful applications, but we wouldn't have thos...
by Something Awesome
Sun Oct 10, 2010 10:13 pm UTC
Forum: Mathematics
Topic: Algebraic Topology! (HW!)
Replies: 3
Views: 1262

Re: Algebraic Topology! (HW!)

For that second one, I'd try showing both are h.e. to a third space - perhaps taking a family of mapping cones corresponding to the homotopy between f and g. So, take X x Y x [0,1] and quotient so that at X x Y x {0} you get the mapping cone of f, at X x Y x {1} you get the mapping cone of Y, and a...
by Something Awesome
Sun Oct 10, 2010 5:40 pm UTC
Forum: Mathematics
Topic: Algebraic Topology! (HW!)
Replies: 3
Views: 1262

Algebraic Topology! (HW!)

I have some lovely homework to do, and being the weekend, my prof isn't available for help. Any hints or gentle nudges toward a proof would be awesome. This one is exercise 0.13 from Hatcher: Show that any two deformation retractions r^0_t and r^1_t of a space X onto a subspace A can be joined by a ...
by Something Awesome
Sun May 16, 2010 6:40 am UTC
Forum: Mathematics
Topic: Show us your articles! Or what's your Erdos number?
Replies: 187
Views: 277234

Re: Show us your articles! Or what's your Erdos number?

I'm a coauthor of a paper that was just accepted to Fractals, which will give me an Erdös Number of 3! (that's 3 excited, not 3 factorial)
by Something Awesome
Sun Mar 21, 2010 5:20 pm UTC
Forum: Mathematics
Topic: Godel Incompleteness Theorem
Replies: 47
Views: 5300

Re: Godel Incompleteness Theorem

Question: I read that Continuum Hypothesis was proved unprovable, but since you can always disprove it by just pointing to a set with cardinality between rationals and reals, doesn't its unprovability imply no such sets exist, proving the hypothesis and contradicting it being unprovable? Because of...
by Something Awesome
Sun Dec 27, 2009 11:24 pm UTC
Forum: Forum Games
Topic: Create a Card: MTG
Replies: 3761
Views: 406075

Re: Create a Card: MTG

Zombie Bludgeon // Zombie Bludgeon 2BB // 2BB Instant // Artifact Creature - Equipment Zombie Target Player loses X life, where X is the number of creatures in his or her graveyard // Equip - 0 Equipped Creature gets +X/-X, where X is one less than its toughness. Good luck figuring this one out... ...
by Something Awesome
Tue Sep 29, 2009 2:45 am UTC
Forum: Mathematics
Topic: "Concatenating" Functions?
Replies: 14
Views: 1696

Re: "Concatenating" Functions?

I peeked ahead to the fundamental group section of my text and they indeed call it concatenation, denoted [imath]f \cdot g[/imath].
by Something Awesome
Tue Sep 29, 2009 12:57 am UTC
Forum: Mathematics
Topic: "Concatenating" Functions?
Replies: 14
Views: 1696

Re: "Concatenating" Functions?

Aha, addition! I've heard of the fundamental group only vaguely: it's one of the topics we're supposed to get to in this class eventually. I'm only using this as part of a proof to show that the relation x \sim y iff there is a path between them is an equivalence relation (obviously the transitivity...
by Something Awesome
Tue Sep 29, 2009 12:15 am UTC
Forum: Mathematics
Topic: "Concatenating" Functions?
Replies: 14
Views: 1696

"Concatenating" Functions?

Given the continuous functions f : [0,1] \rightarrow X and g: [0,1] \rightarrow X such that f(0) = x, f(1) = y, g(0) = y, g(1) = z , define the function h : [0,1] \rightarrow X by h(t) = \begin{cases} f(2t) & t < 1/2 \\ g(2(t-1/2)) ...
by Something Awesome
Tue Aug 04, 2009 3:29 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0618: "Asteroid"
Replies: 188
Views: 52064

Re: "Asteroid" Discussion

How sad! I'm rereading The Little Prince because next year we'll be reading it in the original French, and I'm comparing the two. It's really weird - in one place in the English version there was a reference to 'forty-four sunsets', and in the original it's forty-three ... except later it's suddenl...
by Something Awesome
Mon Aug 03, 2009 1:40 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0618: "Asteroid"
Replies: 188
Views: 52064

Re: "Asteroid" discussion

Rule #1 of life: Don't be a dick. This would include lying about your wife dying. Your avatar is awesomely appropriate here :D J'adore Le Petit Prince . The English translations are actually pretty good; sure, it sounds and reads better in French, but I can't think of anything that's lost in transl...
by Something Awesome
Wed Jul 29, 2009 8:16 pm UTC
Forum: Mathematics
Topic: Polynomials and Possible Zeros
Replies: 5
Views: 1366

Re: Polynomials and Possible Zeros

If you're not familiar with it, there's also the Rational Root Theorem , which tells us what some of the possible roots of an integer polynomial are. If f(x) = a_n x^n + a_{n-1}x^{x-1} +\cdots+ a_0 , then a rational root x=\pm \frac{p}{q} , where p is a factor of a_0 and q is a factor of a_n...
by Something Awesome
Mon Jul 13, 2009 12:37 pm UTC
Forum: Mathematics
Topic: Integrals--Substitution Rule
Replies: 9
Views: 2075

Re: Integrals--Substitution Rule

Mr.RobLikesBrunch wrote:This means that [math]\int^9_0 f(u) \frac{du}{2x}= \int^3_0 xf(x^2)\ dx[/math]

Everything else looks fine, but what happened to the [imath]x[/imath] before the [imath]f(x^2) = f(u)[/imath] on the left side?
by Something Awesome
Sun Jun 28, 2009 6:05 pm UTC
Forum: Mathematics
Topic: Natural math versus foreign language aptitude
Replies: 13
Views: 3953

Re: Natural math versus foreign language aptitude

I've always felt that my aptitude in mathematics has aided and driven my interest in things like language and games. For me, they're all a matter of comprehending the general framework (math: axioms and logic, language: grammar, games: rules) and then the rest are just details that follow (math: the...
by Something Awesome
Sun Jun 21, 2009 7:49 pm UTC
Forum: Gaming
Topic: I need a Game Recommendation
Replies: 1559
Views: 393843

Re: Lovecraftian Games

The card game is in the same vein as Magic, though they've changed over to the "Living" Card Game style (they release small fixed packs of cards every few months or so), though you can still find some of the old booster packs. Mechanically, it's an interesting game where you play character...
by Something Awesome
Sat May 30, 2009 10:47 pm UTC
Forum: Science
Topic: Most geeky thing you've done recently.
Replies: 133
Views: 50136

Re: Most geeky thing you've done recently.

I wrote a MATLAB program that loads an image of a Mercator map, and when you click and drag between two points, it gives you the latitude and longitude of each point and the great-circle distance between them, all for a Dungeons & Dragons world I'm working on.
by Something Awesome
Fri May 01, 2009 12:53 pm UTC
Forum: Mathematics
Topic: number theory solutions
Replies: 17
Views: 1726

Re: number theory solutions

2) Show that no triangle whose vertices are all lattice points can be an equilateral triangle. Hey, these questions look familiar. Are you in my class? I did this second one by assuming an equilateral triangle, fixing a point at (0,0) , letting another point be (x,y) with x,y \in \m...
by Something Awesome
Sun Apr 26, 2009 6:54 am UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 158893

Re: Math: Fleeting Thoughts

Regarding adjective forms of names: It's always amused me to call a set "Zornable" if it satisfies the hypothesis of Zorn's Lemma. I'm also sometimes overly dramatic/graphic when I write proofs: "Since we have shown A to be Zornable, we smack it with Zorn's Lemma and out pops a maxima...
by Something Awesome
Fri Mar 27, 2009 3:17 pm UTC
Forum: Mathematics
Topic: Infinity
Replies: 42
Views: 5230

Re: Infinity

That clears it up quite a bit about omega and aleph. Thanks. I think the big problem was with the lack of rigorous definition that my prof and book gave to the term 'cardinal' (assuming that my notes weren't just sloppy). I had somehow convinced myself that cofinality was cardinality. Can you recom...
by Something Awesome
Thu Mar 26, 2009 1:43 pm UTC
Forum: Mathematics
Topic: Infinity
Replies: 42
Views: 5230

Re: Infinity

I knew I screwed up with the terminology somewhere. Sorry about that. It has been a little while. I was under the impression that alephs and omegas were used interchangeably in the context of set theory. I swear that when asked about that my professor said the reason he uses omegas is that alephs a...
by Something Awesome
Wed Mar 25, 2009 9:20 pm UTC
Forum: Mathematics
Topic: Infinity
Replies: 42
Views: 5230

Re: Infinity

The part about this that always bothered me is this: 0 < 1 < 2 <... < n for any n in N and for any n in N, n < Aleph_0. Aleph_0 < Aleph_1 < Aleph_2 < ... < Aleph_n for any n in N, but Aleph_Aleph = Aleph_0 (because there is a bijection between them). I get why and admittedly my notation is poor her...
by Something Awesome
Wed Feb 18, 2009 10:56 pm UTC
Forum: Mathematics
Topic: The Theorem Thread
Replies: 15
Views: 2044

Re: The Theorem Thread

Here's a cute one I've seen around: Theorem: For all n \in \mathbb{N}, n > 2 , the n^{th} root of 2 is irrational. Proof. Suppose not; let 2^{1/n} = p/q for some integers p,q with q \neq 0 . Then we have \begin{align}2 = \frac{p^n}{q^n}\\ 2q^n = p^n\\ q^n + q^n = p^n,\\ \end{align} contradicting Fer...
by Something Awesome
Sun Jan 25, 2009 4:21 pm UTC
Forum: Mathematics
Topic: Favourite Erroneous "Proofs"
Replies: 194
Views: 43457

Re: Favourite Erroneous "Proofs"

\begin{eqnarray} \lim_{x \to 0}\frac{x}{x} & = & \lim_{x \to 0}\left (\frac{1}{x}x\right) \\ & = & \left (\lim_{x \to 0}\frac{1}{x}\right) \left (\lim_{x \to 0}x\right) \\ \end{eqnarray} Fails here; the limit of the product is equal to the product of the limi...
by Something Awesome
Sun Jan 11, 2009 2:51 am UTC
Forum: Mathematics
Topic: Geometrically hard, algebraically easy problems
Replies: 23
Views: 2901

Re: Geometrically hard, algebraically easy problems

The divided line used by Plato is trivial to prove in terms of algebra, and the geometric proof is a bit more complex, but not too difficult. With algebra, it's a matter of commutativity: r(1-r) = (1-r)r. Using only the ratios given to prove those two ratios are equal is a fun exercise and kinda ele...
by Something Awesome
Tue Nov 11, 2008 3:58 pm UTC
Forum: Mathematics
Topic: LaTeX equation numbering
Replies: 6
Views: 6486

Re: LaTeX equation numbering

It might be best to look up some eqnarray alternatives. I don't know in particular any of them, but perhaps something will be able to do precisely what you want. The ugly way to do it is split the equations into two and manually input the label between them. However, this puts some unwanted space be...
by Something Awesome
Sun Oct 12, 2008 5:01 pm UTC
Forum: Mathematics
Topic: Probability: Expected number of rolls
Replies: 1
Views: 1056

Probability: Expected number of rolls

One of my friends has a pre-D&D ritual where he starts with all of his (say, 12) d6s and rolls them, removes any die that rolled a six, rerolls the remaining dice, and repeats removing any sixes until every die is displaying a six. The question I've been trying to answer is "What is the exp...
by Something Awesome
Sat Sep 13, 2008 5:18 am UTC
Forum: Mathematics
Topic: Set Theory, Anyone?
Replies: 4
Views: 1066

Re: Set Theory, Anyone?

Think about what intersections and unions mean. If a \in A \cap C , then a \in A and a \in C . Union mean or . Now, how do you prove that A \subseteq B ? For every a \in A, show a \in B . One last thing we need to know before we can tackle this proof. What does it mean for A = B ? A \subseteq B and ...
by Something Awesome
Tue Sep 02, 2008 2:44 am UTC
Forum: Movies and TV Shows
Topic: Favorite Foreign Language Films
Replies: 61
Views: 6641

Re: Favorite Foreign Language Films

I've seen a few neat French films, but the one that I love the most is the semi-recent Wasabi , starring Jean Reno who is a bad-ass French cop that finds out he has a 19 year old daughter in Japan whose mother recently died. Reno proceeds to go there and protect his daughter from the Yakuza and kick...
by Something Awesome
Fri Jul 04, 2008 4:02 am UTC
Forum: Gaming
Topic: Favourite Nintendo Series
Replies: 63
Views: 7344

Re: Favourite Nintendo Series

Endless Mike wrote:Last I checked, Nintendo didn't make Mega Man.


D'oh, for some reason I thought the thread was about Nintendo as in NES, not the company.
by Something Awesome
Sat Jun 28, 2008 11:31 pm UTC
Forum: Gaming
Topic: Favourite Nintendo Series
Replies: 63
Views: 7344

Re: Favourite Nintendo Series

I'm a sucker for old school platformers, so my vote goes to...Mega Man. I still play the old ones to try to refine my speed run record (current Mega Man 2 time is 42m 22s, on Difficult of course). My dream is to beat Mega Man 2 while listening to The Protomen's album (around 37m). No disrespect to M...
by Something Awesome
Wed Jun 18, 2008 8:54 pm UTC
Forum: Coding
Topic: data type conversion in matlab
Replies: 2
Views: 1411

Re: data type conversion in matlab

I'm writing a program in matlab. I have a matrix whose entries are all ones and zeros. I want to convert each row vector of the matrix into a binary number whose digits are the entries of the vector. So for example if an arbitrary row of the matrix was [1, 0, 1, 1], I would like to convert it into ...
by Something Awesome
Thu Jun 12, 2008 2:49 am UTC
Forum: Mathematics
Topic: Chaotic Systems
Replies: 13
Views: 1807

Re: Chaotic Systems

marginally_stable wrote:Humm...I would like to see an example where it is not exponential. I cannot think of any simple one at the moment.

Neither can I, which is why I said I'm not sure. As Token said, it doesn't seem to be required in the definition. I have neither a proof nor a counterexample, sadly.
by Something Awesome
Wed Jun 11, 2008 3:20 pm UTC
Forum: Mathematics
Topic: Chaotic Systems
Replies: 13
Views: 1807

Re: Chaotic Systems

Actually, sensitive dependence on initial conditions isn't even a requirement for a system to be chaotic; it's a property that follows from a system being chaotic (if a system is chaotic, then it has sensitivity to initial conditions). The only two requirements for chaos are that the set of periodic...
by Something Awesome
Sat Jun 07, 2008 3:30 pm UTC
Forum: Mathematics
Topic: Quiz me on infinite series!
Replies: 16
Views: 2399

Re: Quiz me on infinite series!

Here's a fun one that shouldn't be beyond your scope, though it may seem complicated.

Prove that the perimeter of the Koch Snowflake is infinite but its area finite.

Hint: Find the sequence/series for each and prove they converge/diverge.

Go to advanced search