## Search found 42 matches

Thu Apr 14, 2011 1:53 am UTC
Forum: Science
Topic: Nonlinear Schrodinger Equation
Replies: 7
Views: 1717

### Nonlinear Schrodinger Equation

Hey all. I'm reading about the derivation of the NLSE ( http://aflb.ensmp.fr/AFLB-303/aflb303m376.pdf ) and while I understand the math, the physical meaning of the equation is hard for me to grasp. As I understand it: a particle is represented/formulated as a complex-valued function. If you take th...
Thu Dec 02, 2010 11:18 pm UTC
Forum: Mathematics
Topic: Explaining Infinity
Replies: 3
Views: 1115

### Re: Explaining Infinity

Because from what i know, infinity can be explained like this: If you take the number-line and draw a circle above it, every tangent relates to a number on the number-line, except for the ones that are parallel to it. So, the infinity-tangents go from -infinite to +infinite. Does it even matter, or...
Thu Dec 02, 2010 11:04 pm UTC
Forum: Mathematics
Topic: Entire Function That Agrees with Log on Natural Numbers?
Replies: 25
Views: 3566

### Re: Entire Function That Agrees with Log on Natural Numbers?

mike-l wrote:I'm pretty sure you can find an entire function with prescribed values on any set that lacks limit points, but I can't find the theorem that says that.

In this context, is infinity a limit point of the natural numbers?
Wed Dec 01, 2010 9:35 pm UTC
Forum: Mathematics
Topic: Entire Function That Agrees with Log on Natural Numbers?
Replies: 25
Views: 3566

### Re: Entire Function That Agrees with Log on Natural Numbers?

Given a set \{z_n\} of complex numbers with \lvert z_n \rvert \rightarrow \infty , it is always possible to find an entire function with a prescribed value at each z_n . This is a consequence of the Weierstrass Factorization Theorem and the Mittag-Leffler Theorem (see Ahlfors or any other complex v...
Thu Nov 18, 2010 11:52 pm UTC
Forum: Mathematics
Topic: Entire Function That Agrees with Log on Natural Numbers?
Replies: 25
Views: 3566

### Entire Function That Agrees with Log on Natural Numbers?

Do you think this can be done? I don't know much complex analysis, I suspect probably not, but I kind of need it. Work so far: I've been trying to work up something so far by cutting out a region and filling it in with something else, but no success. The function Log(x)*[Cos((2^x)*Pi)+1]/2 agrees wi...
Tue Oct 19, 2010 4:53 pm UTC
Forum: Mathematics
Topic: Plotting Arbitrary Julia Sets?
Replies: 0
Views: 1325

### Plotting Arbitrary Julia Sets?

Does anyone know of any Matlab (or any, really) program that will allow you to plot the Julia set of an arbitrary rational function? And hopefully have it look nice( I've found a Maple routine described here http://www.mcs.st-and.ac.uk/~jmf32/julia.pdf that gives you ehhh looking ones, it'd be nice ...
Fri Jul 02, 2010 12:48 am UTC
Forum: Mathematics
Topic: The Tau Manifesto
Replies: 165
Views: 44222

### Re: The Tau Manifesto

The best part of the this paper is when he points out that pi is both transcendental and irrational. Spooky
Thu Apr 22, 2010 12:11 am UTC
Forum: Mathematics
Topic: Master's in Computational Sci?
Replies: 11
Views: 1746

### Re: Master's in Computational Sci?

Ended wrote:@OP: could you clarify whether you mean computational science or computer science?

Computational.

Thanks guy!
Wed Mar 24, 2010 7:55 pm UTC
Forum: Mathematics
Topic: Four color theorem
Replies: 82
Views: 21111

### Re: Four color theorem

mike-l wrote:Classification of finite sets is a very difficult and untractable problem, unlike finite groups which took a mere 1500 pages.

Oh Jesus. Oops.

Though actually isn't it simple finite groups
Wed Mar 24, 2010 5:42 am UTC
Forum: Mathematics
Topic: Four color theorem
Replies: 82
Views: 21111

### Re: Four color theorem

I don't know about that; what is the longest mathematical proof anyone can name? Classification of finite sets, its 1500+ pages, but each part of the proof has been checked and verified....just not by the same person, as opposed to 4 Color Theorem. I don't think it likely 4 color theorem's proofs a...
Wed Mar 24, 2010 2:53 am UTC
Forum: Mathematics
Topic: Famous Math Quotes!
Replies: 32
Views: 8012

### Re: Famous Math Quotes!

Certhas wrote:"Wir müssen wissen — wir werden wissen!" - Hilbert

"Nope" -Godel
Wed Mar 24, 2010 2:52 am UTC
Forum: Mathematics
Topic: Four color theorem
Replies: 82
Views: 21111

### Re: Four color theorem

BlackSails wrote:
Dason wrote:Yeah, aren't there hundreds (thousands?) of cases that a Pornography Storage Apparatus verified for the proof? It's an accepted proof but isn't it possible that something went wrong that we haven't found yet?

Isnt that true of every proof?

Not to this degree
Wed Mar 24, 2010 2:46 am UTC
Forum: Mathematics
Topic: Need a math topic idea
Replies: 8
Views: 928

### Re: Need a math topic idea

lncabin wrote:
Suffusion of Yellow wrote:How long does it have to be?

Preferably a few pages.

Eh my idea probably won't be long enough then.
Wed Mar 24, 2010 1:06 am UTC
Forum: Mathematics
Topic: Need a math topic idea
Replies: 8
Views: 928

### Re: Need a math topic idea

How long does it have to be? If it can be short: Get an intro diff eq text book, find the chapter with equations of the form dy/dx + f(x)y = g(x), find a word problem, solve it by integration.
Tue Mar 23, 2010 1:03 pm UTC
Forum: Mathematics
Topic: Master's in Computational Sci?
Replies: 11
Views: 1746

### Re: Master's in Computational Sci?

Dason wrote:Well what are the other options you have laid out?

Well I'm gonna apply to graduate school in just math, but I'd have to do that not next year but the year after, so I was thinking about doing Computational Sci in the year in between.
Tue Mar 23, 2010 3:43 am UTC
Forum: Mathematics
Topic: Master's in Computational Sci?
Replies: 11
Views: 1746

### Re: Master's in Computational Sci?

Dason wrote:So just so I have this straight... you haven't had any comp sci classes... ever?

Nope
Mon Mar 22, 2010 10:48 pm UTC
Forum: Mathematics
Topic: Master's in Computational Sci?
Replies: 11
Views: 1746

### Re: Master's in Computational Sci?

BlackSails wrote:Why would you apply to a program that you dont even know if you want?

Because the application was free and if I decide I don't want to go, then I don't have to go. The deadline was coming up and if I did decide it was something I wanted to do afterwards it would be to late.
Mon Mar 22, 2010 10:38 pm UTC
Forum: Mathematics
Topic: Master's in Computational Sci?
Replies: 11
Views: 1746

### Master's in Computational Sci?

So I'm graduating with a major in math in a month, and I got accepted into a master's program in computational science. I don't really know anything about computational science except what Wikipedia told me, soooo...is it good for employment? is it good for then getting a PhD? Etc
Sun Mar 21, 2010 3:30 pm UTC
Forum: Mathematics
Topic: Godel Incompleteness Theorem
Replies: 47
Views: 5300

### Re: Godel Incompleteness Theorem

On the other hand, it could lead to people devoting entire lifetimes to proving something without even knowing whether it's possible. 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 a...
Sun Mar 21, 2010 1:44 am UTC
Forum: Mathematics
Topic: Godel Incompleteness Theorem
Replies: 47
Views: 5300

### Re: Godel Incompleteness Theorem

BlackSails wrote:tldr: If people have free will, electrons do too.

If there is a meaningful definition of "free will" I have not yet come across it
Sun Mar 21, 2010 1:27 am UTC
Forum: Mathematics
Topic: Math in Moscow
Replies: 29
Views: 6815

### Re: Math in Moscow

Lemminkainen wrote: I'm currently a freshman at Rice University, and by the end of this year, I'll have completed multivariable calculus, differential equations, linear algebra, complex analysis, and a treatment of Euclidean and non-Euclidean geometry.

I hate being reminded how flimsy my school's math program is
Sun Mar 21, 2010 12:31 am UTC
Forum: Mathematics
Topic: The crux of abstract algebra, I need help
Replies: 4
Views: 1462

### Re: The crux of abstract algebra, I need help

Thanks! These are exactly the kinds of answers I'm looking for. @Suffusion: I'm doing "the whole book". That is, group theory, ring theory, ..., galois theory. It's a first course thing. It seems to me that in the end, all the stuff I'm learning this semester is stuff I absolutely HAVE to...
Fri Mar 19, 2010 12:19 am UTC
Forum: Mathematics
Topic: Four color theorem
Replies: 82
Views: 21111

### Re: Four color theorem

Yakk wrote:As far as I know, the only successful proof of the four color theorem required a huge database of "special cases" to be manually checked. So I doubt that proof you are talking about is a good one.

This is true, I'm writing my senior research paper on it
Thu Mar 18, 2010 11:57 pm UTC
Forum: Mathematics
Topic: The crux of abstract algebra, I need help
Replies: 4
Views: 1462

### Re: The crux of abstract algebra, I need help

Depends what in abstract algebra you're doing, honestly. If its focused on mainly group theory definitely know the Fundamental Homomorphism Theorem, Lagrange Theorem, and the Sylow Theorems.
Thu Mar 11, 2010 12:50 am UTC
Forum: Mathematics
Topic: Understanding Cauchy?
Replies: 12
Views: 1659

### Re: Understanding Cauchy?

Hello, I am a precalculus student, but I have been working quite a bit with calculus and I am ahead of my grade level. I was hoping of learning about Complex Analysis, but I am confused on differentiating and integrating complex functions. I realize that in differentiation, the process is essential...
Wed Mar 03, 2010 2:13 am UTC
Forum: Mathematics
Topic: Have You Been Taught Things Which Aren't True?
Replies: 97
Views: 16322

### Re: Have You Been Taught Things Which Aren't True?

BlackSails wrote:Wiki says the proof of the fundamental theorem of algebra is legit.

There's a real one that use the real Liouville Theorem
Wed Mar 03, 2010 1:37 am UTC
Forum: Mathematics
Topic: Quick question on basic topology
Replies: 18
Views: 2307

### Re: Quick question on basic topology

The closure of the set of rationals is the set of reals Yes: Q is dense in R. The irrationals are boundary points of the set of rationals Yes - in fact, the boundary of Q is the whole of R. Cool, thanks -- my school offers "Topology is a prerequisite" courses but curiously not a Topology ...
Wed Mar 03, 2010 1:36 am UTC
Forum: Mathematics
Topic: Have You Been Taught Things Which Aren't True?
Replies: 97
Views: 16322

### Have You Been Taught Things Which Aren't True?

Last week I had a class on Liouville's theorem in complex analysis where the (usually quite excellent) professor said that it applied to any domain on C, and then used it to prove the Fundamental Theorem of Algebra. Unfortunately, as I realized later, it doesn't apply to any domain on C but only the...
Wed Mar 03, 2010 1:20 am UTC
Forum: Mathematics
Topic: slightly excessive numbers
Replies: 6
Views: 1377

### Re: slightly excessive numbers

I have read that although there are slightly defective numbers (divisors add up to one less that the number, counting each divsor only once, e.g. 4: 1+2=3), there do not appear to be any slightly excessive numbers even though their existence has not been proven or disproven. Why don't prime numbers...
Wed Mar 03, 2010 1:15 am UTC
Forum: Mathematics
Topic: Quick question on basic topology
Replies: 18
Views: 2307

### Re: Quick question on basic topology

Even quicker, even more basic: the closure of the set of rationals is the set of reals, and the irrationals are boundary points of the set of rationals. True?
Tue Jan 26, 2010 3:00 am UTC
Forum: Mathematics
Topic: A subring of the reals???
Replies: 20
Views: 1642

### Re: A subring of the reals???

tom.young84 wrote:Cool.

Finally, is it just four axioms that demonstrate that a subset is a subring?

Also it has to be non-empty, but that's trivial here.
Tue Jan 26, 2010 2:53 am UTC
Forum: Mathematics
Topic: The ideal number.
Replies: 70
Views: 7984

### Re: The ideal number.

e.

gorcee wrote:64 is my lucky number, for a variety of reasons.

Are they "you like music and dislike Kennedy?"
Thu Jan 14, 2010 11:17 pm UTC
Forum: Mathematics
Topic: Real Analysis 1: What Topics Should Be Covered?
Replies: 9
Views: 1649

### Real Analysis 1: What Topics Should Be Covered?

In your opinion. In my school they did series and sequences, epsilon delta proofs for derivatives and continuity, & the Darboux integral, but no mention of metric spaces, topology, so forth, which I seem to find in a lot of other books on Analysis 1. I'm guessing there's a debate over what shoul...
Fri Nov 13, 2009 12:18 am UTC
Forum: Mathematics
Topic: Applying the 5-Color Proof to 4-Color Theorem
Replies: 4
Views: 2013

### Applying the 5-Color Proof to 4-Color Theorem

I'm pretty sure I'm missing something obvious here and this is going to be embarrassing, but for the life of me I can't figure out what it is, soooo...why can't you apply basically the proof of 5 color theorem (this one http://www.proofwiki.org/wiki/Five_Color_Theorem) to the four color problem, wit...
Mon May 04, 2009 4:01 am UTC
Forum: Language/Linguistics
Topic: Old capitalization rules
Replies: 29
Views: 5108

### Re: Old capitalization rules

dalahäst wrote:In some Documents, all Nouns were capitalized as in German. In other Documents, words which the Writer deemed important were also Capitalized. I've always liked these Rules myself, they make Writing look more interesting.

And more expressive I think.
Mon May 04, 2009 4:00 am UTC
Forum: Mathematics
Topic: Help with a Math Problem
Replies: 11
Views: 1719

### Re: Help with a Math Problem

Samuel wrote:Taly and Marc open a Registered Home Ownership Savigs Plan that pays 6% iterest compouded semi-annually. For 4 years, they invest \$500 every 5 months in the plan. Determine the amount of interest they earn.

Determine as in decide? In that case, they make forty bucks. Because I don't like them
Sun May 03, 2009 3:24 pm UTC
Forum: Language/Linguistics
Topic: Words that you are sure exist, but can't find
Replies: 225
Views: 84870

### Re: Words that you are sure exist, but can't find

My English teacher for year ten (tenth grade) marked me down in an assessment paper for using the word "fantastical". I defended myself, claiming it was indeed a word. It much bothered me that she: for one; did not recognise it as a word, and two; I knew that I had heard or read that word...
Sun May 03, 2009 3:27 am UTC
Forum: Mathematics
Topic: Combinatorics Problem
Replies: 1
Views: 427

### Combinatorics Problem

So I have this homework problem (I know, I know) where you have to sit n couples around a table with no couple sitting together. You're supposed to use inclusion-exclusion to solve it, I have no idea how, so I found a recursion I think answers it instead. Then, however, I Googled it to be safe and f...
Thu Jan 01, 2009 11:59 pm UTC
Forum: Mathematics
Replies: 8
Views: 1112

### Re: Getting Into Graduate School

You'll want to be familiar with the basics of topology, real analysis, algebra, complex analysis, and number theory. Personally, I had taken three of those prior to the exam and was concurrently enrolled in real (as I'd mentioned above). I hadn't taken complex, but fortunately there were only two o...
Thu Jan 01, 2009 9:32 pm UTC
Forum: Mathematics