## Search found 676 matches

- Fri Apr 02, 2010 3:04 am UTC
- Forum: Mathematics
- Topic: How to prepare for a mathematics competition?
- Replies:
**3** - Views:
**963**

### Re: How to prepare for a mathematics competition?

I did a problem like this in HS, and we won honorable mention for it. Our approach was this: The previous few competitions always had to do with a problem in mathematical modelling, with the topics being chosen from engineering, economics, and CS. It was a 4 (or 5, I don't exactly remember) person t...

- Fri Apr 02, 2010 2:42 am UTC
- Forum: Mathematics
- Topic: Master's in Computational Sci?
- Replies:
**11** - Views:
**1618**

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

I'm assuming you mean computational science, which is quite different (but related to) computer science. For computational science, you have enough background as a math major, assuming you remember PDEs, Statistics, and Linear Algebra well enough. What would definitely help is a class or two in nume...

- Wed Mar 31, 2010 5:55 am UTC
- Forum: Mathematics
- Topic: Math Summer 2010 Dilemma
- Replies:
**6** - Views:
**1803**

### Re: Math Summer 2010 Dilemma

I've been feeling increasingly despondent regarding my chances in the Goldwater as the date grows ever later. But I guess they're just slow in getting out the notifications -- check online, I've heard they usually post a press release there before winners get notified by mail. I've been feeling exa...

- Wed Mar 31, 2010 3:16 am UTC
- Forum: Mathematics
- Topic: Math Books
- Replies:
**378** - Views:
**253543**

### Re: Math Books

The classification of finite groups is not a string theory topic, and the monstrous group shows up but not in an essential way. If you want some stringy stuff, I think the main thing you will want is complex manifolds. There are a bunch of fun books on this, I don't really have a favorite one. And ...

- Wed Mar 31, 2010 2:51 am UTC
- Forum: Mathematics
- Topic: Math Summer 2010 Dilemma
- Replies:
**6** - Views:
**1803**

### Re: Math Summer 2010 Dilemma

Thanks for the advice everyone. I did end up taking the position at Fermilab after Cornell REU rejected me. I still had a few math REUs left, but Cornell was the big one. So far, my advisor at Fermilab seems to be quite willing to conform to my interests, so I'm hoping to still have a relatively str...

- Tue Mar 09, 2010 5:01 am UTC
- Forum: Mathematics
- Topic: Math Summer 2010 Dilemma
- Replies:
**6** - Views:
**1803**

### Math Summer 2010 Dilemma

I hope you all can give some helpful advice. Unfortunately, no one around me seems to be able to answer in a reasonable way. I'm interested in persuing mathematical physics in Grad school. Currently, I'm an undergrad sophomore, and my current interest is in application of representation theory to Qu...

- Mon Mar 08, 2010 5:32 am UTC
- Forum: Mathematics
- Topic: Math Books
- Replies:
**378** - Views:
**253543**

### Re: Math Books

I'm looking for a good book on the algebraic developments that occured within the last half-century or so, particularly the classification of finite simple groups, mosterous moonshine, and all the rest of the stuff that is used in string theory. I know the basics--undergraduate level classes, introd...

- Sun Feb 28, 2010 3:04 am UTC
- Forum: News & Articles
- Topic: Won't pay attention in class? Fine, I'll smash your laptop.
- Replies:
**80** - Views:
**7969**

### Re: Won't pay attention in class? Fine, I'll smash your laptop.

I go to the University of Oklahoma, and am a physics student, so I know Professor Mullen fairly well. As such, I feel I should say my own personal experience. I haven't taken any classes with him, but he is a very nice and helpful person. It is unfortunate that he is getting featured like this, beca...

- Sat May 30, 2009 6:53 pm UTC
- Forum: Mathematics
- Topic: I accidentally the incompleteness theorem
- Replies:
**14** - Views:
**2985**

### Re: I accidentally the incompleteness theorem

It says something stronger: that if we can use a theory to prove itself consistent, it is necessarily inconsistent.

- Sun Apr 26, 2009 6:16 am UTC
- Forum: School
- Topic: Down to it: MIT or Princeton?
- Replies:
**6** - Views:
**1555**

### Re: Down to it: MIT or Princeton?

It depends on several factors, the most important of which is what you plan on majoring in. Princeton has the best math program in the country (and the world according to many) so if that's your interest then go there. MIT has excellent engineering and computer departments. For most sciences, it's a...

- Sun Apr 19, 2009 7:18 am UTC
- Forum: School
- Topic: Goldwater Scholarship
- Replies:
**1** - Views:
**557**

### Goldwater Scholarship

I'm a freshman and easily the strongest in both mathematics and Physics at my university (University of Oklahoma). I plan on applying next fall for a Goldwater scholarship, which (in case you don't know) is a very prestigious math/science/engineering scholarship. But I'd like to know what kinds of q...

- Tue Mar 31, 2009 4:24 am UTC
- Forum: Mathematics
- Topic: Question
- Replies:
**6** - Views:
**858**

### Re: Question

It wouldn't seem like there's enough information to get a single solution, since we have one equation but two unknowns. Nevertheless, we can find a few solutions by trial and error: x=0, y>0 are all solutions x=1,y=1 is a solution x=2,y=2 is a solution x=4,y=1/2 is a solution I don't think you can f...

- Tue Mar 24, 2009 8:06 am UTC
- Forum: Mathematics
- Topic: Topology Homework Problem
- Replies:
**3** - Views:
**651**

### Re: Topology Homework Problem

I solved it by splitting it up into those three problems, two of which had been proven in class. Thanks for the replies; I can't say they helped because I finished the problem before reading them, but it was nonetheless nice to confirm that my strategy was the correct one. My biggest problem was tha...

- Tue Mar 24, 2009 7:41 am UTC
- Forum: Mathematics
- Topic: Topology Homework Problem
- Replies:
**3** - Views:
**651**

### Topology Homework Problem

As the title implies, this is a problem taken from my homework, so please don't solve it for me. Let f: X->Y be a continuous map, with X compact, Y Hausdorff. Show that for any closed subset C of X, f(C) is closed in Y. (Taken from Topology: An introduction to the Point-Set and Algebraic Areas by Do...

- Fri Mar 20, 2009 3:31 am UTC
- Forum: Mathematics
- Topic: Factual error on my GED locator test.
- Replies:
**26** - Views:
**2560**

### Re: Factual error on my GED locator test.

Part of learning to be a productive individual is listening to others, even when you think you know more than they do. Whether it's a test question that uses definitions that aren't exactly correct, or a teacher who knows very little about what they're actually teaching. My advice is to finish high ...

- Wed Mar 18, 2009 4:04 am UTC
- Forum: Mathematics
- Topic: Tips for Double/Triple Integrals
- Replies:
**7** - Views:
**2161**

### Re: Tips for Double/Triple Integrals

If you notice terms like x^2+y^2 or even just x^2 in a way that is not easy to integrate, try switching. Especially if your domain is easy to express in polar. Evaluating a double or triple or larger integral is the same as a standard integral, but you just can't make mistakes or you'll get impossib...

- Wed Mar 18, 2009 3:43 am UTC
- Forum: Science
- Topic: Expensive Colleges
- Replies:
**24** - Views:
**2431**

### Re: Expensive Colleges

I chose a full ride to OU over going to one of the ivys or another equally good school. It's turned out great. I'm able to excel and still have time for a social life (I'm in 21 hours, doing 2 majors and 2 minors, and plan to be out in 3-3.5 years). It's not boring either. It was definitely a great ...

- Wed Mar 18, 2009 1:26 am UTC
- Forum: Mathematics
- Topic: base e
- Replies:
**14** - Views:
**8103**

### Re: base e

That's what I was thinking as well. Which makes base e quite difficult to use. If it's not even trivial to check if two numeric expansions are equal, then clearly the system is not very efficient for normal computations.

- Wed Mar 18, 2009 1:05 am UTC
- Forum: Mathematics
- Topic: Irrational numbers don't exist
- Replies:
**51** - Views:
**5796**

### Re: Irrational numbers don't exist

Numbers are fairly clearly defined in a mathematical sense. 1 is a number, and Peano arithmetic creates the positive integers from this. From subtraction, we get the integers. Then from division, we get rationals. In much the same way, we extend to the irrationals, complex numbers, etc. Saying that ...

- Mon Mar 16, 2009 5:19 am UTC
- Forum: Mathematics
- Topic: base e
- Replies:
**14** - Views:
**8103**

### Re: base e

Every rational number requires an infinite number of "digits" to express in base e, and this representation is not, as far as I know, unique. And not in the way that base-phi representations aren't unique - there are no "local" shifts in digits that work, because any such relati...

- Mon Mar 16, 2009 5:06 am UTC
- Forum: Mathematics
- Topic: Any reason why half of a graph doesn't appear?
- Replies:
**7** - Views:
**995**

### Re: Any reason why half of a graph doesn't appear?

x^{1/2} is the positive square root of x. This is not always true. If f(x)=x 2 and g(x)=x 1/2 then we'd like g(f(x))=x as closely as possible. But f is not one-to-one, so this is impossible for all x. We can choose g(f(x)) = |x| or -|x|, the first of which is accurate for nonnegative x and the seco...

- Fri Mar 13, 2009 11:41 am UTC
- Forum: School
- Topic: Finding another major or minor
- Replies:
**10** - Views:
**961**

### Re: Finding another major or minor

Thank you all for the suggestions. Computer Science seems like it would definitely be a solid choice. I don't know how useful It'd be for me if I plan on doing theoretical work, but in any case it would also be relatively easy I thought about doing another language, but it doesn't seem interesting t...

- Fri Mar 13, 2009 11:05 am UTC
- Forum: School
- Topic: What's your major?
- Replies:
**77** - Views:
**7141**

### Re: What's your major?

I'm Math/Physics with minor in Japanese. I'll add another major (most likely Computer Science) later. For my school, there are usually 2 options: a standard degree with around 30-40 hours of relevant classes, and a professional one with ~50, with about 50ish hours of Gen-ed. The standard ones are in...

- Fri Mar 13, 2009 5:44 am UTC
- Forum: Serious Business
- Topic: Should drugs be tested on criminals?
- Replies:
**83** - Views:
**8419**

### Re: Should drugs be tested on criminals?

I couldn't find this anywhere mentioned in the thread, but in general this will not give a very large sample size. Most new drugs are not meant to be taken in every situation (the only exception I can think of to this is multivitamins) and thus you'd have to identify prisoners with said condition, t...

- Fri Mar 13, 2009 4:23 am UTC
- Forum: Mathematics
- Topic: Why is 2 not equal to 3? Is this question nonsense?
- Replies:
**7** - Views:
**1466**

### Re: Why is 2 not equal to 3? Is this question nonsense?

We assume that 2 =/= 3 for the sake of continuity, but it's impossible to prove that this is true consistently. The axioms of ZFC can not assert their own consistency without being inherently inconsistent. So if we could know for sure that 2=3, then 2 =/= 3 would also be provable. For the sake of ac...

- Thu Mar 12, 2009 6:56 pm UTC
- Forum: Mathematics
- Topic: What does Standard/General Form Actually Mean?
- Replies:
**4** - Views:
**1375**

### Re: What does Standard/General Form Actually Mean?

If you generalize this to several variables, x,y,z,w,... then finding the solution to the equation is as simple as finding the nullspace of a row vector, and adding this to a particular solution. Or if you have m equations and n variables, then you find the nullspace of an mxn matrix. So it generali...

- Thu Mar 12, 2009 6:47 pm UTC
- Forum: Mathematics
- Topic: Graph: F(x)=x^∞
- Replies:
**25** - Views:
**2881**

### Re: Graph: F(x)=x^∞

On the contrary: this is a good illustration of how a sequence of continuous functions can converge to a function that is not continuous. It's a good motivating example for defining things like uniform convergence. It's an illustration, although I don't know if it's a particularly interesting one. ...

- Thu Mar 12, 2009 7:43 am UTC
- Forum: School
- Topic: Finding another major or minor
- Replies:
**10** - Views:
**961**

### Finding another major or minor

I'm a Physics/Math double major with Japanese minor, and the course load is looking like it'll be easy to finish in 2.5 to 3 years (after 1 year, I have 4 more classes for math, 5 more for Physics, and 6 for Japanese, with basically all the Gen.Ed done). I plan on taking more classes in math and phy...

- Thu Mar 12, 2009 7:16 am UTC
- Forum: Mathematics
- Topic: help with integration
- Replies:
**8** - Views:
**879**

### Re: help with integration

That makes a lot more sense. Then it's unlikely I'd be of any help, as I haven't taken either differential geometry or algebraic topology yet

- Thu Mar 12, 2009 6:38 am UTC
- Forum: Mathematics
- Topic: help with integration
- Replies:
**8** - Views:
**879**

### Re: help with integration

ThomasS wrote:I know enough to say that this is really differential forms/algebraic topology, analysis.

Is it? We haven't done anything like this in my topology or algebra classes so far, but then again we're just now on manifolds in topology.

- Thu Mar 12, 2009 2:24 am UTC
- Forum: Mathematics
- Topic: Graph: F(x)=x^∞
- Replies:
**25** - Views:
**2881**

### Re: Graph: F(x)=x^∞

What is possible is to take g(x,k)=x^k. Then if lim k->Inf g(k) converges, then f(x) is equal to that limit. But your domain will be [0,1], and there will be nothing particularly interesting about the function. Wouldn't it be (-1,1]? While for negative x it alternates positive and negative for even...

- Thu Mar 12, 2009 2:19 am UTC
- Forum: Mathematics
- Topic: help with integration
- Replies:
**8** - Views:
**879**

### Re: help with integration

The title for this is misleading. Many people want help with calculus II integration, so that's what I was expecting. As for the actual question, I honestly have no idea as I've only had a very small amount of analysis.

- Wed Mar 11, 2009 12:11 am UTC
- Forum: Mathematics
- Topic: Definitions & explanations in English/Actual uses for math
- Replies:
**19** - Views:
**1715**

### Re: Definitions & explanations in English/Actual uses for math

Why is the use important? Sure, we can find ways to apply matricies or calculus to real life problems, but this won't make people like math more. For example, in any quantum mechanics class, the people who don't know linear algebra will most certainly learn the applications there. By teaching the ap...

- Mon Mar 09, 2009 9:47 pm UTC
- Forum: Mathematics
- Topic: Graph: F(x)=x^∞
- Replies:
**25** - Views:
**2881**

### Re: Graph: F(x)=x^∞

What is possible is to take g(x,k)=x^k. Then if lim k->Inf g(k) converges, then f(x) is equal to that limit. But your domain will be [0,1], and there will be nothing particularly interesting about the function. It's basically the floor function restricted to [0,1]. So it's not at all an interesting ...

- Mon Mar 09, 2009 9:38 pm UTC
- Forum: Mathematics
- Topic: Love note
- Replies:
**3** - Views:
**784**

### Re: Love note

What level of math are you looking to use? It could be just basic algebra and possibly some calculus, or you could go all out. Since you seem reasonably serious about this, I'll assume you know a decent amount of math. For y, the most common use of y in math is as a function of x, or later as an add...

- Mon Mar 09, 2009 9:26 pm UTC
- Forum: Mathematics
- Topic: What is wrong with this differentiation?
- Replies:
**19** - Views:
**2443**

### Re: What is wrong with this differentiation?

If you have x^2=x+x+...+x with x x's, you can't just differentiate each individual term. The number of terms changes as x does. Plus this expansion doesn't make sense unless x is an integer, and you can't differentiate on the integers.

- Mon Mar 09, 2009 9:20 pm UTC
- Forum: Mathematics
- Topic: Calculating Residues of Complex Functions
- Replies:
**3** - Views:
**962**

### Re: Calculating Residues of Complex Functions

I realized later that we were expected to look up the Laurent Series for cotangent. If I had known this, it would have saved several hours trying to derive it by series division. That makes this problem very easy.

- Mon Mar 09, 2009 10:46 am UTC
- Forum: Mathematics
- Topic: Calculating Residues of Complex Functions
- Replies:
**3** - Views:
**962**

### Calculating Residues of Complex Functions

What would be the best way to determine the course of action to compute residues of complex functions? For example, say I have a function f(z)=cot(z)/z 4 , and I need the residue at 0. What thought process should I use to determine the method to find this? My professor told us several ways to do so,...

- Sun Mar 08, 2009 6:23 pm UTC
- Forum: School
- Topic: SAT Scores
- Replies:
**241** - Views:
**34707**

### Re: SAT Scores

Math: 800

Writing: 800

CR: 780

I almost got a perfect score, but it was ruined by the stupid critical reading section.

Writing: 800

CR: 780

I almost got a perfect score, but it was ruined by the stupid critical reading section.

- Sun Mar 08, 2009 5:44 pm UTC
- Forum: Mathematics
- Topic: Eigenvalues
- Replies:
**8** - Views:
**900**

### Re: Eigenvalues

Alternatively, for a more general solution, you have λ 3 -1=0. You already know that λ=1 is a root, so divide this out. You get (λ-1)(λ 2 +λ+1)=0. The roots of the latter are easy to find using the quadratic equation. Incidentally, for this particular problem, this factorization is very easy to reme...