## Search found 758 matches

- Fri Sep 28, 2012 5:20 am UTC
- Forum: Mathematics
- Topic: Math grad school for a linguistics major: how?
- Replies:
**1** - Views:
**2019**

### Re: Math grad school for a linguistics major: how?

So I'm a first year grad student, and don't really know much about how they pick people. But I did get in, so I suppose I did something correct. Here's my advice: 1. Don't talk about your outside interests too much. They don't want to invest in a student that they feel is going to lose focus and jum...

- Fri Sep 28, 2012 5:04 am UTC
- Forum: Mathematics
- Topic: Linear Algebra Homework: Annihilators, Isomorphisms
- Replies:
**4** - Views:
**2589**

### Re: Linear Algebra Homework: Annihilators, Isomorphisms

1) Yes, you'd want to use the natural map from X* to Y* found by restriction. However, showing this is surjective requires a little work, but not much. You need to show that a linear functional on the subspace Y can be extended. (Are we talking algebraic or topological duals, by the way? If you don'...

- Sat Sep 22, 2012 4:48 am UTC
- Forum: Mathematics
- Topic: Linear algebra question
- Replies:
**4** - Views:
**2226**

### Re: Linear algebra question

It seems reasonable that for an orthogonal matrix, you have the identity R(a x b) = (Ra) x (Rb). Does that help?

- Thu Sep 20, 2012 4:37 am UTC
- Forum: Mathematics
- Topic: PDE Question
- Replies:
**5** - Views:
**1098**

### Re: PDE Question

Are you allowed to carelessly push around Fourier series?

- Wed Sep 12, 2012 1:02 am UTC
- Forum: Mathematics
- Topic: Implications of The Riemann Hypothesis
- Replies:
**2** - Views:
**2394**

### Re: Implications of The Riemann Hypothesis

It's about the Riemann zeta function, so...

Yes.

Yes.

- Fri Sep 07, 2012 8:04 pm UTC
- Forum: Mathematics
- Topic: True or False in Geometry
- Replies:
**17** - Views:
**6271**

### Re: True or False in Geometry

There's no such thing as a "sometimes true" mathematical statement. If there's a single counterexample, the statement is false. Period. The statement "If two lines do not meet, they are parallel." is false with any reasonable interpretation of "line", and you're complet...

- Thu Sep 06, 2012 3:16 pm UTC
- Forum: Mathematics
- Topic: Discrete Mathematics - Equivalence Relations (Intersections)
- Replies:
**9** - Views:
**4014**

### Re: Discrete Mathematics - Equivalence Relations (Intersecti

The point is that you need to translate what you're saying into set theory to be totally correct. Start with something like (x,y) \in R_1 \cap R_2 and use set theoretic language to conclude (y,x) \in R_1 \cap R_2 . You also don't want to use terms like "x is related to y" i...

- Tue Sep 04, 2012 1:52 am UTC
- Forum: Mathematics
- Topic: Which book should I study first?
- Replies:
**9** - Views:
**3031**

### Re: Which book should I study first?

The book by Rudin is really hard. That's not to say you shouldn't read it, but just be aware of the fact that the exercises in that book are very, very hard. And you should do all of them if you want to master analysis. He also sometimes lacks motivation, I think. But there are tons of analysis book...

- Mon Sep 03, 2012 2:22 pm UTC
- Forum: Mathematics
- Topic: Mersenne Prime order field within a field
- Replies:
**7** - Views:
**1644**

### Re: Mersenne Prime order field within a field

I mean... I didn't read all of your post, but your question seems to really just boil down to: Given a cyclic group of order p^k, can you put a multiplicative structure on it that gives you a finite field? And the answer is yes, since you already have a field of order p^k. Just take the additive cyc...

- Mon Aug 27, 2012 12:17 pm UTC
- Forum: Mathematics
- Topic: Eigenvalues problem - bidirectional proof?
- Replies:
**15** - Views:
**4770**

### Re: Eigenvalues problem - bidirectional proof?

What ConMan said. Determinants are worse than useless here imo. Really? Huh. Spoilered for solution Let Q be P's inverse for my own sanity. If det(A - tI) = 0, then 0 = det(P)det(A-ti)det(Q) = det(P(A - tI)Q) = det(PAQ - tI). Since P is in...

- Mon Aug 27, 2012 2:44 am UTC
- Forum: Mathematics
- Topic: Eigenvalues problem - bidirectional proof?
- Replies:
**15** - Views:
**4770**

### Re: Eigenvalues problem - bidirectional proof?

I suggest against crossing out the old problem and posting the new one in an edit...

Anyway, yes, I would solve that using determinants.

Anyway, yes, I would solve that using determinants.

- Sun Aug 26, 2012 1:06 pm UTC
- Forum: Mathematics
- Topic: collection of problems
- Replies:
**10** - Views:
**1908**

### Re: collection of problems

Would you know how to solve the problem if the list were instead:

2, 3, 5, 7

giving remainder

1, 2, 4, 6

?

Note: This is probably not how you want to solve this problem, but this is an easier version that you should know how to do before attempting your problem.

2, 3, 5, 7

giving remainder

1, 2, 4, 6

?

Note: This is probably not how you want to solve this problem, but this is an easier version that you should know how to do before attempting your problem.

- Sun Aug 26, 2012 12:22 pm UTC
- Forum: Mathematics
- Topic: Extend vectors u,v to form a basis of a set
- Replies:
**6** - Views:
**1919**

### Re: Extend vectors u,v to form a basis of a set

Kind of, but here are some things to think about: 1) What dimension does W have? 2) If you could construct a totally different basis for W unrelated to u,v how could you use those vectors with u, v to answer your question?

- Fri Aug 24, 2012 12:03 pm UTC
- Forum: Mathematics
- Topic: Eigenvalues problem - bidirectional proof?
- Replies:
**15** - Views:
**4770**

### Re: Eigenvalues problem - bidirectional proof?

Suppose sλ + t is an eigenvalue of sA + t I_n , then det((sλ + t) I_n -(sA+t I_n )=0 <=> det(sλ I_n - sA+t I_n -t I_n )=0 <=> det(sλ I_n - sA) = 0. Which implies that sA x = sλ x . If λ is an eigenvalue of A, then sA x = sλ x for any real scalar s. Hence, if sλ + t is an eigenvalue of sA + t I_n , ...

- Fri Aug 24, 2012 2:26 am UTC
- Forum: Mathematics
- Topic: PDE's, what type of a PDE is this, and how might I solve it?
- Replies:
**3** - Views:
**972**

### Re: PDE's, what type of a PDE is this, and how might I solve

I didn't explicitly write it all out, but it looks like you can indeed do a linear substitution x = au + bv, t = cu + dv and make it into a wave equation.

- Tue Aug 21, 2012 1:19 am UTC
- Forum: Mathematics
- Topic: Problems for Freshpeople
- Replies:
**9** - Views:
**2119**

### Re: Problems for Freshpeople

I'm in the same boat you are... try asking the professor who's doing the lectures?

- Mon Aug 20, 2012 9:36 pm UTC
- Forum: Mathematics
- Topic: Some help with reversing the order of integration
- Replies:
**3** - Views:
**1023**

### Re: Some help with reversing the order of integration

Mmm... not quite. You should have functions of x for each of the inner integrals. Think about "if I fix a value of y, how can I describe the possible values of x?" I think my flipped picture is rather confusing...

- Mon Aug 20, 2012 9:16 pm UTC
- Forum: Mathematics
- Topic: The saga goes on - Viglen's number incompetency, part three
- Replies:
**38** - Views:
**5119**

### Re: The saga goes on - Viglen's number incompetency, part th

I'm not sure what you're asking. (p-1)/2 is sometimes composite, sometimes not. Similarly, the original expression (2^((p-1)/2) - 1) is prime for some primes (p = 5) and composite for others (p = 13). EDIT: It occurred to me that you are probably asking the question: "For which primes p does p ...

- Fri Aug 17, 2012 1:23 pm UTC
- Forum: Mathematics
- Topic: Some help with reversing the order of integration
- Replies:
**3** - Views:
**1023**

### Re: Some help with reversing the order of integration

Everything looks good up until you write out the very last set of integrals. (See edit below!) You just need to be more careful about writing down everything. You want to make the y's come first, so you need to have actual numbers as your integral limits. Well, what's the smallest value that y takes...

- Wed Aug 15, 2012 5:50 pm UTC
- Forum: Mathematics
- Topic: Analysis and the Real Numbers
- Replies:
**24** - Views:
**3710**

### Re: Analysis and the Real Numbers

Okay, very cool, so if I am understanding correctly, we use the reals because of a few conveniences that they provide, but they aren't necessary. Now would it be true to say that the topics of analysis can be constructed in any metric space? They're totally necessary. You lose too many convergence ...

- Mon Aug 13, 2012 5:17 pm UTC
- Forum: Mathematics
- Topic: Analysis and the Real Numbers
- Replies:
**24** - Views:
**3710**

### Re: Analysis and the Real Numbers

Well, Cauchy sequences in particular can be defined in any metric space, but without convergence, analysis is difficult. Now, you may be talking about the standard way of constructing the reals using Cauchy sequences of rationals. The sketch that you define two Cauchy sequences of rationals to be eq...

- Fri Aug 10, 2012 11:27 am UTC
- Forum: Mathematics
- Topic: "Oh no! We forgot how to say... math... stuff!"
- Replies:
**294** - Views:
**93073**

### Re: "Oh no! We forgot how to say... math... stuff!"

In fact, I just realized that if we always write the integration variable immediately after the integral sign (as we should), then the d becomes an entirely unnecessary symbol. It'll always be there. So we can simply drop it altogether. Simply write ∫x f(x). Wow, that's actually pretty awesome. It'...

- Wed Aug 08, 2012 12:39 pm UTC
- Forum: Mathematics
- Topic: Lost student
- Replies:
**13** - Views:
**4992**

### Re: Lost student

Ah, determinants. They're almost magical. Given some matrix, you do some awful computation, and somehow the single number that comes out gives you so much information about the matrix itself, the (arguably) most important piece is whether or not the matrix is invertible, by Cramer's Rule . As eSOANE...

- Fri Aug 03, 2012 9:47 pm UTC
- Forum: Mathematics
- Topic: Reserach
- Replies:
**11** - Views:
**4226**

### Re: Reserach

As a niave outsider to math research, how is math research typically done? Is it largely running numerical simulations of things that might possibly be interesting (spawned by someone scratching their chin) and hoping to spot a pattern, and then stroking your chin until you can come up with a proof...

- Fri Aug 03, 2012 1:59 am UTC
- Forum: Mathematics
- Topic: Reserach
- Replies:
**11** - Views:
**4226**

### Re: Reserach

My experience with research: there are massive stretches of time where it seems nothing is getting done, but that's okay. I needed to constantly keep the big picture in mind to become discouraged from that lack of progress. And... enjoy yourself, and don't get too hung up if things don't turn out we...

- Thu Aug 02, 2012 12:47 am UTC
- Forum: Mathematics
- Topic: Prime Ideals in C[x,y]
- Replies:
**3** - Views:
**3937**

### Re: Prime Ideals in C[x,y]

Oh, wow. It's been a while since I thought about this one. So I'll just reread what I wrote and untangle it some. Hopefully that will help me answer your questions. Edit: I actually just rewrote the proof. There's a small change, and I included some technicalities that I overlooked in the first proo...

- Thu Jul 19, 2012 1:30 am UTC
- Forum: Mathematics
- Topic: Prime Ideals in C[x,y]
- Replies:
**3** - Views:
**3937**

### Prime Ideals in C[x,y]

Not homework. I'm to find the prime ideals in C[x,y]. I knew that if f is irreducible, then (f) is prime, and I also know that (x-a, y-b) is prime since it's maximal. I sort of cheated and found that these are indeed the only prime ideals, but no proof. Here's my attempt. If there are any errors or ...

- Thu Jul 12, 2012 2:46 am UTC
- Forum: Mathematics
- Topic: How can I tell if Im good at "Real Math"? + Emphasis anxiety
- Replies:
**11** - Views:
**4866**

### 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...

- Mon Jun 25, 2012 5:54 am UTC
- Forum: Mathematics
- Topic: Want to study astronomy... bad at math
- Replies:
**117** - Views:
**31488**

### Re: Want to study astronomy... bad at math

My opinion is probably worth less than dirt, but here's my belief when it comes to mathematics: if you practice, work hard, and try to see it from different perspectives, you can understand it. This applies to things other than mathematics, too. If you decided that you wanted to learn to play the pi...

- Sun Jun 24, 2012 5:08 am UTC
- Forum: Mathematics
- Topic: Math Websites
- Replies:
**125** - Views:
**183614**

### Re: Math Websites

@kizolk:

I don't know if this is what you're looking for, but I've heard great things about Khan Academy.

I don't know if this is what you're looking for, but I've heard great things about Khan Academy.

- Mon Jun 11, 2012 3:03 pm UTC
- Forum: Mathematics
- Topic: unique sums
- Replies:
**16** - Views:
**2513**

### Re: unque sums

I don't think I understand the question, either. 1 + 2 = 3, but 1 + 1 and 2 + 2 are not 3. I hope the OP thought about the question more than I did. The "polynomial with respect to n" is what throws me. Do you mean integers of the form p(n), where p is a polynomial with integer coefficients?

- Sun Jun 10, 2012 6:30 am UTC
- Forum: Mathematics
- Topic: Showing Some Groups are Simple
- Replies:
**16** - Views:
**2672**

### Showing Some Groups are Simple

I would just like another set of eyes to look over these proofs that groups of order 24, 36, and 48 are not simple without using Burnside's theorem, which I haven't learned yet. [24] Applying the Sylow theorems, we may assume that there are 3 subgroups of order 8 and 4 subgroups of order 3. Let H_1,...

- Sat Jun 09, 2012 4:18 am UTC
- Forum: Mathematics
- Topic: Some basic questions on notation
- Replies:
**5** - Views:
**2025**

### Re: Some basic questions on notation

1) You can just write (n, n+1, ..., m-1, m) where n is less than or equal to m and everyone will understand. 2) I don't think there's standard notation for this. You could say "let a be a k-tuple" to let the reader know that a has k elements, or you could say something like "if a is a...

- Fri Jun 08, 2012 2:02 am UTC
- Forum: Mathematics
- Topic: group theory
- Replies:
**64** - Views:
**25083**

### Re: group theory

This is a good exercise for me, as I'm reviewing my algebra at the moment. This proof might be identical to one above. Let x have order p and y have order 2. Now, if xy has order 2p, then we have the cyclic group of order 2p. If xy has order 2, then xyxy = 1 implies that yx = x -1 y, which gives the...

- Wed May 30, 2012 1:58 pm UTC
- Forum: Mathematics
- Topic: functions over finite sets
- Replies:
**8** - Views:
**3023**

### Re: functions over finite sets

I have an idea: g(n)=h(n)-1, where h(n) is the first positive integer that does not divide n factorial. Does this work? No. The sequence was posted, so you can check for yourself with Wolfram. They tell me that 11! = 2 8 x3 4 x5 2 x7x11, so 13 is the first number that doesn't divide it. But g(11) =...

- Tue May 29, 2012 6:33 pm UTC
- Forum: Mathematics
- Topic: The Meaning of Divergent Sums
- Replies:
**1** - Views:
**1339**

### Re: The Meaning of Divergent Sums

If I remember correctly, results like that are found using analytic continuation of functions. For instance, we might have a function like 1^s + 2^s + 3^s + ... that converges for Re(s) < 1 that we can extend through the complex plane, analytically. Now analytic continuation is unique. Once the func...

- Sun May 27, 2012 9:31 pm UTC
- Forum: Mathematics
- Topic: Eigenvalues of A with A^2 = A^T
- Replies:
**2** - Views:
**2002**

### Re: Eigenvalues of A with A^2 = A^T

Of course, 0 should be on the list. But I remember thinking about A^4 = A before I got to sleep last night, and that would force any nonzero eigenvalue c to satisfy c 3 =1, so 0 or the third roots of unity are the only possibilities and the above example shows that the two complex eigenvalues are po...

- Sun May 27, 2012 4:44 pm UTC
- Forum: Mathematics
- Topic: "Oh no! We forgot how to say... math... stuff!"
- Replies:
**294** - Views:
**93073**

### Re: "Oh no! We forgot how to say... math... stuff!"

Sorry to necro this thread, but... I have to get this out of my chest. Index notation is reversed! It should be columns X rows (a row vector should be a n x 1 matrix) in order to obey cartesian coordinates. I'm not sure what you mean by "obey cartesian coordinates", but think about it thi...

- Sun May 27, 2012 8:12 am UTC
- Forum: Mathematics
- Topic: Eigenvalues of A with A^2 = A^T
- Replies:
**2** - Views:
**2002**

### Eigenvalues of A with A^2 = A^T

This isn't HW; I'm reviewing for prelims this fall. It's a problem from Artin's book. Anyway, let A be a real matrix with A^2 = A^T. I'm to find the possible eigenvalues for A. Now, I've managed to show that the eigenvalues must be 2 n -1 roots of unity, but I'm not sure if I'm to leave it at that f...

- Wed May 23, 2012 4:57 pm UTC
- Forum: Mathematics
- Topic: After calculus
- Replies:
**20** - Views:
**4792**

### Re: After calculus

I'll toss some on the list that I didn't spot reading this thread: 1. Partial differential equations 2. Numerical analysis 3. Probability and Monte Carlo methods 4. Topology You need to know PDEs after you learn DEs and multivariable calculus because while DEs are very useful, most of the equations ...