Search found 758 matches

by z4lis
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...
by z4lis
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'...
by z4lis
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?
by z4lis
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?
by z4lis
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.
by z4lis
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...
by z4lis
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...
by z4lis
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...
by z4lis
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...
by z4lis
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...
by z4lis
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.
by z4lis
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.
by z4lis
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?
by z4lis
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 , ...
by z4lis
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.
by z4lis
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?
by z4lis
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...
by z4lis
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 ...
by z4lis
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...
by z4lis
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 ...
by z4lis
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...
by z4lis
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'...
by z4lis
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...
by z4lis
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...
by z4lis
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...
by z4lis
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...
by z4lis
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 ...
by z4lis
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...
by z4lis
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...
by z4lis
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.
by z4lis
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?
by z4lis
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,...
by z4lis
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...
by z4lis
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...
by z4lis
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) =...
by z4lis
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...
by z4lis
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...
by z4lis
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...
by z4lis
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...
by z4lis
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 ...

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