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1. What am I doing wrong?

Actually, I can't really see a problem. So...am I really just that rusty? What's the answer supposed to be?
2. Algebraic expressions - simplifying

It shouldn't be too terrible. The obvious thing to note is that (b - a) = -(a - b), for example.
3. Cyclic Subgroup of GL(2,q)

It seems like you're going about the problem correctly except that obviously the splitting field won't be as described if the quadratic is reducible. Other than that, unless I'm forgetting something (which would hardly be surprising), what you're saying is completely true.
4. Matrix Multiplication

In general. Well, for nonnegative integer exponents anyway.
5. Partial derivatives using definition

The definition of the second partials is just the partial derivatives of the first partials. Why couldn't you just use the same method as before?
6. Fourier series via complex analysis

1. Homework Statement Show that f is 2-pi periodic and analytic on the strip \vert Im(z) \vert < \eta, iff it has a Fourier expansion f(z) = \sum_{n = -\infty}^{\infty} a_{n}z^{n}, and that a_n = \frac{1}{2 \pi i} \int_{0}^{2\pi} e^{-inx}f(x) dx. Also, there's something about the lim sup of...
7. New Here. Question from power series

Well, it looks like you're trying to find the power series of ln(5 - x) by differentiating the series for 1/(5 - x) term by term. But ln(5 - x) is the integral of 1/(5 - x) (give or take a sign).
8. More Abstract Algebra

Oh, I meant for the intersection to be trivial. I'll think about what you said though.
9. Double integral with cos(x^n) term

I think changing the order of integration is the way to go. You'll get an x^3 term in the integral with respect to x. Then it's easy.
10. More Abstract Algebra

1. Homework Statement Show that G is isomorphic to the Galois group of an irreducible polynomial of degree d iff is has a subgroup H of index d such that \bigcap_{\sigma \in G} \sigma H \sigma^{-1} = {1} . 2. Homework Equations 3. The Attempt at a Solution I know that if G acts...
11. Example in Abstract Algebra

1. Homework Statement I'm trying to come up with an example of a quartic polynomial over a field F which has a root in F, but whose splitting field isn't the same as its resolvent cubic. 2. Homework Equations 3. The Attempt at a Solution Well, I know the splitting field of the...
12. Triple integral over a sphere in rectangular coordinates

I think you need to rethink your bounds on that one...
13. Trisectible angles | divisibility

Without additional assumptions on m and n, the implications aren't true...
14. Complex analysis again

Bump before bed
15. Trisectible angles | divisibility

Isn't your first question essentially, "Can you construct an integer multiple of a constructable angle?" Well...can you?
16. Complex analysis again

1. Homework Statement Let p(z) be a polynomial of degree n \geq 1. Show that \left\{z \in \mathbb{C} : \left|p(z)\right| > 1 \right\}[/tex] is connected with connectivity at most n+1. 2. Homework Equations A region (connected, open set) considered as a set in the complex plane has...
17. Volume vs. Area of a Surface of Revolution

Off the top of my head (that is, take this with a huge grain of salt), I think the approximating surface doesn't really matter in the answer, but the cone/cylinder might give the simplest (or maybe easiest to visualize) way to get to the answer.
18. Algebra questions, (emergency)

1. First, the integers aren't even a group under multiplication. So you should be using addition as your operation. Under addition the integers are an (infinite) cyclic group. What does that tell you? 2. I'm not sure what you mean by mapping to an infinite number of items. But for the first...
19. Hints for finding a Galois closure

I think I understand... The splitting field is the minimal field that contains all the roots of the minimal polynomial, and anything that's Galois over the rationals contains all the conjugates of \alpha (i.e., the roots of the minimal polynomial). So it contains the splitting field. Thanks...
20. Hints for finding a Galois closure

I believe the splitting field is just the original extension adjoin i. So that's handy. But it seems like that really shouldn't be the Galois closure. Why would any Galois extension of the rationals that contains \mathbb{Q}(\alpha) have to contain i? It seems like it would only have to be a...
21. Hints for finding a Galois closure

1. Homework Statement Find the Galois closure of the field \mathbb{Q}(\alpha) over \mathbb{Q}, where \alpha = \sqrt{1 + \sqrt{2}}. 2. Homework Equations Um...the Galois closure of E over F, where E is a finite separable extension is a Galois extension of F containing E which is minimal...
22. Weierstrass M-Test and Absolutely Uniformly Convergence

Well, I believe that to use the Weierstrass M-test you have to find a bound that works for all x on whatever set you're testing convergence in, not just a given x in the set. That is, your bound a is allowed to be a function of n, but it cannot be a function of x.
23. Weierstrass M-Test and Absolutely Uniformly Convergence

Yeah, I'm pretty sure the Weierstrass M-test tests for uniform convergence by essentially testing for absolute uniform convergence...
24. Set Theory Proof

Here's a tip that will get you through a good chunk of analysis problems: add 0 inside the absolute value sign in a "creative" way.
25. Galois group of a polynomial

1. Homework Statement Okay, I'm trying to explicitly determine the Galois group of x^p - 2, for p a prime. 2. Homework Equations 3. The Attempt at a Solution Okay, so what I've come up with is that I'm going to have extensions \textbf{Q} \subset \textbf{Q}(\zeta) \subset...
26. Set Theory Proof

No, that's not true. Just because |x - xo| is less than or equal to r doesn't mean that |x| + |xo| is too. Really, think more intuitively about what |x - xo| being less than r says.
27. Series question

Well, if you don't mind a cheat-ish answer, you could just look at the logarithm, then use the facts that logarithmic and exponential functions are continuous and that products of convergent sequences converge to the product of the limits
28. The Center of a Ring and Subrings!

In general, a subring of R is a subset of R which is a ring with structure comparable to R. So you don't actually have to show all the axioms because multiplication being associative and distributive is inherited just by being a subset of R. Similarly, some of the additive group structure is...
29. Ring Theory

What are the requirements for a subset of R to be a subring?
30. Being dense about an Algebra problem

Yeah, I hate to keep doing this, but I still haven't figured it out. So I guess I'll try one more time. Sorry to be irritating.