Recent content by Kummer

You first integrate with z, that gives you rz in the inside. Using Fubini you get (meaning evaluate the integral) r\sqrt{6-r^2} - r(r^2) and now continue with r and theta.

\log_2 5 = a/b so 2^{a/b} = 5 \implies 2^a = 5^b. Now use unique factorization.

I will begin by saying how much I dislike it when non-mathematical philosophers think about math. There are many threads in the mathematics forum like this and they belong in the philosophy forum, so one good thing about this thread is that it at least is in the philosophy subforum. I am not...

Non-zero constant. Not to offend you but that is what I like to call a "physics-type mistake".

Here is a little something to add to what matt-grime was lecturing about. Theorem: Let |F|= \infty and f(x) be a polynomial if f(\alpha)=0 for every \alpha \in F then f(x)=0. Proof: Let \deg f(x) = n (assuming f(x)\not = 0) then f(x) can have at most n zeros. But it clearly does not for...

\frac{1}{n+n}\leq \frac{1}{n+\sqrt{n}}

Place Number theory with Algebra. That makes it better.

In what contour? And what is k? Note if k is zero then it becomes 1/e^z which is analytic. But if k!=0 then there is a singularity which depends on the contour.

The delta function cannot be used for a conterexample about theorems about intergration. Because it is not a "function" eventhough it is called a function, rather it is a Schwartz distribution so the known results about integration might not apply to it.

Yes he did. I should be more careful lest someone accuse me of stealing answers. I deleted my post otherwise it does not look good.

Most of what I know is self-taught, so there really is nothing amazing about teaching youself. All you need is motivation.

I really like the algebra book by Blair. It has Galois theory in it. It is better to use Morandi but he is GTM.

If f is a bounded function on [0,1] which is integrable then |f| is integrable on [0,1]. It is a simple theorem to prove.

How well do you know undergraduate analysis? Do you know the following topics: Completeness property Limits of sequences and delta/epsilon, Cauchy sequences Subsequences Limsups and Liminfs Continous functions, delta/epsilon definition, sequence definition Properties of continuous...

@ehrenfest. It really is not so hard. If n is a number in {2,3,...,100} it not a prime number then we can write n = p*m where p is a prime number. So for any n there exists a smallest possible prime divisor. Given any n the smallest prime divisor is 7 because it cannot be 11 because if it were...