Recent content by E01

If this type of post is not allowed then I completely understand if the mods have to remove it. So I'm a first year Master's student and I'm soon about to take my Real Analysis final exam. I know I'm going to fail the exam most likely as I have to be able to remember all of the homeworks (which...

Can anyone give me a little background on why $$L^p$$ spaces are a thing? What types of problems were they developed to solve? Where they just a sort of generalization of the Euclidean norm? The Analysis class I'm taking right now has very little context to it so I feel like I am learning random...

Thanks for the suggestions. Do you think those sorts of problem solving books can actually make a significant difference in one's problem solving skills?

I was thinking about adding to my collection of math literature and I was wondering what you all consider must have reading material. I just recently got Math It's Contents, Methods, and Meaning and the Princeton Companion to Mathematics. I was thinking things at that level of must have (I might...

I'm a new first year graduate student and I've decided that my way of learning mathematics may not be the most efficient. I often memorize proofs in the book in the hopes that I'll be able to see where to apply the techniques used in the problems(I often understand the logic of a proof but won't...

I'm trying find the minimal polynomial of $$a=3^{1/3}+9^{1/3}$$ over the rational numbers. I am currently going about this by trying to construct a polynomial from a (using what I intuitively feel would be a sufficiently small number of operations). Then I'd show it's irreducible by decomposing...

All right, I'll check them out. Thanks!

Hey, I was just wondering what good math periodicals there are out there. I was looking for something that is readable by a wide audience. I've only taken courses in topology, abstract algebra, and real analysis at the undergraduate level. Any suggestions?

I am trying to do an exercise where I am showing that the set of all elements of $\Bbb{Z}_n$ that are coprime with n form a group under modular addition. So far I have shown associativity, identity, and closure, but I'm having trouble showing the existence of an inverse. I know I can't use...

I have a fairly simple question. My teacher used the fact that $\Delta e^{i\theta} = e^{i\theta}i\Delta \theta$ when theta approaches 0. Does he derive this using the fact that the derivate of $e^t = te^t$ ?

I'm trying to get get a good base for learning further mathematics. Would an intro abstract algebra, analysis, and category theory text be good places to start? There are so many different places you could start and I'd like to first learn about those areas of math which help most when learning...

Yea, after you told me how to set it up it took about ten seconds :P, and here I had sat and wondered about it for like an hour. I had assumed that I could plug N+1 into $$F_{2n-1}F_{2n}$$ and add that back to the left hand side of the equation and get what equaled $$F^2_{2n+2}$$. So now I know...

The problem is as stated: Prove that $$F_1*F_2+F_2*F_3+...+F_{2n-1}*F_{2n}=F^2_{2n}$$ But earlier in my text I proved by induction that $$F_{2n}=F_1+F_2+...+F_{2n-1}$$. Do I need to use this earlier proof in my current proof. I tried adding $$F_{2n+1}F_{2n+2}$$ to the right and left hand side...

Thanks for the response Deveno. That makes sense. So I would say y is an element of Y and y=f(A) for some x element of A. In response to Evgeny. I forgot the starting portion of the definition. Let X and Y be sets. Let f be a function from X onto Y. A is a subset of X. We define the image of A...

This may seem like a dumb question but I'm not sure whether "such that" is equivalent to "iff" or "if then". Here is what confused me. The image of A "f(A)" is defined as y element of Y such that for some x element of A, y=f(A). I could say there exists some element x such that y=f(A). I'm not...