I just counted the number of people I talked to today and I was kind of shocked. The people I talked to today are: someone from one of the school offices(by phone), someone from the leasing office of an apartment(by phone) and a librarian of the science library at my school. Nothing personal...
It is one month into my summer vacation and the only task I have right now is to prepare for the General GRE that is coming up pretty soon. However, I still try to read a bit of math everyday. I feel extremely guilty if I ever get the thought of not doing math for just one day. I think that...
I'm working on a unlimited time final exam. There is a problem that I have been thinking about for the last three days but I still couldnt get it. It is worth about 15% of the final and the final is 35% of my grade. I could work on the final for another 5 days before I turn it in. Now the...
Homework Statement
Let K be a number field. Let a be an irreducible element of K. Prove that if <a>(the ideal generated by a) is not a prime ideal, then it is a product of two prime ideals.
Homework Equations
The Attempt at a Solution
I'm actually quite clueless...:frown: I...
Warning: This is more of an expression of my frustration than a question looking for an answer.
I'm a junior math major in a small elite liberal arts college. Just recently, I became very repelled by the idea of studying sciences or math at a liberal arts institution. There are simply not...
I'm a junior math major in a small liberal arts college. I have taken a lot of math classes and will apply to graduate school this year.
Recently I started to talk a lot with another senior math major. He might not have been taking such an intensive schedule as I do, but he seems to know a...
So I'm a junior in mathematics and I've reached a point to decide about graduate school. I love pure math and am considering getting a PhD in it. But I do not want to go into academia because I don't think I will enjoy teaching. So I want to go into the industry after a PhD. But one of my...
Hey guys,
I want to study algebraic topology on my own. I just finished a semester of pointset topology and three weeks of algebraic topology. We did not use a textbook. Can anyone recommend a book on algebraic topology?
Hatcher is fine but it is not as rigorous as I want. Munkres has...
Homework Statement
I am trying to show that R^n\{x} where x could be any point in R^n is connected for n>1. I have been thinking about this for a while but haven't had any luck. Seems like that I'm missing something simple. I tried to construct a continuous map from R^n to R^n\{x}. All I...
Homework Statement
I have the field F_5 and I adjoin some square root of 2 , say 2^{1/4}. Is there a way to see that the multiplicative group inside F_5(2^{1/4}) is cyclic and find the generator?
Homework Equations
The Attempt at a Solution
I did the F_5(2^{1/2}) case and think the...
Let F be a field. Let c \in F.
I am trying to show that if
c = f^2 where f\in F[[x]], then f\in F.
So I am able to get rid of the terms with negative exponent. So now I'm left with a formal power series. Anyone knows how to do this? Thanks!
Hello guys,
So I made four plots using Mathematica. I am trying to make them the four panels of a collage. Is this doable using Mathematica or using any other software? Any suggestion is appreciated. Thanks!
Homework Statement
I'm working on a problem and as long as I can show that
[tex] \prod_{p\leq n}p \leq \prod_{n<p\leq 2n}p [/ tex]
then I'm done. But I'm having trouble with this..Can someone help? :tongue:
Homework Equations
The Attempt at a Solution
I tried to use PNT but could not...
Hey guys,
I have a question about email addresses in a journal paper. It is natural for authors who are professors to leave their .edu email addresses because are rarely changed. But what about for an undergrad? I am graduating in 2 years and the school will delete my account after I...
Hello guys,
Before I start, I just want to say the what I am going to say below is just my personal opinion. I'd like to hear about it if you disagree. I just hope no one gets offended by this.
I am a math and physics double major and thus spend plenty of time in both departments. Some...
Hey guys,
So I have been playing with LogLogPlot in Mathematica and it seems to me that PlotRange->{a,b} does not work. I also tried Show[%,PlotRange->{a,b}] but somehow my axes got cut off. Anyone knows how to do it if I want to display a certain area of a log-log plot?
Hi! Can someone recommend some books on point set topology for undergraduates? I am going to use it this summer for preview and also during the fall because the instructor is not going to use a textbook. Thank you!
A friend of mine has been urging me to switch to LINUX.. He said that LINUX is way user friendly than Windows and the transition is not that bad. He is a tech-guru so he probably defines 'not bad' differently from me. I am a Window user right now. I am not very familiar with operating...
I just had a weird thought.
One qubit is a 2-d complex vector space which is isomorphic to a 4-d real vector space. Why can't we model the 4-manifold of space-time universe using one qubit?
Hey guys,
I am a rising junior in college. I am doing my first serious research in physics this summer. I just get started. The topic is nothing like something that I'm familiar with. I am the only undergrad in the research group. I have been trying to catch up but I'm going way too...
Hello,
I am a math and physics double major. But somehow I feel that it is very difficult for me to get a deep understanding of some topics in physics. I get all the mathematical muscles needed to solve problems and I score the highest on the exams. But I feel that I am actually faking it...
Homework Statement
Factor x^{16}-x in F_8[x]
Homework Equations
The Attempt at a Solution
I know how to do it in F_2[x] . I also feel the factorizations are the same in the two fields..but not sure how to prove it.
Homework Statement
Hello,
I just have a question about LaTeX. I am writing a math paper. Is there a way to number/label my examples like I do for theorems and definitions? Thank you.
Homework Equations
The Attempt at a Solution
Homework Statement
Prove that a polynomial f of degree n with coefficients in a field F has at most n roots in F.
Homework Equations
The Attempt at a Solution
So we could prove this by induction by using a is a root of f if and only if x-a divides f. My question is: why do...
Hey,
I am just wondering whether there is a good way to get you trained for the Putnam? It may not necessarily for the Putnam, but to teach you to tackle fun and difficult math problems and come up with ideas. I want to use the coming summer to do this and I will have tons of free time at...
Hey guys,
This year is my first time of applying to REUs in mathematics. So far I have not heard any good news. I feel that I might have made a lot of mistakes in the process of applying. Even if I cannot get into the REUs that I am interested in, it is still good to actually learn...
Homework Statement
How to prove that the only irreducible polys over the reals are the linear ones and the quadratic ones no real roots?
What about the ones with higher degree? I feel that I'm missing something that's really obvious.
Homework Equations
The Attempt at a Solution
Homework Statement
I am try to prove :
Let R be a ring, I be a ideal of R.
Then N is a maximal in R/I if and only if N=M/I where M is a maximal ideal in R that contains I.
Homework Equations
The Attempt at a Solution
First I'm not 100% sure that the statement is true, but I'm...
Homework Statement
Hi,
Can someone give me an example where f_n is continuous on [0,1] for each n.
f = \sum_{n=0}^\infty f_n converges pointwise(not uniformly) on [0,1] and f is not continuous on [0,1]?
Thanks!
Homework Equations
The Attempt at a Solution
Technically we need uniform...
Homework Statement
Is f(y)=\sum_{m=1}^\infty \frac{1}{y^2+m^2}
differentiable?
Homework Equations
The Attempt at a Solution
From the graph, it is obvious that f is not differentiable at y=0, but I don't know how to prove that. I proved that \sum_{m=1}^n...