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Homework Statement You are at P(-1,1) on the surface z = (y-x^2)^3. What direction should you move from P so that your height remains the same? Homework Equations The Attempt at a Solution So I basically do not want my height z to change. In this case, I will take a vector...

Thank you so much!

Just a quick question, is the 2nd diagram in Fig 14.1 of order g? I don't see why there are two powers of g in this diagram. We have 2 propagators and one counterterm, giving us one power of g is Y = O(g). Can anyone clear up this quick question? Basically, I'm asking, is it ~ g and hence...

How come there is no h^2 term after we do it this way? Using the definition, I don't see why I only get an h and not h^2.

Apparently there is a technique to get the equivalence without using the Riemannian metric, but just using a Partition of Unity. Having said that, I know that having a Partition of Unity implies the existence of a Riemannian metric, but the book I am using, a Riemannian metric is not even...

One form <-----> vector field How exactly does having a one form yield a vector field in a smooth way? I understand it's a duality relationship, but can anyone give me some more insight into this?

That didn't help me too much, I just looked up the definition of submanifold (explicitly) and just used that. It works quite nicely.

Homework Statement Show that the set of all 2x2 matrices of rank 1 is a submanifold of R^4 Homework Equations The Attempt at a Solution The hint in the book was to show that the determinant function is a submersion on the manifold of nonzero 2x2 matrix M(2) - 0. This is easy to...

I'm currently a grad student and I was hoping some of the more experienced members of this board could give me some guidance. Due to some unfortunate circumstances, I'm really wondering if being in a PhD program is the best possible option for me. I do not want to get into specifics, seeing...

Here is a better question: Is R^3 - {n non-intersecting lines} homeomorphic to R^3 - {n parallel non intersecting lines}?

Homework Statement In R^3, if we have p non-intersecting lines, is it true that there exists a plane Y such that all the lines intersect Y? Up to rotations. Homework Equations The Attempt at a Solution No real attempt, this is just something I found to be interesting. Any thoughts?

Why is there no satisfactory way to define the energy density of a gravitational field? Why must we use global energy concepts? I'm currently reading proofs of the Positive Energy Theorem, but none of the references explains why this is so. Can anyone explain it or point me to a good reference?

Hmm I see. I think once I pass my prelims I will take some programming courses, who cares if they are undergrad courses, I need to start somewhere. I thought the math-finance world was really on the decline? How easy would it be for a math PhD from a top 15 program with good programming...

I have some questions about what direction to take in grad school. First of all, I don't really think I'm going to pursue the academia route. With this being the case, I'm wondering what a math PhD's prospects in industry are. I plan on pursuing PDEs and mathematical physics. Some of the...

I don't know if that's true; a point removed on the projective plane corresponds to a point, antipodal point pair being removed on the sphere, i.e. the sphere is a 2-1 covering of the projective plane. So removing a point on the projective plane corresponds to removing 2 points on the sphere.

So I have been wondering, what is the fundamental group of a projective plane after we remove n points? I tried doing this using Van Kampens Theorem, maybe I am applying in incorrectly, I am getting that it is the Free group on n generators. However, when I think of RP^2 as a quotient of...

Knot Theory

I think we should close this thread before any more damage is done. This guy is saying some borderline unnerving things about a respected scientist.

I will not even make a judgement about whether or not you were treated fairly. I am STUNNED (STUNNED!) you are bringing this up in such a public forum. The fact that you air this issue out on a message board and leave yourself almost no anonymity is astounding.

It's tough to give someone reasons to go to grad school. The hours are so long, it'll take anywhere from 5 - 7 years to finish a degree that has extremely competitive job prospects, especially in physics. I've heard that physicists usually do 2 postdocs before they land a tenure track position...

I don't think anyone that does well in a subject should go to grad school. It depends on the person of course. Grad school will be about research, and if you hate research, it should be a blessing to you. You know what you don't like. Now is the time to save yourself a lot of headaches and...

You might also want to check out Perimeter Institute, they have some QI people there.

ETH Zurich is also excellent.

It depends on the school. Your grades and course load look good. Hopefully you can get very good letters, if so, then you have a good shot at a good school. For Math GRE, if you are applying to the UC's, like UCLA, UCSD, UC Berkeley, etc. I think they really want to be an 80+% score, they say...

Hey everyone, I've been having a moral dilemma lately. I'm not sure if moral dilemma is the exact word. Anyway, I like doing math and delving into physics, but there is something inside of me, urging me to do something more important. While I do enjoy math, physics, I do not believe they are...

How exactly does it work when a beginning graduate student wants to attend a conference? Do they usually take care of the hotel accommodations and flight reservations? How do they approve funding? Do I need a "reference" or do they just see that I'm a real grad student (i.e. my web address and...

Admissions to top 25 schools is still very very competitive. It might be a notch below top 10 admissions, but it is still very difficult. You should contact the department you are interested in and gauge what your chances are. But there is not a significant dropoff in terms of competitiveness...

http://www.university-list.net/us/rank/univ-1047.htm <-- These rankings are the 2007 US News World and Report Grad Rankings. and Overall Engineering: http://www.university-list.net/us/rank/univ-1043.htm Both A&M and Austin are considered top 25 schools for Electrical Engineering and top 15...

Yes I own a copy. I was hoping I could get some input from people who are current grads or professors in the context of today's economy and academic situation. There was a New York Times article about the decline of university and a standard liberal arts program. If less people are forced to...

Since we seem to have a few professors and grad students on this forum, I was hoping to open a discussion on the current employment trends in math academia. It seems as is the road to tenure is incredibly difficult and it takes more than just writing a good thesis to get a job. I am posting...

Let's just say I know what goes on at school B REALLY WELL. I don't want to get into specifics. But I think they are unhappy more so because of the lifeless area around it. Very small town, there is not even a movie theater within walking distance. It's a veritable ghost town. But I'm...

I just got an a very unexpected admissions of the waitlist at school A and I'm not sure what to do. I have pretty much today to decide to go to a school that just admitted me as opposed to a school that admitted me almost 2 months ago, call it school B! The pros of school A are great location...

I suggest you learn LaTeX, a program you use to author math and physics papers and type up your work. Submit it on arXiv or just put it out there somewhere on the internet. Do you copyright such things? I'm not sure how this works, but it's good to get your ideas out there.

I don't think math is as trendy as physics. But on the other hand, I do think there are hot fields and schools want to hire those researchers working in hot fields. And I think organizations like the NSF do follow trends in research. My field is differential geometry and geometric analysis, a...

I would also look into tutoring your fellow high school students. You can charge 10-12 dollars an hour, much cheaper than tutoring from a physics teacher or a physics grad student. I don't want to pick on the original poster, but you mentioned a theory on QM and GR, you list that in your About...

Perelman uses a lot of advanced techniques in differential geometry and geometric analysis. I would recommend you read Peter Petersen's text on Riemannian Geometry, L.C. Evans text on Partial Differential Equations, Peter Li's notes on Geometric Analysis and then read Richard Hamilton's seminal...

Hi, I'm looking for good textbooks or problem books for a 9 and 10th grade students. Maybe not as difficult as the AMC or IMO level math, but some problems that require some thought rather than just plug and chug formulas. For example, I want to find a good problem set for trig proofs, and...

All of this is far from a guarantee. Choose wisely.

I have just finished reading ZapperZ physics thread and some concerns come to mind. (1) ZapperZ mentioned something about pedigree and how these postdoc positions are extremely competitive, so a good tie breaker is who their adviser was. I have researched enough into postdoc, potential advisers...

I need some help picking which math PhD program to attend. My interests are Differential Geometry/Riemannian Geometry, geometric analysis, General Relativity (or Lorentzian geometry in general) and Mathematical Physics. I have been fortunate enough to receive some nice offers from a few...