## Thank You PF!

Posted Sep17-12 at 03:01 PM by velox_xox
Updated Sep17-12 at 11:39 PM by velox_xox

I've been away for a while, and I've also meant to write this for several weeks now, but deadlines in school have kept me away.

I really want to say a general thank you to all of PF for existing and being supportive of people pursuing studies in the sciences. As I said when I first stumbled upon this forum, math isn't my best subject and being in a correspondence school where you are teaching yourself (for the most part) the concepts of math can be especially daunting.
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## Swing states, 2012 U.S. Presidential Election

Posted Sep17-12 at 02:13 PM by Redbelly98
Updated Sep22-12 at 03:42 PM by Redbelly98 (Added to "Detailed Explanation"; added direct link to Real Clear Politics)

My main purpose here is to help keep an appropriate and narrow focus on what will determine the winner in the upcoming 2012 election. That is, NOT the nationwide popular vote that polls often report in the months leading up to the election -- rather, the individual states and their electoral votes.

With that in mind, I look for the states that (1) are pretty well split in terms of which candidate they will vote for, and (2) have a lot of Electoral Votes. As I did 4 years ago, I'll...
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## Introduce Strongart as a phliosopher

Posted Sep16-12 at 12:18 AM by Strongart (Young mathematician Strongart in China)

Hi, I am Strongart, I am a young mathematician in China. I study maths by myself and make some videos to teach commutative algebra, functional analysis and other topics at the internet just like the Khan Academy and MIT open courses. Meanwhile, I am also a philosopher, I create some interesting philosophical propositions, let us have a very short discussing here.

For the soft philosophy, my proposition is "ideal precedes position", how to understand it? You can compare...
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## A Short Proof of Birkhoff's Theorem

Posted Sep14-12 at 08:37 PM by PeterDonis
Updated Mar17-13 at 02:47 PM by PeterDonis

The subject of Birkhoff's theorem came up in a recent (as of Sep 2012) thread, and in the course of researching it I realized that MTW's statement of the proof does something that, strictly speaking, is not mathematically correct. (In fact, this something is not limited to their proof of Birkhoff's theorem; they do it throughout the book.) MTW write the general line element for a spherically symmetric spacetime as follows:

$$ds^2 = - e^{2 \Phi} dt^2 + e^{2 \Lambda} dr^2 + r^2 d\Omega^2$$...
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