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Paul LiuMath. Physics. And a touch of arrogant self-reflection.
http://hippomath.blogspot.com/
Math. Physics. And a touch of arrogant self-reflection.
http://hippomath.blogspot.com/
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Paul Liu | hippomath.blogspot.com Reviews
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Math. Physics. And a touch of arrogant self-reflection.
hippomath.blogspot.com
Paul Liu: First they came...
http://hippomath.blogspot.com/2012/01/first-they-came.html
Math Physics. And a touch of arrogant self-reflection. A very powerful quote that was brought to my attention by a commenter on Hacker News. On the proposed Polish Anti-Counterfeiting Trade Agreement. When citizens are inactive on bad government reforms, what seems like one small alteration could build up to monumental changes. First they came for the communists, and I didn't speak out because I wasn't a communist. Then they came for the Jews, and I didn't speak out because I wasn't a Jew. 11 May 2012 at...
Paul Liu: A curious identity
http://hippomath.blogspot.com/2011/08/curious-identity.html
Math Physics. And a touch of arrogant self-reflection. I was trying to do a question the other day when I found an interesting identity that is a corollary of the double angle formulae. I've searched online for its name, but it might be so trivial that it doesn't have one. Instead of revealing the identity, I'll let you figure it out for yourself:. Frac{1}{2 0} cos(x 1) = cos(x 1) ]. Frac{1}{2 1} left( cos(x 1 x 2) cos(x 1-x 2) right)= cos(x 1) cos(x 2) ]. Frac{1}{2 {2} left( begin{array}{c}. Subscribe t...
Paul Liu: My Favourite Proof
http://hippomath.blogspot.com/2012/04/my-favourite-proof.html
Math Physics. And a touch of arrogant self-reflection. This post is inspired and adapted from Greg Martin's excellent talk on prime numbers (found here. As a student of mathematics, one of the first things I ever learned was the concept of a proof. In fact, the first proof I ever saw was Euclid's classic proof that there were an infinite number of primes. If you have never seen Euclid's proof before, it goes something like this:. Hence, $N$ must have some new. By Murty, 1988). For example, this means...
Paul Liu: July 2011
http://hippomath.blogspot.com/2011_07_01_archive.html
Math Physics. And a touch of arrogant self-reflection. Thin Cars and Parking Lots. A quick question I came across today:. Suppose you had an infinitely thin car. How big do you have to build a parking lot for the car to be able to turn 180 degrees in the parking lot? Think about it for a while, and then highlight the area below to see the answer. Surprisingly, there is no lower limit on the size of the parking lot. In other words, the parking lot can be as small as you want. Posted by Paul Liu. The obser...
Paul Liu: January 2012
http://hippomath.blogspot.com/2012_01_01_archive.html
Math Physics. And a touch of arrogant self-reflection. A very powerful quote that was brought to my attention by a commenter on Hacker News. On the proposed Polish Anti-Counterfeiting Trade Agreement. When citizens are inactive on bad government reforms, what seems like one small alteration could build up to monumental changes. First they came for the communists, and I didn't speak out because I wasn't a communist. Then they came for the Jews, and I didn't speak out because I wasn't a Jew.
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Daily GRE: Physics GRE - # 34
http://dailygre.blogspot.com/2011/09/physics-gre-34.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Monday, 5 September 2011. Physics GRE - # 34. Eigenfunctions for a rigid dumbbell rotating about its centre have a $ phi$ dependence of the form $ psi( phi)=Ae {im phi}$, where $m$ is a quantum number and $A$ is a constant. Which of the following values of $A$ will properly normalize the eigenfunction? Math GRE - ...
Daily GRE: September 2011
http://dailygre.blogspot.com/2011_09_01_archive.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Monday, 5 September 2011. Zai geen, sayonara, goodbye (for now at least). Thanks for all the comments, you guys really taught me a lot. I hope I was able to help all of you too (even if it was just the slightest bit). Posted by Paul Liu. Math GRE - #34. Choice 4 is the answer. F prime(x) = e {-x 2-x {-2} (-2x 2x {...
Daily GRE: July 2011
http://dailygre.blogspot.com/2011_07_01_archive.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Saturday, 30 July 2011. Let us go then, you and I. Two GRE questions a day. One Math. One Physics. That is all. Posted by Paul Liu. Subscribe to: Posts (Atom). Math and Physics Feed. View my complete profile. Let us go then, you and I.
Daily GRE: Math GRE - #33
http://dailygre.blogspot.com/2011/09/math-gre-33.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Sunday, 4 September 2011. Math GRE - #33. How many integers from 1 to 1000 are divisible by 30 by not by 16? Choice 1 is the answer. There are 33 multiples of 30 under 1000 (1000/30 = 33.33.). So we only need to focus our attention on choices 1 to 4. Note that the factorization of 30 is: $2 cdot 3 cdot 5.$. I am 1...
Daily GRE: Physics GRE - #33
http://dailygre.blogspot.com/2011/09/physics-gre-33.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Sunday, 4 September 2011. Physics GRE - #33. A radioactive nucleus decays, with the activity shown in the plot below. The half-life of the nucleus is:. Choice 2 is the answer. Posted by Paul Liu. Subscribe to: Post Comments (Atom). Math and Physics Feed. View my complete profile. Math GRE - #34. Physics GRE - # 34.
Daily GRE: Math GRE - #32
http://dailygre.blogspot.com/2011/09/math-gre-32.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Saturday, 3 September 2011. Math GRE - #32. Let $ mathbb{R}$ be the set of real numbers and let $f$ and $g$ be functions from $ mathbb{R}$ into $ mathbb{R}$. Which of the following is the negation of the statement:. For each $s$ in $ mathbb{R}$, there exists an $r$ in $ mathbb{R}$ such that $f(r) 0$ and $g(s) leq0$.
Daily GRE: Math GRE - #34
http://dailygre.blogspot.com/2011/09/math-gre-34.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Monday, 5 September 2011. Math GRE - #34. F$ is the function defined by: [ f(x)= begin{cases} xe {-x {2}-x {-2} and text{if } x neq0 0 and text{otherwise.} end{cases} ] At how many values of $x$ does $f$ have a horizontal tangent line? Choice 4 is the answer. Posted by Paul Liu. For the LaTeX, I use mathjax (by go...
Daily GRE: Math GRE - #31
http://dailygre.blogspot.com/2011/09/math-gre-31.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Thursday, 1 September 2011. Math GRE - #31. Choice 3 is the answer. Posted by Paul Liu. This webpage is LaTeX enabled. To type in-line formulae, type your stuff between two $. To type centred formulae, type [ at the beginning of your formula and ] at the end. Subscribe to: Post Comments (Atom). Math GRE - #34.
Daily GRE: Physics GRE - #31
http://dailygre.blogspot.com/2011/09/physics-gre-31.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Thursday, 1 September 2011. Physics GRE - #31. Which of the following is nearly the mass of the Earth? The radius of the Earth is about $6.4 cdot10 6 , text{m}$. 6 cdot10 {24} , text{kg}$. 6 cdot10 {27} , text{kg}$. 6 cdot10 {30} , text{kg}$. 6 cdot10 {33} , text{kg}$. 6 cdot10 {36} , text{kg}$. Posted by Paul Liu.
Daily GRE: Zai geen, sayonara, goodbye (for now at least).
http://dailygre.blogspot.com/2011/09/zai-geen-sayonara-goodbye-for-now-at.html
Two GRE questions a day. One Math. One Physics. Currently the LaTeX and hidden solutions on this blog do not work on Google Reader. Email me if you have suggestions on how to improve this blog! Monday, 5 September 2011. Zai geen, sayonara, goodbye (for now at least). Thanks for all the comments, you guys really taught me a lot. I hope I was able to help all of you too (even if it was just the slightest bit). Posted by Paul Liu. How am I going to challenge myself daily now? Are you coming back? I know I s...
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Paul Liu
Math Physics. And a touch of arrogant self-reflection. This post is inspired and adapted from Greg Martin's excellent talk on prime numbers (found here. As a student of mathematics, one of the first things I ever learned was the concept of a proof. In fact, the first proof I ever saw was Euclid's classic proof that there were an infinite number of primes. If you have never seen Euclid's proof before, it goes something like this:. Hence, $N$ must have some new. By Murty, 1988). For example, this means...
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