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Can someone look at my statement of purpose?

  1. Nov 27, 2014 #1
    I'm writing my statement or purpose for a PhD program in physics. Can someone look it over for me please?
  2. jcsd
  3. Nov 27, 2014 #2
    Knowing how things work has always been my passion in life. My favorite subject in school was always science and when I found out physics is the most fundamental of the sciences I was dead set in pursing a career in physics. However when I made this realization I had a huge obstacle in my way at the time. I was in a terrible inner city high which did not offer any of the advanced math classes or even regents physics classes I needed to pursue my dream. I knew that if I wanted to learn physics I would need to get out of that special needs school.

    So I took the SHSAT exam and failed it my 8th grade year. I did not give up hope of going to a high school where I can learn the needed mathematics and physics that I needed to get into college and eventually get into a PhD program in physics. So I retook the test in my 9th grade year and got a 564 landing me a spot at Brooklyn Technical High School. While at Tech I choose the major which offered the most amount of physics and math classes and I took all of the APS in math and science that I could take. I did this methodologically so I could be as prepared as possible for college level physics and mathematics. I knew exactly what I wanted to be and do for a long time.

    When I got into college all of the work I did in high school paid off and I was ahead of my peers. This meant I was able to put in less time in class work and still get an A. This meant I had more free time on my hand I would use that free time to study for classes I would take next year and study topics in physics of interest to me. I would constantly go into the Bobst library and read and do problems from graduate level textbooks such as Goldstein Classical Mechanics when I was just an sophomore. While reading Goldstein I amazed by how beautiful and concrete the formalism was for classical mechanics. The important equations in classical mechanics like Hamilton’s equation can be written in a small section of a page yet they are so powerful. Using the Hamiltonian you can test if a quantity is conserved by seeing if the Hamiltonian commutes with the Poisson bracket of the quantity in question Some of these conserved quantities may not even be energy or momentum . Hamilton’s formalism transcends classical mechanics and the Hamiltonian plays a central role in quantum mechanics. This ability to generalize classical mechanics and its beautiful formalism made me want to do cutting edge research in classical mechanics.

    My goal to do research in classical mechanics came true when I was accepted into the competitive summer research program at NYU Polytechnic. While their I did research in Chaos Theory concerning the double pendulum. I built a double pendulum in a lab and using a high speed camera and tracking software tracked it's motion for initial conditions where it's not chaotic and for regimes for which it's chaotic. I also made a simulation of it on Mathematica and compared the results of my simulation to the experimental results for the given initial conditions. This summer project became my senior project and right now I'm currently studying the seperatix motion of the double pendulum. Because I was so dead set on doing research from the beginning of my high school career I was able to quickly learn mathematica and learn a lot about Chaos theory. I've read my papers over the summer including Double pendulum and θ-divisor from the Journal of nonlinear science. That particular paper inspired to find a solution of the double pendulum when g=0 and than use perturbation theory treating gravity as a small perturbation to analytically understand the motion of the double pendulum where the kinetic energy is much larger then the potential energy.

    At NYU I would like to become the best possible version of myself I can be. I would like to learn as much physics I can and do research which will expand our bubble of knowledge. I would like to earn a PhD and spend my life doing research in either Chaos Theory or Quantum Field theory and teaching physics. I especially love teaching and seeing the awe in students faces when they understand a difficult topic in physics. As a private tutor and head physics tutor at the Polytechnic tutoring center I'm fortunate enough to see that often.

    This is very rough draft.
  4. Nov 27, 2014 #3

    Vanadium 50

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    There is only one sentence in here at all that relates to "purpose".
  5. Nov 27, 2014 #4
    Please describe briefly and concisely your past and present work as it relates to your intended field of study, your educational objectives at NYU, and your career plans. In addition, please include your reasons for choosing your field of study.

    The statement should be concisely written and should not exceed one to two double-spaced pages.

    This is what they told me to write.
  6. Nov 27, 2014 #5

    Vanadium 50

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    Fine. Write whatever the heck you want. (But I don't understand why you asked for advice when you don't want to take it)
  7. Nov 27, 2014 #6
    I do want to take your advice. I just posted the description of what they actually wanted me to write so that someone who is reading my stat
  8. Nov 27, 2014 #7
    Also your advise was very blunt I would hardly call it advise. If you thought it was total crap you should of said so that would of been better advise.
  9. Nov 27, 2014 #8
    So as V50 stated there is essentially no purpose to the statement of purpose...somethings to fix this...

    You really need to be more specific. Cutting out a lot of these buzzwords and backgrounds will help give you the space. Remember that they are paying for you to come here so this is a big investment for the school. You really need to sell yourself. What will YOU do for the school if you got there?
  10. Nov 27, 2014 #9
    Thanks a lot Zapz I'll get to work on making my statement of purpose a lot more specific and a lot less fluff.
  11. Nov 27, 2014 #10
    If I was in a scenario where I can ask a physics related question and I would be given the correct answer I would ask why does sensitivity to initial conditions exist in some mechanical systems. I can understand that the superposition does not hold for non linear equation and that's why it's difficult to solve them. But like some we can solve like the KDV equation to get the solution of a soliton. It totally blows my mind though that some of these non linear equations have solutions which exhibit properties so exotic that we cannot represent them even in terms of “special” functions. That is just one of many question I would like to get a more satisfactory answer for in graduate school.

    While I was a freshmen in college I would spend lots of self studying for classes that were ahead of the classes I was currently taking. When I was a sophomore taking analytical mechanics I was self studying from Herbert Goldstein classical mechanics because I wanted to learn physics as fast as possible so I can start doing research in physics. One of things that struck me about classical mechanics was how orderly the formalism is. Going from the F=ma one can understand the principal of virtual work and derive Lagrangian mechanics from it. From Lagrangian mechanics by applying the Legendre transformation the Hamiltonian mechanics can be derived. Than from by using essentially a built in feature of Hamiltonian mechanics in which if a coordinate transformation is canonical than Hamilton equations are preserved HJE mechanics can be derived. Each one these equations are immensely powerful and yet despite being so powerful can be derived pretty easily from each other. This made me want to do research in classical mechanics.

    I got a chance to do research in Chaos theory with a professor and it increased my scientific maturity levels. I did work in the lab building a physical double pendulum. I than simulated the double pendulum using Mathematica and used tracking software to monitor the motion of the double pendulum. I also constructed bifurcation diagram and Poincare sections and on my own learned some shocking things about Chaos in a double pendulum. For starts you can have two initial conditions with the same energy but one initial condition will lead to Chaos while the other won't. By studying the motion of the double pendulum I learned just how subtle problems can be in physics. I also understood why people who study something in physics are usually left with more question than answers despite seemingly being able to explain the system inside and out. Doing research also got me into the habit of constantly reading journals on nonlinear dynamics. One of my favorite papers Double pendulum and θ-divisor from the Journal of nonlinear science inspired me to use the integrable solution of the double pendulum when g=0 and then use perturbation theory treating g as a small parameter to get an analytical rather than numerical understanding of the motion of a double pendulum. I hopefully would like to use this analytical understanding to be able to predict when a double pendulum which has the energy to go into a seperatix orbit will actually enter one and stay in one forever.

    This is the kind of research I want to do at GSAS physics. I want to study Chaos theory and non linear dynamics because it's such a exotic phenomena yet can be explained by the beautiful and orderly formalism of classical mechanics. In my undergraduate career I will be working for a total three semesters on this research. This means that when I enter graduate school I will have lots of research experience and will have a understanding of the methodology of how to do research in physics even if I have to do research in a completely different field than non linear mechanics. However I'm also interested in continuing from where my research in my undergraduate institutions left off. I can first day of graduate school get an adviser and continue on my research in Chaos theory. Because I took a graduate classical mechanics at GSAS I have the physics and mathematical tools needed to go high level research in Chao theory with faculty one day one. While at NYU I would like to learn as much physics as possible and hopefully be the first to discover something that no one has discovered before. Or perhaps be the first to give a truly satisfying explanation as to why let's say turbulence exists in fluids. I want to live my life doing research as a professor after I get my PhD.
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