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## Main Question or Discussion Point

Hey all,

while I've applied to several REUs for this summer, I've mostly been applying in areas that I'm only tangentially interested in. Last week, I received an email about a new REU that's opened up at Case, and was ecstatic to see the following research program:

(T4) Phase transitions in the early universe (project advisor Harsh Mathur): The focus of my work on cosmology is on the observable consequences of phase transitions in the early universe. Possible REU projects include numerical simulation of such a phase transition or analysis of the impact of such a phase transition on the cosmic microwave background. The minimum background needed is some familiarity with differential equations. Any prior experience with programming and courses in quantum mechanics, statistical mechanics and electromagnetism will be an asset but is not required. No background in cosmology or astrophysics is needed other than a general interest in the field. More information on our work in this area is available at http://www.sciencedaily.com/releases/2008/04/080415143816.htm

Since I'm very much interested in theoretical physics, and especially cosmology, I decided to apply, and more over, give the application a very personal touch. After all, the professor is looking for someone who is extremely interested in the field. So here's my description of my career goals and an explanation of why I selected this program as my top pick:

What do you guys think? Is it compelling and yet informative? I'm mostly concerned about the very light style I've used in writing this. Should I make it more brusque, or perhaps tweak certain areas to be less rambling? I'm hoping it shows sufficient passion and interest to get selected for the position. Thanks for the help!

Arjun

while I've applied to several REUs for this summer, I've mostly been applying in areas that I'm only tangentially interested in. Last week, I received an email about a new REU that's opened up at Case, and was ecstatic to see the following research program:

(T4) Phase transitions in the early universe (project advisor Harsh Mathur): The focus of my work on cosmology is on the observable consequences of phase transitions in the early universe. Possible REU projects include numerical simulation of such a phase transition or analysis of the impact of such a phase transition on the cosmic microwave background. The minimum background needed is some familiarity with differential equations. Any prior experience with programming and courses in quantum mechanics, statistical mechanics and electromagnetism will be an asset but is not required. No background in cosmology or astrophysics is needed other than a general interest in the field. More information on our work in this area is available at http://www.sciencedaily.com/releases/2008/04/080415143816.htm

Since I'm very much interested in theoretical physics, and especially cosmology, I decided to apply, and more over, give the application a very personal touch. After all, the professor is looking for someone who is extremely interested in the field. So here's my description of my career goals and an explanation of why I selected this program as my top pick:

It's precisely on the length limit; not a line to spare.From an early age, I've always tried to figure out the way things worked. Now, I don't mean that in the standard, wrench meet toy, sort of way, but rather in a more academic fashion. That is, I'd encounter an idea, such as a teacher, friend, or family member spouting out that something was so, that this was the way things worked. As a child, I would take that idea, and file it away as best as I could. I'd try to make every idea go through the litmus test of sanity: does it make sense with everything else I know. Throughout high school, I devoured books on physics, math, and computer science, pushing forward my understanding as best as I could. I took it upon myself to learn as much about what we currently know, and more importantly for me, how we got that understanding as best as my current mathematical skills would allow. Since that's what I'm best at, and what I enjoy most, I've decided to make it my life's work to attempt to understand the world. As such, I'm trying to become a theoretical physicist. I'm a Physics and Math major at the Rose-Hulman Institute of Technology, looking to eventually obtain a PhD in some area of physics, either Cosmology or Quantum Field Theory. I have an extremely strong mathematical background, and I plan to expand that as much as I can in conjunction with my ability to discern what makes sense and take what doesn't make sense, and make it sensible if at all possible. That's one skill I have yet to meet another person who possesses.

My interest in understanding the universe naturally led me to select the project that I did. While studying dark matter either computationally or experimentally would be fascinating, my second and third choices, a chance to explore the early moments of the Universe is tough to pass up. Upon reading the article linked to in the description, I'm recalled of the very book that set me upon the path I now tread. In high school, I read “Faster than the Speed of Light” by Joao Magueijo, and was drawn into the exploration of the basic physical concepts. But what strikes me now, is the parallels between what he did, and what this research opportunity strives to do. In the book, he presents Inflationary theory quickly, but gives it a fair look, but eventually discards it due to its inelegance and the lack of data at the time, and begins to formulate his own theory. In a similar fashion, this research work would have me look at the same time period and attempt an alternative formulation for observational data that should be had in just a decade or so; after all, the Planck spacecraft is being sent out for just that purpose.

Based upon the description provided, I have met all the prerequisites. I took Differential Equations in my senior year of high school, receiving a grade of A, and am currently taking Boundary Value Problems, a cursory look at partial differential equations (1D wave equation, heat equation, with Neumann and Dirchilet boundary conditions). Having finished the introductory physics coursework, I have a good background in calculus based physics including Electromagnetism, but no more depth then that. However, having taken Vector Calculus, I've picked up the prerequisites to understanding Electromagnetic theory in greater depth. I've also received an introduction to Quantum Mechanics and Statistical Mechanics via a Modern Physics course I took last quarter. It covered, in a very conceptual way (the mathematics was left to basic calculus and algebra, no matrix mechanics), the breadth of Quantum Mechanics, and built up to the areas of current research. I'm currently taking coursework in Abstract Algebra, Theoretical Mechanics (Marion level), and an introduction to Probability, in addition to Boundary Value Problems.

Prior to starting high school, I developed an interest in computer programming, and so from my 8th grade onward I've been developing my programming skills. Among the various languages I've learned, most relevant is the abundance of experience I have in C. For about a year and a half I worked for an open source project by the name of Compiz Fusion as the team lead for optimization and code management. While I have not taken a Numerical Analysis course as yet, I've experience with Mathematica, Maple, and Matlab, and the ability to pick up the needed basics quickly. In general I learn very quickly, and am always eager to learn more especially with a subject as interesting as Cosmology.

What do you guys think? Is it compelling and yet informative? I'm mostly concerned about the very light style I've used in writing this. Should I make it more brusque, or perhaps tweak certain areas to be less rambling? I'm hoping it shows sufficient passion and interest to get selected for the position. Thanks for the help!

Arjun

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