- #1
Azathanai
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I've written a Statement of Purpose for Physics PhD applications, and I wanted opinions on it from as many people as I can, which is why I am asking here. Honest reviews and tips on how to improve it are really appreciated!
When I joined <my uni> as an undergraduate student in Physics, I had two goals. Firstly, I wanted to figure out which area of Physics interested me enough to be able to pursue it as a research area in my graduate studies. And secondly, I wanted to get some experience in research.
There are many areas of research conducted at <my uni> that intrigued me. I realized that to explore these various fields, I would have to take up advanced courses. I started taking elective courses beyond what was required by the program template every semester at <my uni> right after my first semester. These electives were on the topics of General Relativity, Quantum Field Theory, Statistical Mechanics, and Chaos Theory. While I was able to understand the concepts, perform well in these courses, and overall enjoy the learning experience, I enjoyed the electives of Quantum Field Theory and General Relativity the most. I realized that I wish to do research in an area related to one or preferably both of these fields. I discussed this with my professors for advice, and extensively searched the internet. On doing so, I found out that the areas of String Theory and Quantum Gravity were aligned perfectly with what I wished to research in.
These areas have a large number of prerequisites required to study them. To satisfy these, I have completed all graduate-level courses in Gravitation and Quantum Field Theory that were offered at <my uni> I have also taken all Mathematical Methods courses offered by the Physics department, and also have taken advanced mathematics courses in Topology, Analysis, and Differential Equations. In all of these courses, I have been awarded an A grade. Additionally, I have achieved an A grade in all of the courses I have done in my entire undergraduate degree, barring a B in a couple. I am also the only Physics student of my batch who has received three consecutive <award name>, and I believe I have the highest GPA in my batch, though ranks are not officially given by <my uni>. Thus, I believe I have a solid theoretical background in the prerequisite areas required to study these fields, a strong mathematical foundation required to handle any advanced mathematical concept which arises in the study of these fields, as well as an academic record, which shows that I have academic skills.
In terms of research experience, due to the COVID-19 pandemic, my internship opportunities both on-campus and off-campus were significantly affected. Despite this, I was able to complete two independent research projects and multiple course-related projects by the end of my 7th semester.
My first two projects were group projects in my Optics lab and Modern Physics lab courses. In the Optics project, we constructed a 4f Imaging system, to study the basics of image processing. The Modern Physics project involved recreating an experiment from a published paper. Our group constructed an electronic circuit from an Arxiv paper that demonstrates the Hopf bifurcation. The most important thing I learned from these projects is how to work with a group to collectively solve a particular problem, and how debating and discussing with others help to solve a problem efficiently.
After the Modern Physics course ended, I continued the project from this course under the guidance of <prof name>. We improved the theoretical analysis of the experimental setup that the original paper had, and made it more rigorous. This new analysis provided an analytical expression to determine the condition for the occurrence of a Hopf bifurcation. Another analytical expression describing the behaviour of the circuit close to the bifurcation point was also developed. Additionally, we experimentally verified the validity of these results.
This was my first major experience with research, and it revealed a lot about the process of conducting research. Besides my scientific input, my patience was severely tested, and I learned what it means to persevere and its importance while doing research. This project was also affected by COVID-19, as the labs shut down. Eventually, we were able to complete the analysis and submit a manuscript to AJP, where it is under review.
I have also written two review term papers for projects related to my courses. The first one was in Advanced General Relativity, on the topic of Singularity theorems, under <prof name>. I discussed the definition of singularity based on geodesic incompleteness and reviewed some famous singularity theorems, including the Hawking-Penrose Singularity Theorem, and modern generalizations of these. The second one was in Non-Equilibrium Statistical Mechanics, on the topic of Path Integrals in stochastic dynamics and quantum mechanics, under <prof name>. I reviewed the construction of path integrals for the fundamental probabilistic dynamical equations of both these theories, namely the Fokker-Planck and the Schrodinger equations, and the connections between these two. Along with gaining knowledge on the topic itself, these projects taught me how to browse through a large number of research articles, and select those which are relevant. I also learned how to summarize these papers and present them as written reports and oral presentations.
My latest research experience was under <prof name>, in which I studied Evolutionary Stable Strategies (ESS) in Game Theory. In particular, literature on game theory has a formulation of ESS for two types of systems - for a single finite-population species with two competing variants, and for two infinite-population species, with each species having two competing variants. We extended the definition of ESS to the case of two finite-population species, each with two competing variants, which was not present in current literature, and analysed the consequences of our proposed definition. The most important thing we noted, is that the relation between the finite and infinite population cases for single species is very different than the relation between finite and infinite populations for two species. Investigating why exactly this happens is a future goal. We also plan to extend this definition to include extensive games in the future.
This was my first major theoretical research project and a new and exciting experience for me. The skills I had learned from my previous projects came in handy, and the project went much smoother than my prior attempts at research. I also enjoyed the entire process of performing theoretical research and affirmed that this is, indeed, what I want to be doing in the future.
The Theoretical Particle Physics group at <uni name> is a strong theory group, many of whose members work in research areas I am interested in. I would be happy to work under any of them for my PhD degree. Thus, for my graduate degree, I would like to gain a better understanding of the research areas of my interest, find a particular sub-field that I will work on, and carry out research that contributes towards improving knowledge in this field. After my PhD, I plan on doing a post-doctorate, and subsequently, pursue a career in academics.
Hence, I am confident that my academic preparation, research experience, sincerity, and perseverance will help me excel in my doctoral program in Physics at the <uni name>.
When I joined <my uni> as an undergraduate student in Physics, I had two goals. Firstly, I wanted to figure out which area of Physics interested me enough to be able to pursue it as a research area in my graduate studies. And secondly, I wanted to get some experience in research.
There are many areas of research conducted at <my uni> that intrigued me. I realized that to explore these various fields, I would have to take up advanced courses. I started taking elective courses beyond what was required by the program template every semester at <my uni> right after my first semester. These electives were on the topics of General Relativity, Quantum Field Theory, Statistical Mechanics, and Chaos Theory. While I was able to understand the concepts, perform well in these courses, and overall enjoy the learning experience, I enjoyed the electives of Quantum Field Theory and General Relativity the most. I realized that I wish to do research in an area related to one or preferably both of these fields. I discussed this with my professors for advice, and extensively searched the internet. On doing so, I found out that the areas of String Theory and Quantum Gravity were aligned perfectly with what I wished to research in.
These areas have a large number of prerequisites required to study them. To satisfy these, I have completed all graduate-level courses in Gravitation and Quantum Field Theory that were offered at <my uni> I have also taken all Mathematical Methods courses offered by the Physics department, and also have taken advanced mathematics courses in Topology, Analysis, and Differential Equations. In all of these courses, I have been awarded an A grade. Additionally, I have achieved an A grade in all of the courses I have done in my entire undergraduate degree, barring a B in a couple. I am also the only Physics student of my batch who has received three consecutive <award name>, and I believe I have the highest GPA in my batch, though ranks are not officially given by <my uni>. Thus, I believe I have a solid theoretical background in the prerequisite areas required to study these fields, a strong mathematical foundation required to handle any advanced mathematical concept which arises in the study of these fields, as well as an academic record, which shows that I have academic skills.
In terms of research experience, due to the COVID-19 pandemic, my internship opportunities both on-campus and off-campus were significantly affected. Despite this, I was able to complete two independent research projects and multiple course-related projects by the end of my 7th semester.
My first two projects were group projects in my Optics lab and Modern Physics lab courses. In the Optics project, we constructed a 4f Imaging system, to study the basics of image processing. The Modern Physics project involved recreating an experiment from a published paper. Our group constructed an electronic circuit from an Arxiv paper that demonstrates the Hopf bifurcation. The most important thing I learned from these projects is how to work with a group to collectively solve a particular problem, and how debating and discussing with others help to solve a problem efficiently.
After the Modern Physics course ended, I continued the project from this course under the guidance of <prof name>. We improved the theoretical analysis of the experimental setup that the original paper had, and made it more rigorous. This new analysis provided an analytical expression to determine the condition for the occurrence of a Hopf bifurcation. Another analytical expression describing the behaviour of the circuit close to the bifurcation point was also developed. Additionally, we experimentally verified the validity of these results.
This was my first major experience with research, and it revealed a lot about the process of conducting research. Besides my scientific input, my patience was severely tested, and I learned what it means to persevere and its importance while doing research. This project was also affected by COVID-19, as the labs shut down. Eventually, we were able to complete the analysis and submit a manuscript to AJP, where it is under review.
I have also written two review term papers for projects related to my courses. The first one was in Advanced General Relativity, on the topic of Singularity theorems, under <prof name>. I discussed the definition of singularity based on geodesic incompleteness and reviewed some famous singularity theorems, including the Hawking-Penrose Singularity Theorem, and modern generalizations of these. The second one was in Non-Equilibrium Statistical Mechanics, on the topic of Path Integrals in stochastic dynamics and quantum mechanics, under <prof name>. I reviewed the construction of path integrals for the fundamental probabilistic dynamical equations of both these theories, namely the Fokker-Planck and the Schrodinger equations, and the connections between these two. Along with gaining knowledge on the topic itself, these projects taught me how to browse through a large number of research articles, and select those which are relevant. I also learned how to summarize these papers and present them as written reports and oral presentations.
My latest research experience was under <prof name>, in which I studied Evolutionary Stable Strategies (ESS) in Game Theory. In particular, literature on game theory has a formulation of ESS for two types of systems - for a single finite-population species with two competing variants, and for two infinite-population species, with each species having two competing variants. We extended the definition of ESS to the case of two finite-population species, each with two competing variants, which was not present in current literature, and analysed the consequences of our proposed definition. The most important thing we noted, is that the relation between the finite and infinite population cases for single species is very different than the relation between finite and infinite populations for two species. Investigating why exactly this happens is a future goal. We also plan to extend this definition to include extensive games in the future.
This was my first major theoretical research project and a new and exciting experience for me. The skills I had learned from my previous projects came in handy, and the project went much smoother than my prior attempts at research. I also enjoyed the entire process of performing theoretical research and affirmed that this is, indeed, what I want to be doing in the future.
The Theoretical Particle Physics group at <uni name> is a strong theory group, many of whose members work in research areas I am interested in. I would be happy to work under any of them for my PhD degree. Thus, for my graduate degree, I would like to gain a better understanding of the research areas of my interest, find a particular sub-field that I will work on, and carry out research that contributes towards improving knowledge in this field. After my PhD, I plan on doing a post-doctorate, and subsequently, pursue a career in academics.
Hence, I am confident that my academic preparation, research experience, sincerity, and perseverance will help me excel in my doctoral program in Physics at the <uni name>.