Hi, PhysicsGRE. I am applying for PhD programs to study quantum computing and would like to mention my math and computer science background in my SoP, as they extend a fair amount past what my transcripts suggest. Is there a recommended way to do this without appearing to be simply bragging or application padding? Least of all, I will be mentioning that my quantum mechanics background is at the level of Shankar (my transcripts show a two-part course in quantum chemistry and spectroscopy rather than the standard three-part physics series) and a background and coding (with a nice little website to show for it). Additionally, I have only taken an upper division linear algebra course and two upper division DE courses but have at least partially read through a good chunk of Dover's books on mathematics. Right now I have a paragraph aimed at pointing out the quantum mechanics discrepancy with a quick mention of math (as well as a mention in my CV).
Before concluding this statement, I would like to bring up a possible discrepancy in my application- as someone applying for a PhD program centered around quantum mechanics, it might appear that my background in quantum mechanics is somewhat lacking. UCLA's quantum chemistry and spectroscopy series was the two part quantum mechanics series taken by chemistry majors (I have included the syllabi for review). My primary textbook for the series was Shankar and I would say that my background is at that level. As I am taking a year off before graduate school, I intend to go through Shankar once more to strengthen my quantum mechanics background in addition to strengthening my mathematics background (I recently finished Pinter's book on Abstract Algebra and am currently reading Roman's Advanced Linear Algebra and Kreyszig's Functional Analysis). As the field of quantum computing overlaps quite a bit with the discipline of computer science (and because I have no formal/documented background to speak of), I think it would be beneficial to give a quick summary of my computer science background. Through books and online resources, I have acquired at least a basic level of knowledge and understanding of procedural programming, object-oriented programming, abstraction, computer architecture, Boolean algebra, symbolic algebra, and information theory. Although I am currently occupied with the two aforementioned math books, I feel it would be unseemly to begin graduate studies in quantum computing without knowing a thing or two about algorithms and intend to pick up Sedgewick’s book on the subject in the near future.
Edited (to bring up the issue of my mediocre transcripts):
Before concluding this statement, I would like to bring up a few notes about my educational background. As my initial interest upon starting college was in organic chemistry, my major at the time was chemistry. After taking courses in physics, my interest drifted from organic chemistry to physical chemistry and, ultimately, to physics. As it was not until my senior year that I concluded that I wanted to pursue a physics PhD rather than a chemistry PhD, my bachelor’s degree is in chemistry rather than physics. Aside from the name of my degree, I feel my transcripts may appear to be lacking somewhat. On account of attending a continuation school for 11th grade and skipping 12th, I initially placed into trigonometry and spent much of my time in undergraduate catching up on math. I was able to finish my degree in four years, but have not taken any advanced upper division or graduate level math/physics courses, despite dedicating all of my upper division electives to math and physics. I was at least able to cover all the fundamental branches of physics (I enrolled in classical mechanics my final quarter despite otherwise meeting all of the graduation requirements) and hope that my Physics GRE score adequately displays my graduate school preparedness and determination. Additionally, I have spent a fair amount of time outside of school studying subjects including abstract algebra (Pinter), set theory (Stoll), and information theory (Pierce) and am currently reading through Roman’s Advanced Linear Algebra and Kreyszig’s Functional Analysis in an effort to better understand quantum mechanics related topics such as Hilbert space and operator theory (both are supplementing my rereading of Shankar). As time allows during my year off before graduate school, also on my reading list is Chartrand’s Graph Theory, Petzold’s Code, Sedgewick’s Algorithms, and Paar’s Cryptography.