work
MSC #240, Caltech
Pasadena, CA 91126-0240
United States
Transcript Document
The primary document is the unofficial transcript
generated by Caltech's computerized system (as a PDF
file). This document reflects my state as of the end of my third year,
and also contains the courses I am taking during the upcoming first term of
my fourth year.
Course descriptions can be found by browsing the
Caltech catalog.
Summary
Aside from boring requirements and basic mathematical literacy, my coursework roughly
falls into three areas: abstract mathematics, physics, and computability/mathematical
foundations. I am on track to recieve both an undergraduate Bachelors of Science
in mathematics, and a graduate Masters of Science in physics, by the end of my four-year
stay at Caltech.
With regards to math, I am fluent in undergraduate-level analysis, topology, and
geometry, as well as graduate-level abstract algebra. Although my transcript above
does not show it due to limitations in the online scheduling system, I am considering
taking (or at least auditing, if time does not permit the former) year-long courses
in algebraic topology and algebraic geometry during the upcoming year. Such mathematical
training stems from my strong belief that knowing the more rigorous and abstract
mathematical formulations of physical theories is key to truly understanding them.
Until recently, the physics curriculum has been relatively constrained, but the classes
last year were much more substantive. I took the usual college-physics–level courses
in classical and quantum mechanics, a class on the applications of algebraic techniques
and noncommutative geometry to quantum field theory and the standard model, and
also John Schwarz's supersymmetry class. And next year looks to be even better,
with year-long courses in quantum field theory and general relativity, plus some
one-term courses in topological field theory and conformal field theory. Also of
note are some courses that explore the frontiers in physics, such as the seminar
class Ph 10 during my first year or Ph 199 (“Major Open Questions in Physics”) my
second year.
Finally, my work in computability and mathematical foundations is certainly helpful
for any work in quantum information or computability theory, or other more general
explorations of the logical/axiomatic structure underlying physics. In addition,
it has served to give me a smattering of exposure to some discrete math, with emphasis
on combinatorics, graph theory, and Ramsey theory. Mostly, however, it is a fun
side-interest with the added benefit that I can debate intelligently about Gödelizing
physical law à la Hawking.