Domenic Denicola . com
Programmer, webmaster, thinker
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 middle of this year's term, and also contains (most) of the courses I will be taking next term. This means that only the first term this year will have grades.
Course descriptions can be found by browsing the Caltech catalog.
Although I am not formally registered for the following classes due to administrative reasons, I attend them and do the homework (or will do so, in the case of Ph 199):
Group theory and group representation theory in physics, including Lie groups, Lie algebras, and connections to quantum mechanics and the standard model.
The course website (you will need to scroll down a little to reach 129B, instead of 129A) contains notes and homework assignments.
According to the course catalog, topics will include the following: What is the expansion history of the universe? What are dark matter and dark energy? Where does mass come from? Why is the universe made of matter rather than antimatter? Is nature supersymmetric? Is there a quantum theory of gravity that can describe the universe? Why is there a spectrum of fermion masses? How heavy are neutrinos and what was their role in the formation of the universe? Where do ultrahigh-energy cosmic rays come from? What can we learn from the detection of gravitational waves?
Last year's course website contains more details on the topics, sample readings, and some homework assignments.
Aside from boring requirements and basic mathematical literacy, my coursework roughly falls into three areas: abstract mathematics, physics, and computability/mathematical foundations.
With regards to math, I am fluent in analysis and abstract algebra, and am able to make the connections between these mathematical techniques and the coursework in physics class, even when the typical undergraduate physics presentation does not do so. Interestingly, the course Ma 118 (“Geometrical Paradoxes in Mathematical Logic”) has given me a lot of experience with integration and measure theory over more abstract spaces (in this case the group of isometries of ℝn), which I know is quite important in physics. I hope to continue making these connections, as I think that knowing the more rigorous and abstract mathematical formulations of physical theories is key to truly understanding them.
So far the physics curriculum has been relatively constrained, as being a second-year student I am just now taking my first actual class in quantum mechanics; however, in addition to my extensive extracurricular reading I have also taken several courses that explore the frontiers in physics, such as the seminar class Ph 10 during my first year or the upcoming Ph 199.
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.