Description: A rigorous, in-depth treatment the foundations of quantum mechanics. Topics include Hilbert spaces, the variational principle, coherent states, and angular momentum.

Evaluation: I found the material in this class to be pretty standard, and there weren’t any crazy interesting topics. The homework had a mixture of traditional handwritten PSETs and online MITx PSETs. Personally, I found the MITx PSETs to be quite easy, while the written PSETs had a lot of difficult calculations. Prof. Detmold was a good lecturer, but his grading curve at the end of the course struck me as quite unfair to many students, and that left a bit of a bad taste in my mouth.

Rating: 5.5/10

Grade: A+

Description: Continuation of 8.05. Topics include perturbation theory, the Stark and Zeeman effects, the Born approximation, scattering theory, and the integer quantum Hall effect. CI-M. My final paper for the class can be found here.

Evaluation: I found the material in this course to be a lot more interesting than 8.05. Perturbation theory and scattering in particular were especially fun, and I also enjoyed learning about applications of quantum theory to atomic physics. I did not attend lecture, but Prof. Barton Zwiebach’s old lecture notes for this class were excellent. The final paper was a good experience overall, and I enjoyed getting feedback in scientific communication.

Rating: 7.5/10

Grade: PE (special PE/NE grading due to the COVID-19 pandemic)

Description: An introductory course in experimental physics, including data analysis and statistical methods. I performed three experiments: 21cm Radio Astrophysics (paper), CosmicWatch muon detection (paper), and Hydrogenic Atom Spectroscopy (slides). CI-M.

Evaluation: I have never been very interested in experimental physics, but I found JLab to be a fun and informative experience. It certainly expanded my horizons as a physicist and taught me a lot of the techniques employed by the “other side” of physics. Prof. Paus was an amazing section leader and had great feedback for all of my presentations.

Rating: 8/10

Grade: A

Description: An intermediate quantum field theory course covering topics in nonabelian gauge theory as well as loop calculations and renormalization.

Evaluation: Easily one of my favorited MIT-offered classes. Quantum field theory is such an interesting subject, and the material in 8.324 has been useful to me in so many subsequent classes in theoretical high energy physics, including string theory and holography. Prof. Slatyer was exceptional and really helped make the material crystal clear.

Rating: 9/10

Grade: A+

Description: Advanced quantum field theory class covering several applications of QFT: axiomatic quantum field theory, conformal field theory, and the Standard Model/phenomenology. My final paper for the class can be found here.

Evaluation: This class covered many important topics which have been very useful in research. I would say that the most useful thing I learned from this class was elementary conformal field theory — this was very helpful later on when I was learning string theory. An added bonus: CFT seemed to be Wati’s favorite topic to lecture on, since he is a hardcore theorist 🙂 My final project was also super fun to work on and think about.

Rating: 9/10

Grade: PE (special PE/NE grading due to the COVID-19 pandemic)

Description: Covers the framework and tools of effective field theory, including: identifying degrees of freedom and symmetries; power counting expansions (dimensional and otherwise); field redefinitions, bottom-up and top-down effective theories; fine-tuned effective theories; matching and Wilson coefficients; reparameterization invariance; and advanced renormalization group techniques. Main examples are taken from particle and nuclear physics, including the Soft-Collinear Effective Theory.

Evaluation: This class was super fun and interesting. It covered a lot of topics, and I have to admit that I did not fully internalize every single topic the first time I took the class. Nevertheless, the most important thing I learned from 8.851 was how to think about physics. This class teaches you the very important philosophy of EFT — how to make simplifying approximations in top-down EFT and how to construct effective descriptions in bottom-up EFT. This is useful throughout all areas of physics, and it made a lasting impression on me. Iain was an amazing professor too — I ended up doing a UROP with him after this class, which was one of my most enjoyable and productive research experiences!

Rating: 10/10

Grade: PE (special PE/NE grading due to the COVID-19 pandemic)

Description: First-year graduate course covering the basics of thermodynamics and statistical mechanics. Topics include ensembles, partition functions, and Fermi and Bose statistics.

Evaluation: This class was all right — nothing too memorable. I enjoyed solidifying my foundations in statistical mechanics, and the parts at the end about Fermi and Bose statistics were really cool.

Rating: 7.5/10

Grade: A+

Description: Topics in statistical field theory, including collective phenomena, phase transitions, and renormalization. My final paper for the class can be found here.

Evaluation: Man, this class was good, and for one main reason — Prof. Kardar. Prof. Kardar was one of the best lecturers I have ever had at MIT, and his explanations were always crystal clear and engaging. In addition, the material in this class was a lot more interesting than 8.333. I really enjoyed my final project, and it also gave me an opportunity to explore some topics in string theory.

Rating: 9/10

Grade: A+

Description: An introduction to quantum computation and quantum algorithms. Topics include Grover’s algorithm, Shor’s algorithm, quantum error correction, and fault-tolerant quantum computation.

Evaluation: I have mixed feelings about this class. On one hand, quantum computation is a super interesting and important subject, and Prof. Shor is a genius and a visionary in the field. On the other hand, the lectures did not really contribute to my understanding, and they often left me more confused than when I started. I ended up mainly reading from the textbook in this class, which was a shame.

Rating: 6/10

Grade: A+

Description: A continuation of 8.370, focusing on topics in quantum information theory. Topics include the quantum singular value transformation, fault-tolerant quantum computation, and Holevo’s theorem. My final paper for the class can be found here.

Evaluation: This class was a lot better than 8.370 for me. Like Prof. Shor, Prof. Chuang is also a genius in the field of quantum computation and quantum information. However, Prof. Chuang is also an excellent teacher. His lectures were pristine, well-organized, and featured a surprisingly large amount of student interaction. I really enjoyed the final project, and I went on to UROP with Prof. Chuang after this class.

Rating: 9/10

Grade: A

Description: The basic principles of Einstein’s general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology.

Evaluation: This class was excellent. I highly recommend this class to anyone interested in astrophysics (and even those who are not!), especially if it is taught by Prof. Hughes. It covers a comprehensive selection of topics in general relativity, loosely following the outline of Sean Carroll’s textbook.

Rating: 8.5/10

Grade: PE (special PE/NE grading due to the COVID-19 pandemic)

Description: Elective class on holographic duality and the AdS/CFT correspondence.

Evaluation: This class was really good, even though it only gave a rather cursory overview of topics in holography. Prof. Liu is very knowledgeable about the subject matter, and his lectures were easy to follow and understand. I ended up being a TA for it two years later!

Rating: 8.5/10

Grade: A+

Description: An elective class discussing the black hole information paradox, including topics in quantum information theory.

Evaluation: This class was a very insightful study of the black hole information paradox, covering a wide assortment of relevant topics. Prof. Harlow is an excellent teacher and is one of the foremost researchers in this field, and it was a great experience learning from him.

Rating: 8.5/10

Grade: A+

Description: A rigorous introduction to perturbative string theory, including both the bosonic theory and superstrings. Topics include effective string theory, 2D CFT, Riemann surfaces, string perturbation theory, scattering amplitudes. My final paper for the class can be found here.

Evaluation: Oh, man. This class was a roller coaster. I easily spent more time on this class than all of the other classes combined during my sophomore fall. On the other hand, the amount of material I learned was second to no other class, at MIT or Harvard. Truly, Xi Yin is one of the most knowledgeable string theorists I have ever encountered, and his attention to detail and depth of understanding are inspiring. I suffered greatly, but I pushed myself academically further than I ever did before, and I think the end result was definitely worth it. If you take this class, do not expect an easy ride, but the hard work will be eminently worth your time.

Rating: 10/10

Grade: A

Description: A survey of recent research topics in the string swampland. A focus is on swampland conjectures, such as the No-Global-Symmetries Conjecture, the Distance Conjecture, and the Weak Gravity Conjecture.

Evaluation: The best physics class I have ever taken. This class almost single-handedly convinced me to pursue string theory research. If you ever have the chance to take it, please do. You won’t regret it.

Rating: 11/10

Grade: A

Description: Introductory course in algebra, including linear algebra and basic group theory.

Evaluation: This was a fun class. Prof. Artin was a wonderful person (even if his lectures were not always audible), and I enjoyed the entire experience.

Rating: 8/10

Grade: A+

Description: Continuation of 18.701, covering the basics of finite-group representation theory and commutative algebra (rings and ideals).

Evaluation: This class was my first exposure to some topics in “real” math — before, I had only ever studied things like representation theory from a physics perspective. Prof. Shankar was a great lecturer, and I really felt like I internalized many of the topics in this class. Importantly, this class is foundational for basically any further classes in algebra or number theory.

Rating: 8.5/10

Grade: PE (special PE/NE grading due to the COVID-19 pandemic)

Description: An introduction to the theory of Lie groups and Lie algebras. Topics include the exponential map, Lie’s theorems, the classification of simple complex Lie algebras, and the representation theory of \mathfrak{sl}_2 .

Evaluation: The first class in my saga with Prof. Etingof, this class proved to be an enjoyable and illuminating experience. This was my first graduate math class, and I really enjoyed being able to tackle harder problems for the first time in my math classes. The PSETs were rarely easy, but I found that working on them really improved my understanding of Lie theory (which at the time I had only learned at the physicist’s level of rigor).

Rating: 9/10

Grade: A

Description: Continuation of 18.745. Topics include the representation theory of compact Lie groups, the Peter-Weyl theorem, and real forms of complex Lie algebras.

Evaluation: Oh, boy. This was another one of those classes. After the relatively mild 18.745, 18.755 hit me like a ton of bricks. Prof. Etingof really ramped up the difficulty, and the PSETs got to the point of near-impossibility. I think I ended up turning in a majority of them late, and that was not because I didn’t start early enough. I think the material in this class is still very important and foundational, but I think I would perhaps have been better served by two semesters worth.

Rating: 9/10

Grade: A+

Description: Advanced graduate class on the representation theory of noncompact Lie groups. Topics include topological vector spaces, Harish-Chandra modules, and the representation theory of SL_2(\mathbb{R}) .

Evaluation: The madness continues. Prof. Etingof already had a reputation among my friends and I for assigning insanely hard problems, and 18.757 took that to a whole new level. This class went far beyond 18.755, almost to the point that I didn’t really understand anything anymore. It was very difficult, and while I did get some things out of it, I think I will have to revisit the material in the future. Prof. Etingof was a great lecturer — the main issue I had was that I was not sufficiently prepared for this class.

Rating: 7/10

Grade: A+

Description: Exactness, direct limits, tensor products, Cayley-Hamilton theorem, integral dependence, localization, Cohen-Seidenberg theory, Noether normalization, Nullstellensatz, chain conditions, primary decomposition, length, Hilbert functions, dimension theory, completion, Dedekind domains.

Evaluation: This class moved slowly and covered many of the basic topics of commutative algebra in great detail. Prof. Zhang was a fairly clear lecturer, and the PSET problems were usually engaging.

Rating: 7.5/10

Grade: A

Description: Dedekind domains, unique factorization of ideals, splitting of primes. Lattice methods, finiteness of the class group, Dirichlet’s unit theorem. Local fields, ramification, discriminants. Zeta and L-functions, analytic class number formula. Adeles and ideles. Statements of class field theory and the Chebotarev density theorem.

Evaluation: I’m not going to sugarcoat it — this class is not easy. It covers a large amount of material (in fact, it goes through the 18.705 curriculum in about two weeks at the beginning). However, there are some very rewarding moments later on, and I particularly enjoyed the discussion of class field theory and the analytic class number formula. Prof. Sutherland was an excellent lecturer.

Rating: 8/10

Grade: A+

Description: Singular homology, CW complexes, universal coefficient and Künneth theorems, cohomology, cup products, Poincaré duality.

Evaluation: This class was the right level of difficulty — engaging without being prohibitively hard. It covered some very important topics in algebraic topology and homological algebra. I did not attend most of the lectures, but from the ones I did attend, I found Prof. Hahn to be a good lecturer.

Rating: 8/10

Grade: A

Description: Differential forms, introduction to Lie groups, de Rham’s theorem, Riemannian manifolds, curvature, the Hodge theory.

Evaluation: This class was very fun, and I really enjoyed learning about differential geometry from a math perspective after having taken general relativity. Prof. Minicozzi was an excellent lecturer and always made sure to check that everyone understood the material.

Rating: 8.5/10

Grade: A