Berkeley

Spring 2008:

• Math 253: Homological Algebra (Peter Teichner)
• Math 277: Characteristic Classes (Elizabeth Gasparim)
• Math 290: Toric Varieties (Seminar)
• Math 295: Research units (Bjorn Poonen)
• Student Algebraic and Arithmetic Geometry Seminar (David Brown, Dan Erman, Anthony Varilly)
• Graduate Student Instructor: Math 74: Transition to Upper Division Mathematics (Anthony Varilly)

Spring 2007:

• Math 274: Algebraic Stacks (Martin Olsson)
• Math 254b: Algebraic Algebraic Number Theory (Ken Ribet)
• Math 295: Research units (Bjorn Poonen)
• Student Number Theory Seminar (Anthony Varilly)
• Graduate Student Instructor: Math 1b: Single Variable Calculus II (Marina Ratner)

Fall 2006:

• Math 215a: Algebraic Topology (Peter Teichner)
• Math 295: Research units (Bjorn Poonen)
• Graduate Student Instructor: Math 1a: Single Variable Calculus (Mark Haiman)

Spring 2006:

• Math 274: Logarithmic Geometry (Arthur Ogus)
• Math 295: Research units (Bjorn Poonen)

Fall 2005:

• Math 252: Representation Theory (Vera Serganova)
• Math 290: Rational Points Seminar (Bjorn Poonen)
• Math 295: Research units (Bjorn Poonen)
• Graduate Student Instructor: Math 53: Multivariable Calculus (Alan Weinstein)

Spring 2005:

• Math 256b: Algebraic Geometry (Paul Vojta)
• Math 290: Reading course: The Arithmetic of Elliptic Curves (Bjorn Poonen)
• Math 205: Complex Analysis (Maciej Zworski)
• Graduate Student Instructor: Math 1b: Second Semester Calculus

Fall 2004:

• Math 256a: Algebraic Geometry (Robin Hartshorne)
• Math 254a: Number Theory (Marty Weissman)
• Math 300: Teaching Workshop (Alex Diesl)
• Iwasawa Theory seminar Student run seminar. Active participant.
• Graduate Student Instructor: Math 1a: First Semester Calculus (Daniel Tataru)

Cambridge

Spring 2004:

• Cyclotomic Fields (John Coates)
• Lie groups (Charles Thomas)
• Geometric Invariant Theory (Burt Totaro)
• Modular Forms (Tony Scholl)
• Pro-p-groups (first half) (Rachel Camina)

Fall 2003

• Noetherian Algebras (C. Brookes)
• Ramsey Theory (Imre Leader)
• Class Field Theory (Tom Fisher)
• Algebraic Topology (Ivan Smith)

Harvard

Spring 2003:

• Math 250b: Higher Algebra II Wow. This class was spectacular. Professor Mazur is one of the most outstanding teachers I've had. I took four classes with him and I wish I could take at least another four. The class was really fast-paced...spicy ;) All the better. I learned a ton and I also gave two gratuitous presentations, one on representations of GL2(F_q) and another on how to use Hilbert symbols to construct rational quaternion algebras with given (allowed) ramification. The latter talk I developed as part of my thesis and Professor Mazur claims to have learned from my exposition (he is a God, there is nothing he doesn't know, but his comment was encouraging!). Overall an awesome choice. I finally understand group cohomology!!!
• Math 251r: Arithmetic Theory of Quadratic Forms Perfect senior spring class. Manjul (the professor, he like to be called by his first name) taught us a lot about quadratic forms and explained a good deal of his PhD thesis and recent results to us. His methods are so so simple and elegant! He's a magician at the board, and made us all feel like we can DO math, not just learn it. Fantastic class. I put together a final project rather quickly, but it came out great!
• Math 60r: Reading Course for Seniors (Thesis) on Elliptic curves and Complex Multiplication (prof. Dick Gross) Another amazing semester with a God of number theory. I am amazed how much time professor Gross had for me given that he was Dean of the College. He always had a smile to welcome me (and quite a bit of work to assign :) ). He is an inspiration.
• Foreign Cultures 19: El poder y lo sagrado Yeah...I kinda coped out and took a Spanish core. But hey, truth is most people take cores in English and that's their mother tongue. So why can't I do something similar? Professor Cifuentes was extremely funny. His dark wit and sarcasm added a touch of necessary cynicism to senior spring. I also did most of the reading for this class. And I absolutely crushed it. I wish my other core experiences had been as smooth as this one.
• Course Assistant: Math 123: Abstract Algebra II (prof. Peter Kronheimer) I feel bad about this class. I definitely did not put as much time into it as I should have. I got sooooo behind with grading I even had to ask Prof. Kronheimer to stall when the registrar was asking him for course grades. But office hours were definitely fun. Some people in this class were students of mine for 3 semesters. It was thrilling to see their mathematical and personal growth. They will be fine mathematicians one day :)

Fall 2002:

• Math 230a: Differential Geometry Professor Raoul Bott taught this class, at the tender age of 79. It is simply amazing how lucid his lectures were. He even suffered an accident in the middle of the semester and lectured in crutches. His handwriting was a bit shaky, but that's only to be expected. And he is great human being. I sat next to him at the senior honors dinner and we talked for hours. He was a Master of Dunster house and he knows soooo many famous mathematicians. Names like Atiyah, Milnor, De Rham, etc. came to life in his anecdotes. It was an unforgettable experience. Anyways...back to diff geo. The class was HARD, especially since I jumped straight to the graduate level with no background on the subject (I was *not* going to miss the opportunity to take a class with Bott). Problem sets were a bit tough and we didn't put in enough time for them. I was scared I'd get like a B- in this class. I had never been in a position like that before. So when I went home for Winter break I studied really hard with *tons* of help from my dad. When the final came I was ready for it and was able to save the grade.
• Math 60r: Reading Course for Seniors (Thesis) on Elliptic curves and Complex Multiplication (prof. Dick Gross) This reading course was intense to say the least. I met with Prof. Gross for about half an hour a week. And then I went and read about all sorts of cool things on my own. It was great! Professor Gross is a terrific advisor!!! It's too bad he's dean of the college now because he can't take advisees anymore. But at least Harvard is in good hands.
• Math 91r: Reading Course in Commutative Algebra (prof. Barry Mazur) This has to be one of the hardest reading courses ever offered in the Math dept. Most people take for granted an A in reading courses, and although that was the end result, it was not clear it would happen till the very end. Wei, Dimitar and I basically took a full blown graduate course on the subject (weekly sets, two midterms, in-class final). It was a 10-13 hour commitment a week (not much at all for a math class, but substantial for a reading course). Still, Prof. Mazur's lectures were spectacular as usual. And since we had taken algebraic number theory and a little algebraic geometry we were all psyched about commutative algebra. A fantastic choice. Thanks go to Wei for getting me to take this course.
• Science B-53: Marine Biology Bob Woolacott was extremely funny. I never thought I'd take a class on Marine Bio. It was a ton of fun and a bit of a joke for a math major (science b is the ''biology for poets''--I don't understand why math majors have to take it...the core works in mysterious ways). I wrote my final project on equiangular spirals and how the Fibonacci numbers arise in shell patterns. It was kinda neat.
• Math 213a: Functions of One Complex Variable (auditing)
• Course Assistant: Math 113: Complex Analysis (prof. Frank Calegari)

Spring 2002

• Math 129: Topics in Number Theory
• Math 137: Algebraic Geometry
• German Bab: Elementary German (Intensive) The review for ths class is long overdue. What can I say? Where to start? Without a doubt the best class I took at Harvard. Six hours a week of pure fun. I had sworn I'd never take a class at 9am again, but I'm glad I took German. Workwise the class did not demand tons of me, but I fell behind towards the middle of the semester when I found out that my mother's cancer had reached its final stages and when things went painfully sour with my then girlfriend. On that note, I have to say German Bab saved me from insanity. Geraldine (the teacher, but above all an awesome friend), as well as Sonya and I had many conversations that helped me get through the semester. I will never forget Geraldine. She's one of those people who can touch your heart and make a difference in your life. I want to be like that some day. We all admire her greatly.

  In this class I also met an amazing group of people. We got along extremely well. Thirteen students, thirteen highly distinct worlds. And yet...well, I guess things happen when you make people spend 6 hours of fun every week for a semester. I thought I had escaped the whole ``crush'' circle myself. And I did until a year after I took the class when I got to know Anya a lot better after a shuttle ride of serendipity. She definitely made my senior spring. I didn't think German Bab would still be having such an impact (and a very positive one at that) in my life a year after the end of the class.

• Course Assistant: Math 112: Real Analysis (prof. Curtis McMullen)

Fall 2001

• Math 250a: Higher Algebra
• Math 212a: Functions of a Real Variable
• HSB-56: The Russian Revolution
• Philosophy 3: Problems of Philosophy
• Course Assistant: Math 25a: Honors Multivariable Calc. & Linear Algebra I (prof. Kalle Karu)

Spring 2001

• Math 131: Topology Professor McMullen is a teaching God. His lectures were simply outstanding, albeit a bit fast sometimes. General Topology was a review of Math 25a, but the second half of the course (Algebraic Topology) was awesome. The take-home final for this class was a killer though... For 4 days I did Topology, drank coffee, slept and ate, in that order.
• Math 123: Abstract Algebra II Galois Theory is beautiful. Ideal Class groups can be fun to compute. It's just that 9 o' clock classes and I don't go so well together. I managed to write a beautiful set of notes thanks to Prof Mazur, but I do not recall writing any of them. It is my handwriting though, so I guess I was there.
• Physics 143a: Quantum Mechanics I So I figured, "I took Chem 160, so Quantum has to be a piece of cake!" Wrong. I did not take into account the Physicist's fudge factor: Professor Fisher. Oh the horror...the pain. Ok, breathe. Problem sets took forever, and it was all a bunch of unenlightening calculations, differential equations that took 5 sides to solve, etc.. Worst class I've taken at Harvard. It completely ruined my semester. I have no intuition for physics. As a mathematician, I was frustrated by the Fisher's reply to all interesting questions "we don't worry about such details here. We leave those annoyances for mathematicians to work out." Physics is not the study of Nature's Laws, but rather the study of all clever exceptions to these laws ever concocted by evil, twisted minds. Enough, let us leave it at that. I'm still breathing.
• HSA-18: Science and Society in the 20th Century Yeah, I guess this was not the best of semesters... Serves me right for taking the premed attitude and coping out of my History A requirement. Prof Mendelsohn went to the front of the lecture hall every day and let us know exactly what was on his mind. The human mind does not think linearly. That's what I learned in this class. Papers were hard cause they were short (boy, I never thought I'd say something like that). Nitin and I didn't study for this final till late the night before. All I remember was we learned Aldo Leopold's biography and regurgitated it verbatim in the final. I learned my lesson: never go by the CUE-guide's workload figures when picking a core.
• Math 115: Methods of Analysis and its applications (auditing)
• Course Assistant: Math 21a: Multivariable Calculus (prof. Yang Liu) hehe...what to say... I had 11 students this time. They were al amazing people. I can't belive they toughed it out. About 50% of the class dropped out after Prof Liu's first few lectures. Let me just summarize what I felt about this class in the following anecdote. Towards the end of the semester, I was at the CA's picnic with Andy Engelward (the CA coordinator at the time) and he asked me what I had CA'ed in the fall. I said I had done math 21a with Spiro. He said, "that's right, you guys made a great team! So, tell me, who did I assign you to this semester?" I replied. Then he smiled and said, "that's right. Well I thought I'd give you a bit of a rough time this semester seeing as you did so well the first time around." I still think Andy is a great guy, mind you.

Fall 2000

• Math 122: Abstract Algebra I What a great way to start sophomore year. This was tons of fun and definitely the easiest math class I've had at Harvard. Professor Mazur went pretty slowly for the first few weeks. Then when he found out we thought the pace was too slow he introduced categories and did a whole lot of stuff using universal properties. But it was nice to get one's hands dirty with groups and semi-direct products.
• Applied Math 105a: Complex and Fourier Analysis This was kind of a mixed bag. I'm sure glad I took this and not Math 113. Nitin took this class, which made things fun once we had our act together. Problem sets were long and frustrating cause there was lots and lots of computation. I learned my contour integrals though. And the TF Dionisios Margetis was the bomb. I mean, when I asked him about a question I thought was ill-posed he said "Stupid Problem!!! Say whatever you feel like in your answer. Talk about the weather!!!" I also learned I cannot count and I cannot do probability to save my life. The mean score for question 6 in the final exam (which was some simple probability question) was like 19.2/20; I got 6/20. Somehow, I feel the distribution of scores was not normal.
• Chemistry 160: Physical Chemistry The one and only chemistry class I took at Harvard. Why on earth chem 160? Well I wanted to take some chem, and somehow this course also counted for my math major. I was one of 4 sophomores in a class of about 60, and everyone else knew chemistry inside out. But that didn't scare me; this class was mostly math. Quantum Mechanical fun. We learned lots of neat numerical methods for atomic and molecular problems. The sets were a total joke. The exams...well that's altogether another story. Two midterms, each worth 37.5% of my grade. But they were all math. In fact, they even asked us for derivations and proofs!!! So it was great. I did my final project with Alex Ioannidis and Lisa Carlivati (two of the other sophomores in the class). They were both bigshot International Chem Olympiad people, though extremely humble and friendly. I was heavily outclassed in that team, but I loved working with such smart people. In the end, we took the three highest grades in the class. Go sophomores!!!
• LAB-51: First Nights What a class!!! I thought nothing could possibly top this course (unfortunately German Bab did :)). Professor Kelley is the best public speaker/entertainer I've ever seen. I loved going to lecture, and the workload was pretty painless. I also took this class with my girlfriend; we'd sit at the back and have an entire row or two of the mezzanine in Sanders theater to ourselves. ;-)
• Course Assistant:Math 21a: Multivariable Calculus ( Spiro Karigiannis) My first class as a Course Assistant. And what a class!!! 31 extremely bright people. Our section wrecked the curve in every exam. And most people came to section (God bless freshmen), which was extremely exciting. I LOVED teaching these students. They were all very outgoing. Miss them all much :(

Spring 2000

• Math 25b: Honors Multivariable Calculus & Linear Algebra II Definitely cooler than Math 25a. Professor Karu went ballistics with De Rham Cohomology at the end. He's the man. Plus I started working with other people on the sets, so all of a sudden things became easier. My only complain is I saw too many sunrises Friday morning at the Math Lounge.
• Physics 15b: Electricity and Magnetism I loved this class. Professor Vafa is the best Physics lecturer I've ever had, and although that doesn't mean much, I really really did like him. His board technique...technique??? board??? but besides that I had a fun time. Sets were easy, lab exercises were cool and painless. All in all an excellent choice.
• MR-60: Reason and Morality One of the best classes I've taken at Harvard. Hobbes, Mill, Kant, Nietzche. Great Stuff. The most valuable lesson I learned though is I should not think about grades when I don't want to study for a final exam. I calculated I could get a B-/C+ on the final and still end up with a B+ in the class. And so it was...
• LAC-20: The Hero of Irish Myth and Saga This has the distinction of being one of the most BS courses I've taken at Harvard. I took it cause my dad's Irish, so I figured I should learn about Irish myth. That minuscule amount of motivation was worth an A in the class. All you ever had to say was "Clearly, it all comes down to Dumezil's tripartite function of society applied to the present context."

Fall 1999

• Math 25a: Honors Multivariable Calculus & Linear Algebra I This was definitely a fun class. A bit stressful. For some stupid reason I did all the problem sets by myself, which is exactly the way you're not supposed to do them. So needless to say this class ate half my week. Professor Karu was fantastic. Good times.
• Physics 15a: Introductory Mechanics and Special Relativity Hell on Earth. It was clear Professor Tinkham did not want to teach this class. I sympathized: I did not want to be there. I even bought Venti-size cups of coffee before lecture and still fell asleep. The moral of this story: Never sit second row in a large lecture-type class; the professor will surely notice.
• Expository Writing 20: Shakespeare and Memory Well, what can I say? where to start? Expos is like that horrible cough medicine mom made me take when I was little. I was always happy about it after the fact, but I complained bitterly during the process. I learned a lot from Expos, but I'm not sure it was worth the ten years of my life it robbed me of through sleep deprivation.
• Freshman Seminar 34: The Large Scale Structure of the Universe You just gotta LOVE Freshman Seminars. Fun, easy and relaxing. Professor Lecar was funny and very knowledgeable. I regret not doing the extra-credit stuff, but I had too much on my plate that fall.