Courses

These are the courses I have taken so far at UCSB. I hope to post notes for many of these classes eventually.

Fall 2003

Math 201A: Real Analysis (Denis Labutin). This is the first quarter of a graduate course on real analysis. We covered measure theory.

Math 221A: Foundations of Topology (Darren Long). This is a graduate course on point-set topology.

MathCS 101: Putnam Seminar (Charles Ryavec).

Music 15: Music Appreciation (Bill Prizer). This is a large lecture class which covers an overview of Western music. I was really not the right audience for this class.

Music A42/142/242: Orchestra (Jeffrey Schindler).

Math 220A: Modern Algebra (audit) (Adebisi Agboola). This quarter covered group theory. Notes.

Winter 2004

Math 147A: Differential Geometry (Michael Crandall). This is the first quarter of an undergraduate course on differential geometry. We covered various topics in the theory of curves and surfaces up to the first fundamental form. Notes.

Math 201B: Real Analysis (Denis Labutin). This is the second quarter of a graduate course on real analysis. We covered a bit more measure theory and some functional analysis.

MathCS 120:

Music A42/142/242: Orchestra (Jeffrey Schindler).

Math 220B: Modern Algebra (audit) (Adebisi Agboola). This quarter covered ring and module theory. Notes.

Math 221B: Homotopy Theory (audit) (Stephen Bigelow). This quarter covered fundamental groups.

Music 5E: Music Theory (audit) (Pieter Van Der Toorn). This is the fifth quarter of a six-quarter sequence on theory required for all music majors. (All these required sequences keep me from double-majoring.) We spent most of the quarter on suspensions.

Spring 2004

Math 118C: Real Analysis (Mihai Putinar). This is the third quarter of a three-quarter undergraduate sequence on real analysis. (Yes, I only took the third quarter of this one.) We covered differential forms, Fourier analysis, and basic measure theory.

Math 147B: Differential Geometry (Michael Crandall). This is the second quarter of an undergraduate course on differential geometry. We covered more topics in the theory of surfaces, such as Gaussian and mean curvature and the Gauss-Bonnet theorem. Notes.

Math 201C: Real Analysis (Denis Labutin). Thisis the third quarter of a graduate course on real analysis. We covered some special topics in functional analysis, such as Fredholm operators.

MathCS 101: Putnam Seminar (Charles Ryavec).

MathCS 120: Calculus on Manifolds (Martin Scharlemann). This is a course designed for first-year CCS math majors. We covered mostly differentiation, including the inverse and implicit function theorems. Notes.

Music A42/142/242: Orchestra (Jeffrey Schindler).

Math 220C: Modern Algebra (audit) (Adebisi Agboola). This quarter covered Galois theory and representation theory. Notes.

Math 221C: Differential Topology (audit) (Daryl Cooper). This quarter covered the theory of differentiable manifolds.

MathCS 199 Elliptic and Modular Functions (audit) (Charles Ryavec). This is a reading class on theory of elliptic functions and modular functions. I did not request credit.

Fall 2004

Math 190: Functional Analysis (Mihai Putinar). This is a special topics course on functional analysis. We spent a fair amount of time on the theory of unbounded operators.

Math 202A: Complex Analysis (Milen Yakimov). This is a basic graduate course on complex analysis.

Math 220A: Modern Algebra (Ken Goodearl). This quarter we covered group theory. The topics differed significantly from the Math 220A course in Fall 2003, with a greater emphasis being places on universal constructions. Notes.

MathCS 101: Putnam Seminar (Charles Ryavec).

MathCS 199: Prime Number Theorem (Charles Ryavec). This is a reading class I took on the Erdos-Selberg proof of the prime number theorem.

Music 103: Eighteenth-Century Counterpoint (Joel Feigin). Amazingly, I was the only student in this class, so I had private lessons in counterpoint. I wrote a two-part invention and a dance movement in the style of a Goldberg variation and started on a fugue.

Music 160D/260D: Tuning and Temperament (Scott Marcus). We spent about half of each lecture discussing tuning systems from various parts of the world and the other half teaching the mathematically-challenged music majors how to use their calculators to take logarithms. Needless to say, the former were far more instructive to me than the latter.

Winter 2005

Ger 95B: Intermediate Yiddish (Arthur Schwartz).

LitCS 110: F. Scott Fitzgerald (Charles Ryavec).
(Yes, this class was taught by a math professor. He also happens to know a lot
about F. Scott Fitzgerald.) We read *This Side of Paradise*,

LitCS 113: Hungarians! (John Ridland).
We read *John the Valiant* (Sandor Petofi,
translated by the professor), *Under the Frog* (Tibor
Fischer), *Embers* (Sandor Marai),
*Prague**Forced March* (Miklos Radnoti), and *Fateless* (Imre Kertesz).

Math 202B: Complex Analysis (Milen Yakimov). We covered more basic complex analysis.

Math 209: Set Theory (John Doner). We studied the ZFC axiom system, the continuum hypothesis, ordinals, cardinals, and some other stuff.

Math 220B: Modern Algebra (Milen Yakimov). This quarter was ring and module theory.

Music 212A: Canon and Fugue (Joel Feigin). We studied the Art of Fugue and the Mass in B Minor and wrote fugues as well. This time there were two students in the class, but there was still plenty of individual attention.

Spring 2005

Ger 95C: Advanced Yiddish (Arthur Schwartz).

Math 202C: Complex Analysis (Milen Yakimov). We studied Riemann surfaces. Some specific topics covered were sheaves, de Rham and Dolbeault cohomologies, and meromorphic functions on compact Riemann surfaces.

Math 220C: Modern Algebra (Birge Huisgen-Zimmermann). We covered Galois theory and a bit of algebraic geometry, including several versions of Hilbert’s Nullstellensatz.

MathCS 101: Putnam Seminar (Charles Ryavec.)

MathCS 199: Topics in Analytic Number Theory (Charles Ryavec). This was a reading course. We covered various topics, such as Dirichlet’s Theorem on primes in arithmetic progression and Roth’s Theorem.

Music 26B: Cello Lessons (Geoffrey Rutkowski). We worked on the Beethoven sonata Op. 5, No. 1 and Bach’s third suite, in addition to a number of etudes. We also sometimes worked on orchestra music.

Music 199: Independent Study in Counterpoint (Joel Feigin). I finished the fugue from Music 212A and started on a vocal fugue.

Math
116: Combinatorics (audit) (Jon McCammond).
This is a basic undergraduate combinatorics course.
We covered basic combinatorial methods, generating functions, and

Math 199: Seminar in Linear Algebra (audit) (Stephan Garcia). This was a series of lectures on linear algebra topics given by members of the math faculty and graduate students mostly.

Music A42/142/242: Orchestra (audit) (Jeffrey Schindler).

Fall 2005

Econ 210B: Game Theory (Rod Garratt). This is a basic graduate course on game theory. We covered Nash equilibria, Bayesian equilibria, correlated equilibria, and signaling games, among other topics. Notes.

Math 231A: Lie Groups and Lie Algebra (Milen Yakimov). This is an introduction to Lie groups and Lie algebras. We covered tangent Lie algebras, nilpotent and solvable Lie algebras, Cartan and Borel subalgebras, finite dimensional representations of SL(2,C), and Dynkin diagrams.

Math 240A: Differential Geometry (Doug Moore). This is the first quarter of a three-quarter graduate sequence on differential and Riemannian geometry. This quarter we covered differentiable manifolds, including de Rham cohomology. Notes.

Math 260Q: Noncommutative Noetherian Rings (Ken Goodearl). This is a special topics course on noncommutative noetherian rings. We covered polynomial rings twisted by automorphisms and derivations, rings of fractions and localizations, and Goldie’s theorem. Notes.

MathCS 101: Putnam Seminar (Charles Ryavec).

Music A42/142/242: Orchestra (Sean Newhouse).

Pstat 213A: Probability Theory and Stochastic Processes (Raya Feldman). This is the first quarter of a three-quarter graduate sequence on probability theory and stochastic processes. This quarter we covered Markov chains. Notes.

Winter 2006

History
160A: History of the South through 1865 (Carl Harris). We discussed the history
of the southeastern portion of the

Math 225A: Algebraic Number Theory (Adebisi Agboola). This is a two-quarter graduate sequence on algebraic number theory. This quarter we covered rings of integers, ramification, ideal class groups, decomposition and inertia groups, and quadratic reciprocity. Notes.

Math 236A: Homological Algebra (Birge Huisgen-Zimmermann). This is a two-quarter graduate sequence on homological algebra. We covered projective, injective, and flat modules, and derived functors.

Math 240B: Differential Geometry (Doug Moore). This is the second quarter of a three-quarter graduate sequence on differential and Riemannian geometry. This quarter we covered Riemannian manifolds, connections, and curvature, especially its relations to algebraic topology. Notes.

Math 260Q: Quantum Groups (Ken Goodearl). This is a continuation of the course from the Fall. We saw several examples of quantum groups and studied some noncommutative algebraic geometry.

MathCS 101: Putnam Seminar (Simon Rubinstein-Salzedo). I ran it this quarter.

Music 182/282: Proseminar in Classical Music (Stefanie Tcharos). The topic of this course was the relationships between audiences and composers in instrumental music in the Classical period. We mainly studied Mozart and Haydn, reading many scholarly articles, both from our time and from the eighteenth century.

Spring 2006

GenCS 10: Dreams (Brendan Barnwell). We read some books and articles on dream theories and discussed them with examples from our own dreams.

Math 225B: Algebraic Number Theory (Adebisi Agboola). This quarter we covered completions, local fields, zeta functions, Dirichlet and Artin L-series, and class field theory. Notes.

Math 236B: Homological Algebra (Birge Huisgen-Zimmermann). This quarter we covered specific properties of the Ext and Tor functors and path algebras.

Math 240C: Differential Geometry (Doug Moore). This quarter we covered Cartan’s method of moving frames, the exterior and Clifford algebras, and the generalized Gauss-Bonnet theorem. Notes.

MathCS 101: Putnam Seminar (Simon Rubinstein-Salzedo). I ran it again.

Music A42/142/242: Orchestra (Sean Newhouse).

Fall 2006

CS 138: Formal Languages and Automata (Oscar Ibarra). We discussed regular languages, context-free languages, and Turing machines.

Math 227A: Khovanov Homology (Stephen Bigelow). We defined Khovanov homology for knots and then used it to prove Milnor’s conjecture on unknotting numbers of torus knots.

Math 237A: Algebraic Geometry (Bill Jacob): This quarter was devoted to algebraic varieties, mostly over algebraically closed fields. We also touched upon a few other topics such as toric varieties.

Math 260Q: Combinatorics (Jon McCammond). We covered basic counting principles, inclusion/exclusion, poset combinatorics, and rational generating functions.

MathCS 101: Advanced Putnam Seminar (Simon Rubinstein-Salzedo). I ran it once again.

Music
181/292: Secular Music of Claudio Monteverdi (Bill Prizer).
We discussed and listened to the first eight madrigal books and also the operas
*L’Orfeo* and
*L’incoronazione** di Poppea*.

Winter 2007

CS 220: Theory of Computation and Complexity (Oscar Ibarra). We studied efficient algorithms, mostly on Turing machines, but also on push-down automata and other simpler machines.

Math 225A: Elliptic Curves (Adebisi Agboola). This quarter we covered elliptic curves over the complex numbers, finite fields, and local fields. Notes.

Math 227B: Combinatorial 3-Manifolds (Martin Scharlemann). Mostly we did normal surface theory stuff.

Math 232A: Algebraic Tooplogy (Daryl Cooper). This quarter was devoted to homology and its applications.

Math 237B: Algebraic Geometry (Bill Jacob). This quarter was devoted to schemes, but we also took some detours into topics such as vector bundles and K-theory.

MathCS 101: Advanced Putnam Seminar (Simon Rubinstein-Salzedo). Not too different from before.

Music
113A: 19^{th} and 20^{th} Century Opera (Derek Katz). We mostly
studied Verdi’s *Rigoletto*
and *Un Ballo in
Maschera*, but we also spent some time on Wagner’s
*Tannhäuser*
and *Die Walküre*
and Kurt Weill’s *The Rise and Fall of the
City of Mahagonny*.

Phil
153/253G: Aristotle (Voula Tsouna).
We read sections of the *Nicomachean** Ethics*, *Physics*, *Metaphysics*, and
*Categories*.

GenCS 10: History and Philosophy of the

Spring 2007

CS 290A/Physics 250: Quantum Information and Quantum Computing (Wim Van Dam). We studied some basic quantum mechanics and then discussed some advantages of quantum computers over classical computers, especially algorithms with an exponential speedup, such as Shor’s algorithm for factoring.

Math 197A: Senior Thesis (Birge Huisgen-Zimmermann). My thesis is on finitistic dimensions of monomial algebras. You can read it.

Math 225B: Elliptic Curves (Adebisi Agboola). This quarter we mostly covered elliptic curves over local and global fields. Some highlights included a proof of the Mordell-Weil Theorem and Diophantine approximation on elliptic curves. Notes.

Math 260E: Distributions, Fourier Transforms, and Paley-Wiener Theory (Mihai Putinar).In addition to the material in the course title, we covered Sobolev spaces and partial differential equations.

Math 260Q: Number Theory and Cryptography (Larry Gerstein). We studied some elementary and computational number theory that is (at least potentially) relevant to cryptosystems and some instances in which cryptosystems can be attacked.

MathCS 10: Combinatorial Game Theory (Simon
Rubinstein-Salzedo). We talked about