Daniel Erdmann Dissertation Proposal

In a rough division of mathematics, mathematical analysis deals with inequalities and limits. In some of its branches, such as asymptotic analysis, these aspects of the subject matter are readily apparent.  in others, such as operator algebras, they are concealed in the topology of an algebras or its structure as an infinite-dimensional vector space. Our department offers a wealth of different perspectives on mathematical analysis.


Undergraduate upper divison courses

Math C103. Introduction to Mathematical Economics.
Math 104, H104. Introduction to analysis.
Math 105. Second course in analysis.
Math 118. Fourier analysis, wavelets, and signal processing.
Math 121A,B. Mathematical Tools for the Physical Sciences.
Math 123. Ordinary Differential Equations.
Math 126. Introduction to Partial Differential Equations.
Math 140. Metric Differential Geometry.
Math 141. Elementary Differential Topology.
Math 185, H185. Introduction to Complex Analysis.
Math 189. Mathematical Methods in Classical and Quantum Mechanics.

Graduate courses

Math 202A,B. Introduction to Topology and Analysis.
Math 203. Asymptotic Analysis in Applied Mathematics.
Math 204. Ordinary Differential Equations.
Math 205. Theory of Functions of a Complex Variable.
Math 206. Banach Algebras and Spectral Theory.
Math 208. C*- algebras.
Math 209. Von Neumann algebras.
Math 212. Several Complex Variables.
Math 214. Differentiable Manifolds.
Math C218A,B. Probability Theory.
Math 222A,B. Partial Differential Equations.
Math 224A,B. Mathematical Methods for the Physical Sciences.
Math 240. Riemannian Geometry.
Math 241. Complex Manifolds.
Math 242. Symplectic Geometry.
Math 258. Classical Harmonic Analysis.
Math 261A,B. Lie Groups.
Math 278. Topics in Analysis.
Math 279. Topics in Partial Differential Equations


Fall 2008

Analysis Seminar (Bade, Cordes, Helson, Sarason)
PDE/Analysis Seminar (Tataru, Zworski)
Probabilistic Operator Algebra (Voiculescu)
Quantum Geometry Seminar (Rieffel, Tucker-Simmons)
Student PDE Seminar (Evans)
Subfactor Seminar (Jones)
Interdisciplinary Stochastic Processes Colloquium (Aldous)
Probability Seminar (Aldous, Haulk)
The Berkeley Bonn Paris Analysis Seminar (Delort, Koch, Zworski)

Spring 2009

Analysis Seminar (Bade, Cordes, Helson, Sarason)
PDE/Analysis Seminar (Tataru, Zworski)
Probabilistic Operator Algebra (Voiculescu)
Quantum Geometry Seminar (Rieffel, Tucker-Simmons)
Student PDE Seminar (Evans)
Subfactor Seminar (Jones)
Interdisciplinary Stochastic Processes Colloquium (Aldous)
Probability Seminar (Aldous)
The Berkeley Bonn Paris Analysis Seminar (Delort, Koch, Zworski)

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