Method of characteristics for first- and second-order partial differential equations, conservation laws and shocks, classification of second-order systems and applications.

Basic theories of testing statistical hypotheses, including a thorough treatment of testing in exponential class families. A careful mathematical treatment of the primary techniques of hypothesis testing utilized by statisticians.

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Spectral theory of bounded and unbounded operators, major theorems of functional analysis, additional topics.

Independent research conducted under the guidance of a faculty member.

Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series.

Mathematical logic and proof, mathematical induction, counting methods, recurrence relations, algorithms and complexity, graph theory and graph algorithms. Credit not awarded for both MATH 2603 and MATH 2602.