Linear algebra eigenvalues, eigenvectors, applications to linear systems, least squares, diagnolization, quadratic forms.

Integral calculus: Definite and indefinite integrals, techniques of integration, improper integrals, infinite series, applications. Credit not awarded for both MATH 1552 and MATH 1502, MATH 1504, MATH 1512 or MATH 1555.

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.