Arno Berger

Research

MATH 201 - Differential Equations

First-order equations; second-order linear equations: reduction of order, variation of parameters; Laplace transform; linear systems; power series; solution by series; separation of variables for PDEs. Prerequisite or corequisite: MATH 209 or 214. Notes: (1) Open only to students in Engineering and Specialization Geophysics. (2) Credit can be obtained in at most one of MATH 201, MATH 334, MATH 336, or MA PH 251. (3) Students in all sections of this course will write a common final examination. Non-Engineering students who take this course will receive 3 units.

MATH 216 - Introduction to Analysis

Sets and functions. Induction. Axiomatic introduction of the real numbers. Sequences and series. Continuity and properties of continuous functions. Differentiation. Riemann integral. Corequisite: One of MATH 101, 115, 136, 146, 156 or SCI 100. Note: This course may not be taken for credit if credit has already been obtained in MATH 117. Credit can only be obtained in one of MATH 216 or MATH 314.

MATH 447 - Elementary Topology

General point-set topology. Compactness, Tychonoff's theorem, connectedness. Metric spaces, completeness, Baire's theorem. Urysohn's lemma. Topological manifolds. Homotopy theory, fundamental group, covering spaces at the discretion of the instructor. Prerequisite: MATH 216 or MATH 217. Offered in alternate years. It may be offered in intervening years if demand is sufficient.

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