Xi Chen

Research

MATH 225 - Linear Algebra II

Vector spaces. Inner product spaces. Examples of n-space and the space of continuous functions. Gram-Schmidt process, QR factorization of a matrix and least squares. Linear transformations, change of basis, similarity and diagonalization. Orthogonal diagonalization, quadratic forms. Applications in a variety of fields. Prerequisites: One of MATH 100, 113, 114, 117, 134, 144, 154 or SCI 100, and one of MATH 102, 125 or 127. Note: Credit can be obtained in at most one of MATH 225 or 227.

MATH 411 - Honors Complex Variables

Complex number system. Analytic functions. Cauchy's Integral theorem and formula. Applications including the maximum modulus principle, Taylor expansion and Laurent expansion. Harmonic functions. The residue theorem with applications; calculus of residues, argument principle, and Rouche's theorem. Basics of analytic continuation. Additional topics at the instructor's discretion such as: Normal families, The Riemann mapping Theorem, Picard's Theorem. Prerequisite: MATH 314 or 317. Notes: (1) This course is primarily for Honors students in Mathematics or Physics. (2) Offered in alternate years. It may be offered in intervening years if demand is sufficient.

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