Feng Dai

Research

MATH 315 - Calculus IV

Vector calculus. Line and surface integrals. The divergence, Green's, and Stokes' theorems. Differential forms. Prerequisite: One of MATH 102, 125 or 127, and either MATH 214 or MATH 217. Notes: Credit can be obtained in at most one of MATH 215 and MATH 315. This course may not be taken for credit if credit has already been obtained in MATH 209 or 317.

MATH 373 - Introduction to Optimization

Introduction to optimization. Problem formulation. Linear programming. The simplex method and its variants (revised Simplex method, dual simplex method). Extreme points of polyhedral sets. Theory of linear inequalities (Farkas Lemma). Complementary slackness and duality. Post-optimality analysis. Interior point methods. Applications (elementary games, transportation problems, networks, etc.). Prerequisites: One of MATH 102, 125 or 127, and one of MATH 209, 214 or 217.

MATH 417 - Real Analysis

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisite: MATH 317 or 414.

MATH 514 - Measure Theory I

Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisites: Math 317.

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