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MATHEMATICS

MATH-596
Selected Topics: Non-recurring (1-6)

Course Level: Undergraduate/Graduate

Topics vary by section, may be repeated for credit with different topic.

MATH-596
002
MATHEMATICS
FALL 2014

Course Level: Undergraduate/Graduate

Selected Topics: Non-recurring (1-6)

Advanced Mathematical Tools in Economics

This course surveys ideas and techniques from calculus, linear algebra, and differential equations, focusing on their applications to economics. Topics covered include differentiation, integration, and optimization of multivariable functions; systems of linear equations; vector spaces; linear transformations; eigenvectors; systems of first-order differential equations; and the Laplace transform.

MATH-596
001
MATHEMATICS
SPRING 2015

Course Level: Undergraduate/Graduate

Selected Topics: Non-recurring (1-6)

Matrix Groups and Representation Theory

The theory of matrix groups provides a framework for studying the symmetry of objects that arise in diverse branches of mathematics, as well as in chemistry, quantum mechanics, the theory of relativity, and quantum computing. Matrix groups are collections of invertible matrices that can be viewed as geometric transformations of various interesting spaces, e.g., rotations of 2- and 3-dimensional space and isometries of 4-dimensional space-time. This course studies matrix groups using techniques from calculus, linear algebra, and group theory. It is also an introduction to representation theory, which studies abstract groups by "representing" them as matrix groups. Applications to topics in science (physics, chemistry, etc.) are also discussed.