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Dec 15, 2025
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MATH 5330 - Hilbert Spaces and Applications
A course in applied linear analysis, especially Hilbert spaces, for advanced undegraduate and graduate students in mathematics, the sciences or engineering. The course will introduce both the practical and theoretical aspects of linear analysis and students will be expected to complete both computational and proof-oriented exercises. Topic covered will include: Normed Vector Spaces, the spaces L1 and L2, Hilbert Spaces, orthonormal systems, linear operators on Hilbert space and applications to differential equations.
Requisites:
Credit Hours: 3
Repeat/Retake Information: May not be retaken.
Lecture/Lab Hours: 3.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Learning Outcomes:
- Can prove basic properties of Hilbert spaces and other functions spaces.
- Can use Hilbert space techniques in applications.
- Students will understand the concepts and properties of function spaces and their properties.
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