Division III; Quantative/Formal Reasoning;
This is not the current course catalog
Functional analysis can be viewed as linear algebra on infinite-dimensional spaces. It is a central topic in Mathematics, which brings together and extends ideas from analysis, algebra, and geometry. Functional analysis also provides the rigorous mathematical background for several areas of theoretical physics (especially quantum mechanics). We will introduce infinite-dimensional spaces (Banach and Hilbert spaces) and study their properties. These spaces are often spaces of functions (for example, the space of square-integrable functions). We will consider linear operators on Hilbert spaces and investigate their spectral properties. A special attention will be dedicated to various operators arising from mathematical physics, especially the Schrodinger operator.
The Class: Type: lecture
Requirements/Evaluation: weekly problem sets, two midterm exams, final exam
Prerequisites: MATH 350 or 351 or permission of instructor
Enrollment Preference: Mathematics and Physics majors; seniors
Distributions: Division III; Quantative/Formal Reasoning;