Analysis I
MATH 514
Spring 2026
| Section:
01
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| This course may be repeated for credit. |
MATH513 and MATH 514 constitute the first-year graduate course in complex analysis, real analysis, and functional analysis. The Fall semester is devoted to complex analysis and measure theory. Fall topics include holomorphic functions, Cauchy's theorem, Cauchy's integral formulas, analytic continuation, the calculus of residues, the maximum modulus principle, and conformal mappings; sigma algebras, Borel measures, Lebesgue-Stieltjes measures, measurable functions, the dominated convergence theorem, Egorov's theorem, and Littlewood's principles. Spring topics continue with the development of measure theory before moving on to functional analysis. Spring topics may include product measures, Fubini's theorem, and the Radon-Nikodym theorem; Banach spaces, Hilbert spaces, linear functionals, linear operators, the Banach-Alaoglu theorem, and the Hahn-Banach theorem. |
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| Credit: 1 |
Gen Ed Area Dept:
None |
| Course Format: Lecture | Grading Mode: Graded |
| Level: GRAD |
Prerequisites: None |
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Fulfills a Requirement for: None |
| SECTION 01 |
| Instructor(s): Ramirez,Felipe Times: .M.W... 01:20PM-02:40PM; Location: SCIE618; |
| Total Enrollment Limit: 16 | | SR major: 4 | JR major: 2 | | |
| | GRAD: 10 | SR non-major: 0 | JR non-major: 0 | SO: 0 | FR: 0 |
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