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Department of Mathematics
MATH339 - Real and Functional
Analysis
Unit Syllabus
- The number system, completeness and
consequences.
- Countability, cardinal numbers, Cantor-Bernstein-Schröder
theorem.
- Sequences and limits, subsequences,
general principle of convergence.
- Series, real series, complex series,
power series.
- Functions and continuity.
- Metric spaces, open and closed sets,
limits and continuity.
- Connectedness, completeness, compactness,
continuous functions with compact domains.
- Normed vector spaces, Banach spaces.
- Inner product spaces, Hilbert spaces.
- Orthogonal expansions, orthonormal systems,
orthonormal bases.
- Isomorphism of Hilbert spaces.
- Splitting up a Hilbert space.
- Linear functionals, dual space.
- Linear transformations, bounded linear
transformations.
- Linear transformations on Hilbert spaces.
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