Course Description
Students will be able to:
- Identify metric and normed spaces and make mathematical connections between these two notions.
- Apply Bolzano Weiestrass and Ascoli theorems, characterize compact sets in metric and normed spaces.
- Demonstrate proficiency with Banach spaces in mathematical construction of proofs and reasoning procedures in working with continuity and linearity concepts of operators defined on Banach spaces.
- Demonstrate proficiency with the concept of dual spaces and norms on dual spaces.
- Know fundamental theorems in functional analysis (Baire theorem, Banach- Steinhauss theorem, open mapping theorem, closed graph theorem and Hahn- Banach theorem).
- Identify Hilbert spaces and Hilbert bases, and show familiarity with the basic notions defined on Hilbert spaces.
- Recognize adjoint operators and show familiarity with the basic notions of adjoint operators.
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Course ID: MATH 484N
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 3 | 4 | 4 | MATH 342N\ MATH 362N |
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