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 Academic Year: | 2017/8 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Masters UG & PG (FHEQ level 7) |
| Period: |
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| Assessment Summary: | EX 100% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: | Before taking this module you must take MA30252 OR take MA40043 OR take MA30041 |
| Description:
| Aims: To introduce and study the theory of Hilbert spaces, the mappings between them, and spectral theory. Learning Outcomes: By the end of the unit, students should be able to state and prove the principal theorems relating to Hilbert space theory and spectral theory of self-adjoint, compact linear operators, and to apply these notions and theorems to simple examples and applications. Skills: Numeracy T/F, A Problem Solving T/F, A Written Communication F (on problem sheets). Content: Inner-product spaces, Hilbert spaces. Cauchy-Schwarz inequality, parallelogram identity. Examples. Orthogonality, Gram-Schmidt process. Bessel's inequality. Orthogonal complements. Complete orthonormal sets in separable Hilbert spaces. Projection theorem. Bounded linear operators, dual spaces. Riesz representation theorem. Compact operators. Adjoint of an operator, self-adjoint operators. Spectrum of an operator. Spectral theory of self-adjoint, compact operators. Applications and further topics, which might include: Fourier series, Gauss approximation problem, Lax-Milgram theorem. |
| Programme availability: |
MA40256 is Optional on the following programmes:Department of Computer Science
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Notes:
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