
Academic Year:  2019/0 
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: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites:  Before taking this module you must take MA30252 OR take MA40043 
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 selfadjoint, 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: Innerproduct spaces, Hilbert spaces. CauchySchwarz inequality, parallelogram identity. Examples. Orthogonality, GramSchmidt 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, selfadjoint operators. Spectrum of an operator. Spectral theory of selfadjoint, compact operators. Applications and further topics, which might include: Fourier series, Gauss approximation problem, LaxMilgram theorem. 
Programme availability: 
MA40256 is Optional on the following programmes:Department of Computer Science

Notes:
