MA30252: Advanced real analysis
Academic Year:  2020/1 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Honours (FHEQ level 6) 
Period: 
Semester 1 
Assessment:  EX 100% 
Supplementary Assessment: 

Requisites:  Before taking this module you must take MA20219 
Description:  Aims: To introduce and study abstract spaces and general ideas in analysis, to apply them to examples, and to lay the foundations for the MA4 analysis units. Learning Outcomes: By the end of the unit, students should be able to state and prove the principal theorems relating to completeness, compactness, and dense sets in metric and normed spaces, and to apply these notions and theorems to simple examples. Skills: Numeracy T/F, A Problem Solving T/F, A Written Communication F (on problem sheets) Content: Metric spaces and normed spaces, convergence and continuity. Examples. Completion of a metric space. Dense and nowhere dense sets, separable spaces, Baire category theorem. Equivalence of compactness and sequential compactness in metric spaces, relatively compact sets, ArzelaAscoli theorem. Uniform approximation of continuous functions, Polynomial and trigonometric polynomial approximation. Further topics, which might include: the abstract StoneWeierstrass theorem, existence of nowhere differentiable functions, connectedness and path connectedness. 
Programme availability: NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020 
MA30252 is Compulsory on the following programmes:Department of Physics
MA30252 is Optional on the following programmes:Department of Computer Science

Notes:
