
Academic Year:  2017/8 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Intermediate (FHEQ level 5) 
Period: 

Assessment Summary:  EX 100% 
Assessment Detail: 

Supplementary Assessment: 

Requisites: 
Before taking this module you must take MA10207 AND take MA10209 AND take MA10210 
Description:  Aims: To extend the notions of continuity and limit from R to R^{n}, normed spaces and metric spaces, and develop some topology in these spaces. To study sequences of functions and their relation with integration and power series. Learning Outcomes: After taking this unit students should be able to: * state definitions and theorems in real analysis and present proofs of the main theorems * construct their own proofs of simple unseen results and of simple propositions * present mathematical arguments in a precise, lucid and grammatical fashion * apply definitions and theorems to simple examples * carry out computations with integrals and power series * manipulate sequences and limits in R^{n}, normed spaces and metric spaces. Skills: Numeracy T/F A Problem Solving T/F A Spoken and Written Communication F (in tutorials and on problem sheets). Content: Sequences of functions, uniform convergence. Integrals and limits, differentiating under the integral. Complex differentiation, real and complex power series, Weierstrass Mtest, differentiation and integration of power series, exp, log and trig functions, Euler's formula. Real and complex normed vector spaces, L^{2} and uniform norm, operator norm Metric spaces, sequences, convergence, completeness. Open, closed and bounded sets, neighbourhoods; limits and continuity, characterisations via sequences and open sets. Topology on R^{n}: BolzanoWeierstrass, HeineBorel, and Weierstrass theorems. Decreasing sets, Lipschitz maps and uniform continuity, Contraction mapping theorem. 
Programme availability: 
MA20218 is Compulsory on the following programmes:Department of Computer Science
MA20218 is Optional on the following programmes:Department of Economics

Notes:
