MA20218: Analysis 2A
[Page last updated: 10 August 2020]
Academic Year:  2020/1 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Intermediate (FHEQ level 5) 
Period: 
 Semester 1

Assessment Summary:  EX 100% 
Supplementary Assessment: 
 Likeforlike reassessment (where allowed by programme regulations)

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
 USCMAFB20 : BSc(Hons) Computer Science and Mathematics (Year 2)
 USCMAAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
 USCMAKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
 USCMAFM14 : MComp(Hons) Computer Science and Mathematics (Year 2)
 USCMAAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 2)
 USCMAKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 2)
Department of Mathematical Sciences
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 2)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 2)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 2)
 USMAAFB13 : BSc(Hons) Mathematics (Year 2)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 2)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 2)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 2)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 2)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 2)
 USMAAFB05 : BSc(Hons) Statistics (Year 2)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 2)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 2)
 USMAAFM14 : MMath(Hons) Mathematics (Year 2)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 2)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 2)
Department of Physics
 USXXAFB03 : BSc(Hons) Mathematics and Physics (Year 2)
 USXXAAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 2)
 USXXAKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 2)
 USXXAFM01 : MSci(Hons) Mathematics and Physics (Year 2)
 USXXAAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 2)
 USXXAKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 2)
MA20218 is Optional on the following programmes:
Department of Economics
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 2)
 UHESAFB04 : BSc(Hons) Economics and Mathematics (Year 3)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 2)
 UHESAAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 2)
 UHESAKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 2)
 UHESACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
