## MA203Half UnitReal Analysis

This information is for the 2013/14 session.

Teacher responsible

Availability

This course is compulsory on the BSc in Mathematics and Economics and BSc in Mathematics with Economics. This course is available on the BSc in Business Mathematics and Statistics, BSc in Econometrics and Mathematical Economics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Pre-requisites

Introduction to Abstract Mathematics (MA103), or some equivalent giving experience with formal proofs, convergence of sequences and continuity of functions.

Course content

This is a course in real analysis for those who have already met the basic concepts of sequences and continuity in R. Here we generalize these concepts to Rn and to more general normed spaces and metric spaces.  These more general spaces are introduced at the start and are emphasized throughout the course.
Topics covered are: metric and normed spaces, open and closed sets, sequences in metric spaces, pointwise and uniform convergence of sequences of functions, series in R and in normed spaces, continuous functions between metric spaces, compactness, uniform continuity, the mean value theorem, differentiation of functions between Rn and Rm, partial derivatives, the Riemann integral.

Teaching

20 hours of lectures and 9 hours of classes in the MT. 1 hour of classes in the LT. 2 hours of lectures in the ST.

Formative coursework

Written answers to set problems will be expected on a weekly basis.

Lecture notes will be provided. The following may prove useful: Robert G Bartle & Donald R Sherbert, Introduction to Real Analysis; K G Binmore, Mathematical Analysis: a straightforward approach; Victor Bryant, Yet Another Introduction to Analysis; W A Sutherland, Introduction to Metric and Topological Spaces.

Assessment

Exam (100%, duration: 2 hours) in the main exam period.

Key facts

Department: Mathematics

Total students 2012/13: 109

Average class size 2012/13: 14

Value: Half Unit

Guidelines for interpreting course guide information

PDAM skills

• Self-management
• Problem solving
• Application of information skills
• Communication
• Application of numeracy skills
• Specialist skills

Course survey results

(2010/11 - 2012/13 combined)

1 = "best" score, 5 = "worst" score

The scores below are average responses.

Response rate: 78.6%

Question

Average
response

2.5

Materials (Q2.3)

2.2

Course satisfied (Q2.4)

2.2

Lectures (Q2.5)

2.3

Integration (Q2.6)

2

Contact (Q2.7)

2.3

Feedback (Q2.8)

2.5

Recommend (Q2.9)

 Yes 51% Maybe 35.1% No 13.9%