MA203 Half Unit
Real Analysis
This information is for the 2025/26 session.
Course Convenor
Prof Amol Sasane
Availability
This course is compulsory on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science and BSc in Mathematics with Economics. This course is available on the BSc in Actuarial Science, BSc in Actuarial Science (with a Placement Year), BSc in Data Science, BSc in Mathematics, Statistics and Business, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is available with permission to General Course students.
Requisites
Pre-requisites:
Students must have completed MA102 or MA103 before taking this course.
Course content
This is a course in real analysis for those who have already met the basic concepts of sequences and continuity on the real line. Here we generalize these concepts to Euclidean spaces and to more general metric and normed 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, compactness, completeness.
- Pointwise and uniform convergence of sequences of functions.
- Continuity of real valued functions and of functions between metric spaces, and uniform continuity.
- Differentiation of real valued functions, the mean value theorem, differentiation of functions between Euclidean spaces, and partial derivatives.
- Series, including power series and series in normed spaces.
- Riemann integral and the fundamental theorem of calculus.
Teaching
1 hours of lectures in the Spring Term.
20 hours of lectures and 10 hours of classes in the Autumn Term.
Formative assessment
Written answers to set problems will be expected on a weekly basis.
Indicative reading
A comprehensive pack of lecture notes will be provided.The following book may prove useful for some aspects of the course:
- Walter Rudin, Principles of Mathematical Analysis, Third edition, McGraw-Hill, 1976.
Assessment
Exam (100%), duration: 120 Minutes in the Spring exam period
Key facts
Department: Mathematics
Course Study Period: Autumn and Spring Term
Unit value: Half unit
FHEQ Level: Level 5
CEFR Level: Null
Total students 2024/25: 178
Average class size 2024/25: 16
Capped 2024/25: NoCourse selection videos
Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.
Personal development skills
- Self-management
- Team working
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills