MA203      Half Unit
Real Analysis

This information is for the 2023/24 session.

Teacher responsible

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 and BSc in Mathematics, Statistics and Business. 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 Mathematical Proof and Analysis (MA102) are essential.

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, uniform continuity and Lipschitz condition.
  • 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

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Autumn Term, and an hour at the start of Spring Term.

Formative coursework

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: 2 hours) in the spring exam period.

Key facts

Department: Mathematics

Total students 2022/23: 162

Average class size 2022/23: 13

Capped 2022/23: No

Lecture capture used 2022/23: Yes (MT)

Value: Half Unit

Guidelines for interpreting course guide information

Course 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