MA203      Half Unit
Real Analysis

This information is for the 2020/21 session.

Teacher responsible

Prof Martin Anthony


This course is compulsory on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics and BSc in Mathematics with Economics. This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics 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.


Introduction to Abstract Mathematics (MA103).

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.



This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Michaelmas Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.

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:

  • Robert G Bartle & Donald R Sherbert, Introduction to Real Analysis 


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

Important information in response to COVID-19

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2019/20: 173

Average class size 2019/20: 13

Capped 2019/20: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

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