Real Analysis

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 5
Thursday 03 October 2019
Saturday 14 December 2019
26 April 2019


Requisites for this module



Key module for

BSC L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Mathematics and Statistics (Including Foundation Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad)

Module description

This course provides a gentle but rigorous introduction to real analysis.

Module aims

Syllabus - Monotonic and convergent sequences; related results such as sums, products and quotients of convergent sequences. - Cauchy sequences and the equivalence of the Cauchy property and convergence - Limits of functions - Continuous and differentiable functions of one real variable; related results such as sums, products, quotients and compositions (chain rule). - Boundedness of continuous functions on closed bounded intervals. - Theorems related to continuous and differentiable functions, such as Rolle's Theorem and the Mean Value Theorem

Module learning outcomes

On completion of the course students should be able to: - understand principles underlying proofs of basic theorems concerning limits, continuity and differentiability. - use correctly the quantifiers and other logical notation needed in analysis; - reproduce elementary epsilon-delta arguments;

Module information

No additional information available.

Learning and teaching methods

This course runs at 3 hours per week in the autumn term. In the Summer term 3 revision lectures are given.


The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.
Assessment items, weightings and deadlines
Coursework / exam Description Deadline Weighting
Coursework Test 1 50%
Coursework Test 2 50%
Exam 120 minutes during Summer (Main Period) (Main)
Overall assessment
Module supervisor and teaching staff
Dr David Penman,
Miss Claire Watts, Department Manager, Tel. 01206 873040, email



External examiner

No external examiner information available for this module.
Available via Moodle
Of 35 hours, 29 (82.9%) hours available to students:
6 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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