Module Directory

MA203-5-AU-CO:Real Analysis

The details
2019/20
Mathematical Sciences
Colchester Campus
Autumn
Current
Thursday 03 October 2019
Saturday 14 December 2019
15
01 October 2019

Requisites for this module
MA101
(none)
(none)
(none)

(none)

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 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;

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.

Bibliography

This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

Coursework / exam Description Deadline Weighting
Coursework Test 1
Coursework Test 2
Exam 120 minutes during Summer (Main Period) (Main)

Coursework Exam
20% 80%

Reassessment

Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr David Penman, dbpenman@essex.ac.uk; Dr Alastair Litterick, a.litterick@essex.ac.uk
Dr David Penman (dbpenman@essex.ac.uk)

Availability
Yes
Yes
No

External examiner

Dr Tania Clare Dunning
The University of Kent
Resources
Available via Moodle
Of 37 hours, 33 (89.2%) hours available to students:
4 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).

Further information
Mathematical Sciences

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