MT3502 Real Analysis

Academic year

2024 to 2025 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 9

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

11.00 am Mon (even weeks), Tue & Thu

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof M J Todd

Prof M J Todd
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module continues the study of analysis begun in the 2000-level module MT2502 Analysis. It considers further important topics in the study of real analysis including: integration theory, the analytic properties of power series and the convergence of functions. Emphasis will be placed on rigourous development of the material, giving precise definitions of the concepts involved and exploring the proofs of important theorems. The language of metric spaces will be introduced to give a framework in which to discuss these concepts.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2502

Assessment pattern

90% exam, 10% class test

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5-hours of lectures and 1 tutorial.

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Appreciate the differing cardinalities of infinite sets and be able to determine whether sets are countable or uncountable
  • Understand the formal development of the Riemann integral and the proof of the fundamental theorem of the calculus
  • Understand the utility of uniform convergence of sequences and series of functions leading to differentiation and integration of power series
  • See how many ideas in analysis can readily be extended to the settings of metric and normed spaces