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Module

MAS8754 : Measure Theory

  • Offered for Year: 2024/25
  • Module Leader(s): Dr Christian Bönicke
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters

Your programme is made up of credits, the total differs on programme to programme.

Semester 1 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System

Aims

To familiarise students with the theory of measure spaces. To understand Lebesgue integration and applications that arise both in pure and applied sciences. To reinforce the ability of students to follow research in Analysis.
Module summary
Measure theory gives the appropriate language for measuring subsets of a space in a systematic way. The common example is Lebesgue measure on the real line which gives the length of an interval. This idea can be used to further produce a notion of integration. Unlike Riemann integration which is based on a partition of the domain of a function, Lebesgue integration relies on partitions of the range. As such it can tackle, in a sense, more functions than usual. Measure theory is a basic tool
for Analysis and Algebra but also has vast applications in Applied Sciences, including Physics, Medicine and Economics. By the end of the course the students will understand Lebesgue integration

in Rn and how it can be used as a language to encode a variety of examples through the notion of Hilbert spaces.

Outline Of Syllabus

Systems of sets and measures.
Measure theory on Rn (Lebesgue integration).
Comparison with Riemann integration

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Guided Independent StudyIndependent study158:0058:00Preparation time for lectures, background reading, coursework review
Total100:00
Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1201A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

Timetable