Global Opportunities

MAS3706 : Topology

Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

Aims

To present the basic ideas of topology essential to an understanding of modern analysis and geometry.

Module Summary

Topology is an elegant and abstract subject that arose from disparate sources but is now fundamental in analysis and geometry. One way of viewing topology is to say it answers the question: what are the last features of a subset on n-dimensional Euclidean space to discover when one progressively deforms space? Another approach would be through the question: what do the many limiting procedures in mathematics have in common? It turns out that just three axioms are enough to produce a rich subject which provides the right setting in which to understand both the local aspects of sets and mappings (such as continuity) and the global aspects (such as the overall nature of a set).

Outline Of Syllabus

Topological spaces. Open sets, closed sets, neighbourhoods. Interior, closure, boundary. Nets and convergence. Continuous functions, homeomorphisms. Separation axioms. Connected spaces, Compact spaces, Locally compact spaces.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes – Synchronous On-Line
Guided Independent StudyIndependent study151:0015:00Completion of in course assessments
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Total100:00
Jointly Taught With
Code Title
MAS8706Topology
Teaching Rationale And Relationship

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 Examination1202A80N/A
Exam Pairings
Module Code Module Title Semester Comment
MAS8706Topology2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M7Coursework assignments
Prob solv exercises2M7Coursework assignments
Prob solv exercises2M6Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. 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.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.

Reading Lists

Timetable