The module is in two complementary parts. Firstly, it introduces students of topological design to the field of topology and some case studies of its application. The module will introduce students to the principal subfields of topology (such as algebraic topology, differential topology, point set topology, geometric topology, combinatorial topology) and the related ideas of continuity, connectedness and compactness of topological spaces, fibre bundles and manifolds.

This will be example driven from various sciences and engineering, focusing on helping the students develop an intuitive grasp of the fundamental principles complementing technical definitions and formal proofs.

The concepts will be reinforced by a parallel set of lectures on applications of topology to different disciplines in science and engineering, such as topological insulators (physics), liquid crystal phases and defects (chemistry), topology optimization (materials/engineering) and topological data analysis (maths/computer science).

Learning Outcomes

By the end of the module students should be able to:

Demonstrate an understanding of the basic notions of the mathematical discipline of topology, and appreciate the aspects and connections between the different subfields;

Perform basic topological calculations (involving elementary arithmetic, algebra and calculus);

Demonstrate an appreciation of the applications of topology to a broad range of topics in science and engineering;

Explain, in detail, a topic related to topology or how topological design underpins an area of science and engineering appropriate to the studentsâ€™ background and interests and other materials that have been observed;

Assessment

35089-05 : Class Test 1 : Class Test (25%)
35089-06 : Seminar and Report : Presentation (50%)
35089-07 : Class Test 2 : Class Test (25%)

Assessment Methods & Exceptions

Assessment:
50% class test
50% seminar and report

Reassessment:
Resubmission of the relevant summative elements i.e. Supplementary class test.
Resubmission of report
Give presentation again.