This page is for the academic year 2021-22. The current handbook year is 2022-23
Department: Mathematical Sciences
||Available in 2021/22
- Complex Analysis II (MATH2011) AND Analysis in Many Variables II (MATH2031) AND Algebra II (MATH 2581).
Excluded Combination of Modules
- To provide a balanced introduction to Point Set, Geometric and
Algebraic Topology, with particular emphasis on surfaces and knots.
- Topological Spaces and Continuous Functions: Topology on a
set, open sets, closed sets, limit points and closure, examples of
- Compactness and Connectedness.
- Topological groups and group actions.
- The Orthogonal groups. The Fundamental Group: calculation
for circle, homotopy type, homotopy equivalence.
- Generators and relations of groups, Tietze theorem, Van
- Compact surfaces, classical knots, basic knot
- By the end of the module students will: be able to solve
novel and/or complex problems in Topology.
- have a systematic and coherent understanding of theoretical
mathematics in the field of Topology.
- have acquired a coherent body of knowledge of these subjects
demonstrated through one or more of the following topic areas:
- Topological Groups and group actions.
- Fundamental group, homotopy type.
- Group presentations and Van Kampen's Theorem.
- Surfaces and Knots.
- In addition students will have specialised mathematical
skills in the following areas which can be used with minimal guidance:
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the
application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and
enable students to test and develop their knowledge and
- Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired
and the ability to solve predictable and unpredictable
Teaching Methods and Learning Hours
||2 per week for 20 weeks and 2 in term 3
||Four in each of terms 1 and 2
|Preparation and Reading
||Component Weighting: 100%
||Length / duration
|three-hour end of year examination
Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University