Undergraduate Programme and Module Handbook 2026-2027
Module MATH3551: Analysis & Topology III
Department: Mathematical Sciences
MATH3551: Analysis & Topology III
| Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2026/2027 | Module Cap | Location | Durham |
|---|
Prerequisites
- Complex Analysis II (MATH2791 OR MATH2011).
Corequisites
- None
Excluded Combination of Modules
- None
Aims
- To provide an introduction to Topology by building up the theory of topological spaces, or point-set topology, from axioms.
- To enhance understanding in Analysis by developing further concepts including measure theory, integration, and continuity and convergence of functions.
- To provide the background necessary for applying Analysis and Topology in other areas of mathematics.
- To support students to develop their ability to construct proofs.
Content
- Topology:
- Metric spaces.
- Point set topology.
- The product and quotient topologies.
- Introduction to topological groups.
- Analysis:
- Introduction to measure theory.
- Continuous functions and approximation.
- Integration and convergence theorems.
- Introduction to Lebesgue spaces.
Learning Outcomes
Subject-specific Knowledge:
- By the end of the module students will:
- Be able to solve seen and unseen problems on the given topics.
- Be able to reproduce theoretical mathematics in the fields of Topology and Analysis.
- Have a knowledge and understanding of fundamental theories and abstract concepts of these fields demonstrated through one or more of the following topic areas: metric and topological spaces, the product and quotient topologies, continuity and convergence of functions, measure theory and integration.
Subject-specific Skills:
- Students will have highly specialised and advanced mathematical skills which will be used with minimal guidance in the following areas: Topology and Analysis.
- In addition, students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: abstract reasoning.
Key Skills:
- Students will develop mathematical skills in the following areas: abstract reasoning, problem solving.
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.
- Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
- Formative assignments provide feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
- Summative assignments test achievement of learning outcomes and provide feedback to students about their mastery of the topics.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.
Teaching Methods and Learning Hours
| Activity | Number | Frequency | Duration | Total/Hours | Attendance Monitored |
|---|---|---|---|---|---|
| Lectures | 40 | 2 per week for 20 weeks | 1 | 40 | |
| Problem Classes | 10 | 4 in Michaelmas; 4 in Epiphany; 2 in Easter | 10 | Yes ■ | |
| Preparation and Reading | 1 | 150 | |||
| Total | 200 |
Summative Assessment
| Component: Examination | Component Weighting: 70% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| On Campus Written Examination | 2 hours | 100% | |
| Component: Summative Assignments | Component Weighting: 30% | ||
| Element | Length / duration | Element Weighting | Resit Opportunity |
| Assignment | 100% | ||
Formative Assessment:
Four assignments to be submitted.
■ Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.