Last modified: 14 Nov 2025 12:16
The aim of the course is to introduce the basic concepts of metric spaces and their associated topology, and to apply the ideas to Euclidean space and other examples.
An excellent introduction to "serious mathematics" based on the usual geometry of the n dimensional spaces.
| Study Type | Undergraduate | Level | 3 |
|---|---|---|---|
| Term | First Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
| Co-ordinators |
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Syllabus
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 70 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Students will be invited to contact Course Coordinators for feedback on the final examination. |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Remember | Be able to define closed sets and give examples. |
| Conceptual | Remember | Be able to define metric spaces and give examples of metric spaces. |
| Conceptual | Understand | Understand convergence and continuity in terms of open sets. |
| Conceptual | Understand | Understand connectedness and path-connectedness and how they relate to each other. |
| Conceptual | Understand | Be able to define products and subspaces and understand examples. |
| Conceptual | Understand | Understand completion and examples of complete metric spaces. |
| Conceptual | Understand | Be able to define compactness and understand examples of compact spaces. |
| Conceptual | Understand | Understand what is a general topological spaces and generalise notions from metric spaces to topological spaces. |
| Procedural | Analyse | Analyse metric spaces with respect to the properties introduced in the course. |
| Procedural | Create | Create examples illustrating the relationship between properties of metric and topological spaces introduced in the course. |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback | ||||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Understand | Be able to define compactness and understand examples of compact spaces. |
| Conceptual | Understand | Understand connectedness and path-connectedness and how they relate to each other. |
| Conceptual | Understand | Understand completion and examples of complete metric spaces. |
| Conceptual | Understand | Be able to define products and subspaces and understand examples. |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback | ||||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Remember | Be able to define closed sets and give examples. |
| Conceptual | Remember | Be able to define metric spaces and give examples of metric spaces. |
| Conceptual | Understand | Understand convergence and continuity in terms of open sets. |
There are no assessments for this course.
| Assessment Type | Summative | Weighting | 100 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Best of (resit exam mark) or (resit exam mark with carried forward CA marks) |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
|
|
||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Understand | Be able to define products and subspaces and understand examples. |
| Conceptual | Understand | Understand convergence and continuity in terms of open sets. |
| Conceptual | Understand | Be able to define compactness and understand examples of compact spaces. |
| Conceptual | Remember | Be able to define metric spaces and give examples of metric spaces. |
| Conceptual | Understand | Understand completion and examples of complete metric spaces. |
| Conceptual | Remember | Be able to define closed sets and give examples. |
| Procedural | Analyse | Analyse metric spaces with respect to the properties introduced in the course. |
| Conceptual | Understand | Understand what is a general topological spaces and generalise notions from metric spaces to topological spaces. |
| Procedural | Create | Create examples illustrating the relationship between properties of metric and topological spaces introduced in the course. |
| Conceptual | Understand | Understand connectedness and path-connectedness and how they relate to each other. |
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