Postgraduate Programme and Module Handbook 2024-2025
Module MATH41220: Analysis
Department: Mathematical Sciences
MATH41220: Analysis
| Type | Tied | Level | 4 | Credits | 20 | Availability | Available in 2024/2025 | Module Cap | None. |
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| Tied to | G1K509 |
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Prerequisites
- Prior knowledge of Complex Analysis and Anaysis in Many Variables at undergraduate level.
Corequisites
- None
Excluded Combination of Modules
- None
Aims
- To provide the student with basic ideas of measure, integration, and their applications
Content
- Set theory.
- Analysis of subsets of the real line.
- Advanced concepts in continuity.
- Measure theory.
- Integration.
- Convergence theorems.
- Banach and Hilbert spaces.
- Harmonic analysis.
- Reading material on special topics in real analysis.
Learning Outcomes
Subject-specific Knowledge:
- By the end of the module students will:
- be able to solve novel and/or complex problems in Analysis.
- have a systematic and coherent understanding of theoretical mathematics in the field of Analysis.
- have acquired a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
- Topology.
- Measure theory.
- Functional analysis.
Subject-specific Skills:
- Students will have highly specialised and advanced mathematical skills which will be used with minimal guidance in the following areas: Analysis.
- Ability to read independently to acquire knowledge and understanding in special topics in real analysis.
Key Skills:
- Students will have enhanced problem solving and abstract reasoning skills.
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.
- Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- 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 problems.
Teaching Methods and Learning Hours
| Activity | Number | Frequency | Duration | Total/Hours | |
|---|---|---|---|---|---|
| Lectures | 42 | 2 per week for 20 weeks and 2 in term 3 | 1 Hour | 42 | |
| Problems Classes | 8 | Four in each of terms 1 and 2 | 1 Hour | 8 | |
| Preperation and Reading | 150 | ||||
| Total | 200 |
Summative Assessment
| Component: Examination | Component Weighting: 100% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| Written examination | 3 Hours | 100% | |
Formative Assessment:
Eight written or electronic 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