Undergraduate Programme and Module Handbook 2006-2007 (archived)
Module MATH3011: ANALYSIS III
Department: MATHEMATICAL SCIENCES
MATH3011: ANALYSIS III
| Type | Open | Level | 3 | Credits | 20 | Availability | Available in 2007/08 and alternate years thereafter | Module Cap | None. | Location | Durham |
|---|
Prerequisites
- Complex Analysis II (MATH2011) and Analysis in Many Variables II (MATH2031).
Corequisites
- None.
Excluded Combination of Modules
- Analysis IV (MATH4201)
Aims
- To provide the student with basic ideas about topology and integration and to introduce the student to the theory and application of function spaces.
Content
- Metric Spaces.
- Integration in n-dimensional real space.
- Harmonic functions.
- Compactness in function spaces.
- Conformal mapping.
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: Metric spaces: compactness.
- Completeness.
- Contraction mappings.
- Picard theorem.
- Function Spaces: Stone-Weierstrass theorem.
- Arzela-Ascoli theorem.
- Normal families.
- Integration: Riemann integral.
- Darboux theorem.
- Sets of measure zero.
- Harmonic functions: maximum principle.
- Dirichlet problem and poisson formula.
- Conformal mapping: Schwarz lemma.
- Reflection principle.
- Schwarz-Chistoffel formula.
- Riemann mapping theorem.
Subject-specific Skills:
- Students will have highly specialised and advanced mathematical skills which will be used with minimal guidance in the following areas: spatial awareness.
Key Skills:
- Students will have enhanced problem solving 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.
- 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 | 40 | 2 per week for 19 weeks and 2 in term 3 | 1 Hour | 40 | |
| Preparation and Reading | 160 | ||||
| Total | 200 |
Summative Assessment
| Component: Examination | Component Weighting: 100% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| three hour written examination | 100% | ||
Formative Assessment:
Four 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