MATH41220: Analysis

• Prior knowledge of Complex Analysis and Anaysis in Many Variables at undergraduate level.

• None

• None

• To provide the student with basic ideas of measure, integration, and their applications

• 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.

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.

• 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.

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.

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