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MATH3011: ANALYSIS III

Please ensure you check the module availability box for each module outline, as not all modules will run in each academic year. Each module description relates to the year indicated in the module availability box, and this may change from year to year, due to, for example: changing staff expertise, disciplinary developments, the requirements of external bodies and partners, and student feedback. Current modules are subject to change in light of the ongoing disruption caused by Covid-19.

Type Open
Level 3
Credits 20
Availability Available in 2023/24
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Complex Analysis II (MATH2011) and Analysis in Many Variables II (MATH2031)

Corequisites

  • None

Excluded Combinations of Modules

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.

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.

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.
  • 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

ActivityNumberFrequencyDurationTotalMonitored
Lectures422 per week for 20 weeks and 2 in term 31 Hour42 
Problems Classes8Four in each of terms 1 and 21 Hour8 
Preparation and Reading150 
Total200 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
Written examination3 Hours100 

Formative Assessment

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

More information

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