Analysis module (MA32001)

Analysis is an area of pure mathematics. Its purpose is to form a solid foundation that other areas of maths can build on. Results are often considered in an abstract setting which makes analysis very powerful.

Often, mathematical models in physics, biology, and economics use complicated equations, often solved by computers. You will learn that computer-based methods often use a sequence of approximate solutions which require a robust framework.

This framework uses convergence, a concept that will be covered in detail throughout the module. Interesting concepts of calculus and statistics are discussed to help give real examples of these complicated equations.

What you will learn

In this module, you will:

• learn about normed and metric spaces and why they are important
• define and measure convergence of sequences
• define and check continuity of functions
• classify sets using the correct definitions and their relevance to the convergence of sequences
• understand special properties of sequences and series of functions

By the end of this module, you will be able to:

• apply key theoretical results to determine properties of examples
• construct rigorous theoretical calculations, called proofs, in analysis
• reflect on various connections between given concepts
• carry out library searches to write literature reviews

Assignments / assessment

• coursework (20%)
• final exam (80%)

Teaching methods / timetable

• one-hour lectures weekly
  • key points of the week's content will be discussed
  • lecture notes covering the full module content will be available before classes
  • video content on key concepts will also be available
  • in-class time will be prioritised for interactive discussion
• two hours of tutorials weekly
  • solve problems individually and in groups
  • support with difficulties will be provided by your lecturers and peers