Education Aims

The aim of this module is to introduce the main notions and methods of proof in analysis through a mathematically rigorous approach. It follows on from the core modules G11ACF, where properties of real numbers were introduced, and G11CAL where knowledge of calculus was extended. This module, together with G12ALN, is a key component of the Pure Mathematics pathways, being a pre-requisite to further modules in Analysis at level 3 (G13MTS, G13LNA) and 4 (G14FTA). 

Learning Outcomes

A student who completes this module successfully should be able to:

Knowledge and understanding

• define and state the main concepts and theorems of analysis;
• apply these in the investigation of examples;
• prove basic propositions in analysis.

Intellectual skills

• apply complex ideas to familiar and to novel situations;
• work with abstract concepts and in a context of generality;
• reason logically and work analytically;
• perform with high levels of accuracy;
• transfer expertise between different topics in mathematics.

Professional skills

• select and apply appropriate methods and techniques to solve problems;
• justify conclusions using mathematical arguments with appropriate rigour;
• communicate results using appropriate styles, conventions and terminology.

Transferable skills

• communicate with clarity;
• work effectively, independently and under direction;
• analyse and solve complex problems accurately;
• make effective use of IT;
• apply high levels of numeracy;
• adopt effective strategies for study.