Mathematics

Analysis 1

Module code: G5135
Level 4
15 credits in autumn semester
Teaching method: Lecture, Workshop
Assessment modes: Coursework, Unseen examination

Starting from the concept of limit of a sequence, learn how it is possible to give a precise meaning to the concepts of "infinite", "infinitely small", and "infinitely large". You will also learn how to work with series, and understand how these tools can be applied to define limits of functions.

You will see some of the concepts that you have covered in school in a new light, and analyse them in great depth. You will learn how to give rigorous proofs of mathematical statements, and how to sketch the graph of a function. This module will pave the way for what will later be covered in Analysis 2.

Having a good understanding of analysis will prepare you to deal with modern mathematics that is used in branches of science, physics, biology, probability, and finance. 

Module learning outcomes

• Appreciate rigorous arguments in analysis and deploy them to solve problems;
• Understand sequences and series and the concepts of convergence and divergence;
• Demonstrate knowledge of the definitions and the elementary properties of continuous functions of one real variable.