Introductory description

Mathematical Analysis is the heart of modern Mathematics. This module is the first in a series of modules where the subject of Analysis is rigorously developed.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

• Inequalities
• Real numbers
• Sequences of numbers
• Limits
• Series
• Continuity
• Uniform continuity

Learning outcomes

By the end of the module, students should be able to:

• develop deep understanding of the real numbers and the symbol `infinity'
• develop working knowledge of sequences and series, including limits, conditional and absolute convergence
• learn the properties of continuous and absolutely continuous functions

Indicative reading list

M. Hart, Guide to Analysis, Macmillan.
M. Spivak, Calculus, Benjamin. R.G Bartle and D.R Sherbert, Introduction to Real Analysis (4th Edition), Wiley (2011)
L. Alcock, How to think about Analysis, Oxford University Press (2014)

View reading list on Talis Aspire

Subject specific skills

Analysis gives first-year undergraduates a first excursion in to pure mathematics. The students will gain a new perspective and a deeper understanding of familiar mathematics which they have seen in school (e.g. real numbers, functions and differentiation). In Analysis, these concepts are developed with mathematical rigour, which characterises much of university mathematics to follow.

Transferable skills

Students will acquire key reasoning and problem solving skills, empower them to address new problems with confidence.