## MA1RA1-Real Analysis I

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:4
Terms in which taught: Autumn / Spring / Summer module
Pre-requisites:
Non-modular pre-requisites: A level Mathematics Grade B or higher
Co-requisites: MA1FM Foundations of Mathematics MA1CA Calculus MA1LA Linear Algebra
Modules excluded:
Module version for: 2016/7

Module Convenor: Dr Tristan Pryer

Summary module description:
This module provides an introduction to mathematical analysis. We cover concepts such as inequalities, sequences and series as well as functions and their fundamental properties.

Aims:
To provide a formal introduction to mathematical analysis by rigorously approaching concepts crucial in subsequent analytical topics.

Assessable learning outcomes:
By the end of the module students are expected to be able to:

• Understand the Real number system;
• Manipulate simple inequalities;
• Define convergence of sequences and series;
• Understand concepts of convergence for sequences and series;
• Introduce continuity and differentiation and prove some fundamental properties of continuous and differentiable functions;
• Apply definitions & theorems presented throughout the course to solve unseen problems;
• State and prove some fundamental theorems;
• Understand definitions of boundedness, continuity, uniform continuity, differentiability and determine by proof whether certain functions possess said properties;
• Communicate mathematical arguments.

Outline content:
The module developsalongside the content of MA1FM, beginning with the Real number system, fundamental inequalities, concepts of limits of sequences, infinite series and continuity, before finally developing these into a rigorous understanding of the calculus.

Brief description of teaching and learning methods:
Lectures supported by problem sheets and tutorials.

Contact hours:
 Autumn Spring Summer Lectures 20 20 4 Tutorials 9 9 Guided independent study 69 69 Total hours by term 98.00 98.00 4.00 Total hours for module 200.00

Summative Assessment Methods:
 Method Percentage Written exam 60 Set exercise 20 Class test administered by School 20

Other information on summative assessment:
One examination; 60%, one class test, 20%, and a number of assessed exercise sheets.

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Length of examination:
3 hours.

Requirements for a pass:
A mark of 40% overall.

Reassessment arrangements:
One examination paper of 3 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous class test and coursework marks (60% exam, 20% class test, 20% coursework).