MA2RA1-Real Analysis I
Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:5
Terms in which taught: Autumn / Spring / Summer module
Pre-requisites: MA1FM Foundations of Mathematics
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA1RA1 Real Analysis I
Current from: 2021/2
Module Convenor: Prof Michael Levitin
Email: m.levitin@reading.ac.uk
Type of module:
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, differentiability and determine by proof whether certain functions possess said properties;
• Communicate mathematical arguments.
Additional outcomes:
Outline content:
The module develops on 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.
| Autumn | Spring | Summer | |
| Lectures | 20 | 20 | 4 |
| Tutorials | 9 | 9 | |
| Guided independent study: | 69 | 69 | |
| Total hours by term | 98 | 98 | 4 |
| Total hours for module | 200 |
| Method | Percentage |
| Written exam | 70 |
| Written assignment including essay | 30 |
Summative assessment- Examinations:
3 hours.
Summative assessment- Coursework and in-class tests:
One examination; 70% and a number of assessed exercise sheets.
Formative assessment methods:
Problem sheets.
Penalties for late submission:
The Support Centres will apply the following penalties for work submitted late:
- where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that 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.
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.
Assessment 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 coursework marks (70% exam, 30% coursework).
Additional Costs (specified where applicable):
1) Required text books:
2) Specialist equipment or materials:
3) Specialist clothing, footwear or headgear:
4) Printing and binding:
5) Computers and devices with a particular specification:
6) Travel, accommodation and subsistence:
Last updated: 12 April 2021
THE INFORMATION CONTAINED IN THIS MODULE DESCRIPTION DOES NOT FORM ANY PART OF A STUDENT'S CONTRACT.