MA1RA1: Real Analysis I

Module code: MA1RA1

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: 4

When you’ll be taught: Semester 2

Module convenor: Dr Sugata Mondal , email: s.mondal@reading.ac.uk

Pre-requisite module(s):

Co-requisite module(s):

Pre-requisite or Co-requisite module(s): BEFORE OR WHILE TAKING THIS MODULE YOU MUST TAKE MA1FM (Compulsory)

Module(s) excluded:

Placement information: NA

Academic year: 2025/6

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 3 April 2025

Overview

Module aims and purpose

This module provides an introduction to mathematical analysis and covers concepts such as inequalities, sequences and series as well as functions and their fundamental properties.  

The module aims to provide a rigorous foundation for further topics in analysis and its applications with the emphasis on understanding the concepts rather than mechanical computations. 

Module learning outcomes

By the end of the module, it is expected that students will be able to: 

1. Understand the real number system 
2. Understand the basic theory of sequence and series of real numbers 
3. Understand the basic properties of real-valued functions of one real variable 
4. Apply the theory to solve problems in mathematics 

Module content

The module builds on MA1FM, beginning with the real number system, fundamental inequalities, concepts of limits of sequences, infinite series, and the basic properties of functions, such as continuity, before finally developing these into a rigorous understanding of calculus. 

Structure

Teaching and learning methods

Lectures supported by exercise sheets and tutorials. 

Study hours

At least 52 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• 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 three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/qap/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.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Weekly exercise sheets and tutorials. 

Reassessment

Additional costs