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.