MA1FM: Foundations of Mathematics

Module code: MA1FM

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

Credits: 20

Level: Level 1 (Certificate)

When you'll be taught: Semester 1

Module convenor: Professor Michael Levitin, email: m.levitin@reading.ac.uk

Pre-requisite module(s): Before taking this module, you must have at least a grade B in A-Level Mathematics grade B, or equivalent. (Open)

Co-requisite module(s): IN THE SAME YEAR AS TAKING THIS MODULE YOU MUST TAKE MA1CA (Compulsory)

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 21 May 2024

Overview

Module aims and purpose

This module introduces fundamental topics in mathematics and it will motivate students' appreciation for the rigorous study of mathematics.  Emphasis will also be given to the concepts of sets, functions and various familiar number systems.  A central goal of the module is to understand the need for proofs and to develop the skills required to construct them.  It will develop the skills necessary for the study of mathematics at university. 

Module learning outcomes

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

1. Understand and use logical notation and arguments;
2. Construct simple mathematical proofs;
3. Perform calculations within a given number system.

Module content

The module develops the essential skills of pure mathematics, and begins the process of learning how to think like a mathematician; in particular, how to construct logical arguments and work with definitions, theorems, and proofs. The topics discussed are likely to include: 

• sets and functions;  
• relations and operations;  
• logical arguments and proofs; direct proof, proof by induction, and proof by contradiction; 
• some elementary number theory (e.g. the Euclidean algorithm); complex numbers; 
• a brief introduction to group theory. 

Structure

Teaching and learning methods

Lectures supported by tutorials. Learning materials (lecture notes/reading lists, tutorial problem sheets, assessments) made available via Blackboard. 

Study hours

At least 50 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.

Reassessment

Additional costs