MA1FM-Foundations of Mathematics

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: MA1LA Linear Algebra and MA1CA Calculus
Modules excluded:
Current from: 2023/4

Module Convenor: Dr Chris Daw
Email: chris.daw@reading.ac.uk

Type of module:

Summary module description:

This module introduces fundamental topics in mathematics.

Aims:

To motivate students' appreciation for the rigorous study of mathematics and to begin that process. Emphasis will be given to the concepts of sets, functions and various familiar number systems. A central goal of this module is to understand the need for proof and develop the skills to enable the student to construct for themselves formal proofs. To develop the manipulative skills and mathematical intuition necessary for the study of mathematics at university.

Assessable learning outcomes:

By the end of the module students are expected to be ableÌý to:

• understand and use logical notation and arguments; construct simple mathematical proofs;


• perform appropriate calculations within a given numberÌý system.

Additional outcomes:

The ability to construct simple but rigorous mathematical arguments, and express correctly statements and proofs of simple mathematicalÌý theorems.

Outline content:

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

• sets and functions; relations and operations; logical arguments and proofs;


• direct proof, by induction and byÌý contradiction;


• some elementary number theory (e.g. the Euclidean algorithm); complex numbers;


• a brief introduction to group theory.

Brief description of teaching and learning methods:

Lectures supported by problem sheets and tutorials.

Contact hours:

Ìý	Autumn	Spring	Summer
Lectures	20	20	4
Tutorials	9	9
Guided independent study:	69	69
Ìý	Ìý	Ìý	Ìý
Total hours by term	98	98	4
Ìý	Ìý	Ìý	Ìý
Total hours for module	200

Summative Assessment Methods:

Method	Percentage
Written exam	70
Set exercise	30

Summative assessment- Examinations:

Length of examination: 3 hours.

The examination for this module will require a narrowly defined time window and is likely to be held in a dedicated exam venue.

Summative assessment- Coursework and in-class tests:

ÌýOne examination and a number of assignments.

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.

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

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:Ìý

2) Specialist equipment or materials:Ìý

3) Specialist clothing, footwear or headgear:Ìý

4) Printing and binding:Ìý

5) Computers and devices with a particular specification:Ìý

6) Travel, accommodation and subsistence:Ìý

Last updated: 30 March 2023