## 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 MA1CA Calculus
Modules excluded:
Module version for: 2017/8

Module Convenor: Dr Rachel Newton

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 able to:

• understand and use logical notation and arguments;

• construct simple mathematical proofs;

• perform appropriate calculations within a given number system.

The ability to construct simple but rigorous mathematical argument, and express correctly statements and proofs of simple mathematical 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 be discussed:

• sets and functions; relations and operations;

• logical arguments and proofs;

• direct proof, by induction and by 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:
 Autumn Spring Summer Lectures 20 20 4 Tutorials 9 9 Guided independent study 69 69 Total hours by term 98.00 98.00 4.00 Total hours for module 200.00

Summative Assessment Methods:
 Method Percentage Written exam 80 Set exercise 20

Other information on summative assessment:

A number of assignments and one examination.

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convenor will apply the following penalties for work submitted late, in accordance with the University policy.

• where the piece of work is submitted up to one calendar week after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for the 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: http://www.reading.ac.uk/web/FILES/qualitysupport/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.

Length of examination:
3 hours.

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 (80% exam, 20% coursework).