Foundations of Mathematics

Summary module description:

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;
- manipulate simple inequalities;
- perform appropriate calculations within a given number system.

Additional outcomes:
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; induction and contradiction;
- real number system; completeness;
- some elementary number theory (e.g. division algorithm);
- some classical inequalities;
- complex numbers.

Brief description of teaching and learning methods:
Lectures supported by problem sheets and tutorials.

Summative Assessment Methods:
Written exam 60%
Class test administered by School 40%

Other information on summative assessment:
One class test and one examination.

Formative assessment methods:
Problem sheets.

Penalties for late submission:
The Module Convener 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.