# Foundations of Mathematics

## Course Description

• ### Course Name

Foundations of Mathematics

Mathematics

• ### Language Level

Taught In English

• ### Prerequisites

Non-modular pre-requisites: A level Mathematics Grade B or higher

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• ECTS Credits

10
• Recommended U.S. Semester Credits
6
• Recommended U.S. Quarter Units
8
• ### Overview

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.

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.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.