MA0FMNU-Foundations of Mathematics

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:F
Semesters in which taught: Semester 1 module
Pre-requisites:
Non-modular pre-requisites: High School Mathematics
Co-requisites: MA0MANU Mathematical Analysis
Modules excluded:
Current from: 2023/4

Module Convenor: Dr Jani Virtanen
Email: j.a.virtanen@reading.ac.uk

NUIST Module Lead: Vahid Darvish
Email: vdarvish@gmail.com

Type of module:

Summary module description:

This module focuses on introducing basic mathematical techniques such as proof by induction, and basic concepts such as Set Theory and Group Theory.

The Module lead at NUIST is Dr Vahid Darvish (vdarvish@gmail.com).Ìý

Aims:

To help the students transition from pre-university mathematics to university mathematics. To introduce them to the idea of definition, theorem and proof, and to rigorously cover topics they should have mostly seen in high school

Assessable learning outcomes:

By the end of the course, students are expected to be able to:

• State several key definitions and important results;


• Understand basic concepts of propositional and predicate logic;


• Effectively use various methods of proof, e.g. proof by induction and proof by contradiction;


• Handle sets and the functions between them. In particular, students should know what is meant by injective, surjective and bijective functions;


• Understand and work with the supremum and infimum of a set;


• Perform basic number theory computations;


• Understand the concept of a group and a subgroup. Be comfortable working with various finite groups such as cyclic groups, dihedral groups and symmetric groups.

Additional outcomes:

Outline content:

The module will focus on the following areas and topics:

• Logic and proof


• Sets and functions


• Real numbers


• Basic number theory


• Group theory

Brief description of teaching and learning methods:

Lectures enhanced by self-study and peer-group learning.

Contact hours:

Ìý	Semester 1	Semester 2
Lectures	45
Guided independent study:	Ìý	Ìý
Ìý Ìý Wider reading (independent)	36
Ìý Ìý Wider reading (directed)	7
Ìý Ìý Exam revision/preparation	12
Ìý	Ìý	Ìý
Total hours by term	100	0
Ìý	Ìý	Ìý
Total hours for module	100

Summative Assessment Methods:

Method	Percentage
Written exam	70
Class test administered by School	30

Summative assessment- Examinations:

2 Hours

Summative assessment- Coursework and in-class tests:

One examination and a number of class tests.

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 re-examination paper of 2 hours duration in August - 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