MA2ALANU-Algebra

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:5
Semesters in which taught: Semester 1 module
Pre-requisites: MA1LANU Linear Algebra and MA0FMNU Foundations of Mathematics
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2022/3

Module Convenor: Dr Basil Corbas
Email: b.corbas@reading.ac.uk

Type of module:

Summary module description:

This module is an introduction to the basic concepts of algebra, centred around group, ring and field theory.

The Module lead at NUIST is Dr Raul Sanchez GalanÌý(raul.galan.13@alumni.ucl.ac.uk).

Aims:

To develop the basic theory of groups, rings and fields; to illustrate the fascinating and unexpected interconnections among seemingly unrelated topics, especially between concrete and "abstract" algebra.

Assessable learning outcomes:

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

1. Work with groups, subgroups and quotient groups;


2. Recognise homomorphisms and establish simple isomorphisms;


3. Work with permutations expressed in cycle notation;


4. Recognise subrings and ideals;


5. Construct quotient rings;


6. Construct simple algebraic extensions.

Additional outcomes:

By the end of the course, students are expected to have acquired skill in logical reasoning and construction of proofs.

Outline content:

The first half of the module studies in detail the basic theory of groups, i.e.. sets equipped with an abstract operation of multiplication satisfying certain axioms modelled on a plethora of motivating examples. This provides both an understanding of the common properties of many different kinds of mathematical objects and insight into the differences between them. In particular the following topics will be discussed:

• Groups, subgroups, quotient groups, Lagrange's Theorem, cyclic groups, symmetric groups, homomorphisms and isomorphisms, Cayley's Theorem.


• The second part of the module proceeds along the same pattern to introduce the theory of rings and fields. In particular the following topics will be discussed:


• Rings, subrings, ideals, the quotient ring with respect to an ideal, ring homomorphisms, polynomials and polynomial rings, algebraic and transcendental extensions, finite fields.

Brief description of teaching and learning methods:

Lectures supported by tutorials and problem sheets.

Contact hours:

Ìý	Semester 1	Semester 2
Lectures	96
Guided independent study:	Ìý	Ìý
Ìý Ìý Wider reading (independent)	68
Ìý Ìý Wider reading (directed)	20
Ìý Ìý Exam revision/preparation	16
Ìý	Ìý	Ìý
Total hours by term	200	0
Ìý	Ìý	Ìý
Total hours for module	200

Summative Assessment Methods:

Method	Percentage
Written exam	80
Class test administered by School	20

Summative assessment- Examinations:

3 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 examination paper of 3 hours duration in January/December - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (80% exam, 20% 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: 22 September 2022