MA2ALANU: Algebra

Module code: MA2ALANU

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 2 (Intermediate)

When you'll be taught: Semester 2

Module convenor: Dr Chris Daw, email: chris.daw@reading.ac.uk

NUIST module lead: Yi Zhang, email: zhangyi2016@nuist.edu.cn

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST TAKE MA0FMNU AND TAKE MA1LANU (Compulsory)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: No

Talis reading list: No

Last updated: 21 May 2024

Overview

Module aims and purpose

This module is an introduction to basic concepts of abstract algebra; namely, groups, rings, and fields.

It aims to develop the basic theory of these objects, illustrating the fascinating connections between them, and bridging the gap between concrete and abstract algebra.

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Work with groups, subgroups and quotient groups, recognise homomorphisms, and establish simple isomorphisms;
2. Recognise subrings and ideals, and construct quotient rings;
3. Construct simple algebraic extensions

Module content

The first half of the module studies in detail the basic theory of groups (which are sets equipped with an abstract operation of multiplication satisfying certain axioms modelled on familiar examples). This provides both an understanding of the common properties of many different 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 introduces, in a similar fashion, 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.

Structure

Teaching and learning methods

Lectures supported by tutorials. Learning materials (lecture notes/reading lists, tutorial problem sheets, assessments) made available via Blackboard.

Study hours

At least 54 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• 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 three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: https://www.reading.ac.uk/cqsd/-/media/project/functions/cqsd/documents/qap/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.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Reassessment

Additional costs