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Session: 2022/23
Last modified: 10/01/2023 11:13:57
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Title of Module: Abstract Algebra |
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Code: MATH09013 |
SCQF Level: 9
(Scottish Credit and Qualifications Framework) |
Credit Points: 20 |
ECTS: 10
(European Credit Transfer Scheme) |
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| School: | School of Computing, Engineering and Physical Sciences |
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| Module Co-ordinator: | TBC
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| Summary of Module |
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This module discusses the fundamental ideas from abstract algebra.
Groups:
Definitions, properties, and examples will be discussed, e.g., symmetry and permutation groups as well as groups of transformations and isometries. The concept of an Abelian group will be introduced. Use will be made of Cayley tables. Isomorphisms of groups will be considered as will cyclic groups. The concept of a subgroup will be introduced, including normal subgroups, and Lagrange’s Theorem will be considered.
Rings
Definitions, properties, and examples will be discussed as well as important theorems in ring theory. Specific discussion of Polynomial and Euclidean rings will occur as will that of commutative rings. Homeomorphisms of rings will be covered. There will be a treatment of subrings, ideals, and integral domains.
Fields
Definitions, properties, and examples will be discussed as well as important results in field theory. Mention will be made of extension fields as well as polynomial fields. Subfields will be discussed.
The Graduate Attributes relevant to this module are given below:
- Academic: Critical thinker; Analytical; Inquiring; Knowledgeable; Problem-solver; Autonomous.
- Personal: Motivated; Resilient
Professional: Ambitious; Driven.
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| Module Delivery Method |
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| Face-To-Face | Blended | Fully Online | HybridC | HybridO | Work-based Learning |
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Face-To-Face
Term used to describe the traditional classroom environment where the students and the lecturer meet synchronously in the same room for the whole provision.
Blended
A mode of delivery of a module or a programme that involves online and face-to-face delivery of learning, teaching and assessment activities, student support and feedback. A programme may be considered “blended” if it includes a combination of face-to-face, online and blended modules. If an online programme has any compulsory face-to-face and campus elements it must be described as blended with clearly articulated delivery information to manage student expectations
Fully Online
Instruction that is solely delivered by web-based or internet-based technologies. This term is used to describe the previously used terms distance learning and e learning.
HybridC
Online with mandatory face-to-face learning on Campus
HybridO
Online with optional face-to-face learning on Campus
Work-based Learning
Learning activities where the main location for the learning experience is in the workplace.
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| Term(s) for Module Delivery |
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(Provided viable student numbers permit).
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| Term 1 | | Term 2 | | Term 3 | |
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| Learning Outcomes: (maximum of 5 statements) |
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On successful completion of this module the student will be able to:
L1.
Demonstrate a good understanding of standard techniques and results in group theory.
L2.
Demonstrate a good understanding of standard techniques and results in ring and field theory.
L3.
Synthesise fundamental concepts to solve a range of problems in abstract algebra. |
| Employability Skills and Personal Development Planning (PDP) Skills |
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| SCQF Headings |
During completion of this module, there will be an opportunity to achieve
core skills in:
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| Knowledge and Understanding (K and U) |
SCQF Level 9.
Demonstrating a knowledge and understanding of a range of standard techniques in abstract algebra.
Demonstrating critical awareness of established techniques of enquiry in application of these techniques. |
| Practice: Applied Knowledge and Understanding |
SCQF Level 9.
Using a range of standard techniques to solve problems at an advanced level, sometimes in non-routine contexts.
Carrying out defined investigative problems within a mathematically based subject.
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| Generic Cognitive skills |
SCQF Level 9.
Conceptualising and analysing problems informed by professional and research issues. |
| Communication, ICT and Numeracy Skills |
SCQF Level 9.
Making formal written presentation(s) based on the output from an investigative problem. |
| Autonomy, Accountability and Working with others |
SCQF Level 9.
Exercising independence and initiative in carrying out a range of activities.
Identifying learning needs through reflection based on self, tutor and peer evaluation of work.
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| Pre-requisites: |
Before undertaking this module the student should have
undertaken the following:
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Module Code:
MATH08006
| Module Title:
Discrete Mathematics
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| Other: | or equivalent |
| Co-requisites | Module Code:
| Module Title:
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* Indicates that module descriptor is not published.
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| Learning and Teaching |
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| The material will be presented through lectures and directed reading and the students will test their understanding of the material through tutorials. |
Learning Activities
During completion of this module, the learning activities undertaken to
achieve the module learning outcomes are stated below:
| Student Learning Hours
(Normally totalling 200 hours):
(Note: Learning hours include both contact hours and hours spent on other learning activities) |
| Lecture/Core Content Delivery | 36 |
| Tutorial/Synchronous Support Activity | 0 |
| Independent Study | 164 |
| 200
Hours Total
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**Indicative Resources: (eg. Core text, journals, internet
access)
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The following materials form essential underpinning for the module content
and ultimately for the learning outcomes:
Modern Algebra, JR Durbin, John Wiley & Sons, 1999
A First Course in Abstract Algebra, JB Fraleigh, Pearson, 2013
Groups, Rings, and Fields, David Wallace, Springer, 2001
Resources available on the University VLE.
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(**N.B. Although reading lists should include current publications,
students are advised (particularly for material marked with an asterisk*) to
wait until the start of session for confirmation of the most up-to-date
material)
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| Engagement Requirements |
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In line with the Academic Engagement Procedure, Students are defined as academically engaged if they are regularly engaged with timetabled teaching sessions, course-related learning resources including those in the Library and on the relevant learning platform, and complete assessments and submit these on time. Please refer to the Academic Engagement Procedure at the following link: Academic engagement procedure |
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Supplemental Information
| Programme Board | Physical Sciences |
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| Assessment Results (Pass/Fail) |
No
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| Subject Panel | Physical Sciences |
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| Moderator | Dr Wan R Mekwi |
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| External Examiner | P Wilson |
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| Accreditation Details | |
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| Version Number | 1.05 |
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| Assessment: (also refer to Assessment Outcomes Grids below) |
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| Assignment: a coursework assignment, 30% of the final mark |
| Examination: a final, closed book assessment, 70% of the final mark |
(N.B. (i) Assessment Outcomes Grids for the module
(one for each component) can be found below which clearly demonstrate how the learning outcomes of the module
will be assessed.
(ii) An indicative schedule listing approximate times
within the academic calendar when assessment is likely to feature will be
provided within the Student Handbook.)
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Assessment Outcome Grids (Footnote A.)
Footnotes
A. Referred to within Assessment Section above
B. Identified in the Learning Outcome Section above
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Note(s):
- More than one assessment method can be used to assess individual learning outcomes.
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Schools are responsible for determining student contact hours. Please refer to University Policy on contact hours (extract contained within section 10 of the Module Descriptor guidance note).
This will normally be variable across Schools, dependent on Programmes &/or Professional requirements.
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| Equality and Diversity |
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The module is suitable for any student satisfying any of the stated pre-requisites.
UWS Equality and Diversity Policy |
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(N.B. Every effort
will be made by the University to accommodate any equality and diversity issues
brought to the attention of the School)
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