UNIVERSITY OF KENT
MODULE SPECIFICATION TEMPLATE
SECTION 1: MODULE SPECIFICATIONS
1.
Title of the module : Groups and Rings (MA565)
2.
School or partner institution which will be responsible for management of the module
School of Mathematics, Statistics and Actuarial Science
3.
Start date of the module : January 2015
4.
The number of students expected to take the module: 80
5.
Modules to be withdrawn on the introduction of this proposed module and consultation with other
relevant Schools and Faculties regarding the withdrawal
MA554 (Groups, Rings and Fields). The new module will be a suitable substitute for all programmes
offering MA325 (the prerequisite module). This module will not, therefore, be available to BSc (Hons)
Mathematics and Accounting & Finance students. No programme has MA554 as a required module.
6.
The level of the module (e.g. Certificate [C], Intermediate [I], Honours [H] or Postgraduate [M]): I
7.
The number of credits and the ECTS value which the module represents : 15 (ECTS 7.5)
8.
Which term(s) the module is to be taught in (or other teaching pattern): Spring term
9.
Prerequisite and co-requisite modules:
Prerequisite modules: MA325 (From Geometry to Algebra)
There are no co-requisite modules.
10. The programmes of study to which the module contributes
BSc (Hons) Mathematics, BSc (Hons) Mathematics & Statistics, BSc (Hons) Financial Mathematics
(including programmes with a year in industry), BSc (Hons) Mathematics with Secondary Education,
BSc (Hons) Mathematics with a Foundation Year, MMath Mathematics, MMathStat Mathematics and
Statistics
11. The intended subject specific learning outcomes
On successful completion of this module students will be able to:
a) cite and understand a representative selection of the definitions and terms of basic Group
Theory and Ring Theory;
b) cite examples of the main mathematical structures introduced including groups, subgroups,
quotient groups, rings, subrings, ideals and homomorphisms;
c) execute simple proofs and deductions from the axioms for these structures and express the
reasoning with reasonable clarity;
d) perform simple calculations for specific examples of these structures;
e) appreciate the relevance of abstract algebraic structures to related areas of mathematics.
12. The intended generic learning outcomes
Students who successfully complete this module will have further developed:
a) a logical, mathematical approach to solving problems;
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UNIVERSITY OF KENT
b)
c)
d)
e)
their ability to communicate solutions, simple proofs and calculations;
their numeracy and computational skills;
their ability to plan and carry out effective ways of studying;
their ability to read and comprehend mathematical ideas.
13. A synopsis of the curriculum

Review of the basic concepts introduced in MA325, including the definition of a group, the
subgroup test, the order of an element and Lagrange’s Theorem.
 Group homomorphisms, the kernel of a homomorphism, normal subgroups,
quotient groups and the First Isomorphism Theorem.
 Permutation groups, group actions and Cayley’s Theorem.
 Matrix groups.
 Rings and subrings: examples and definitions.
 Ring homomorphisms, the kernel of a ring homomorphism, the definition of an ideal, the First
Isomorphism Theorem for rings.
 Polynomial rings and quotients of polynomial rings.
 Factorization, zero divisors, units.
 Principle Ideal Domains, Euclidean Domains and the field of fractions of a domain.
Additional topics might include finitely generated abelian groups, the Smith Normal Form, or the
Weyl algebra.
14. Indicative Reading List
a) P.J. Cameron, Introduction to Algebra, Oxford UP, 1998.
b) L.N. Childs, A Concrete Introduction to Higher Algebra, Springer, 2000.
15. Learning and Teaching Methods, including the nature and number of contact hours and the total
study hours which will be expected of students, and how these relate to achievement of the intended
module learning outcomes.
Number of contact hours: 48.
Number of independent learning hours: 102.
Total study hours: 150.
Teaching methods will involve a mix of lectures, examples classes and supervised problem solving
workshops. Subject specific learning outcomes 11(a), (b), (e) and generic learning outcomes 12 (a),
(e) will be addressed by lectures. Subject specific learning outcomes 11(c), (d) and generic learning
outcomes 12(a),(b),(c),(d),(e) will be addressed by examples classes, workshops and written
assessments.
16. Assessment methods and how these relate to testing achievement of the intended module learning
outcomes
The module will be assessed by examination (80%) and coursework (20%).
Coursework: This will involve two or three assignments, which will include some element of computer
calculation and of written exposition, assessing learning outcomes 11(c),(d),(e), 12(a),(b),(c),(e).
Examination: This will be a two hour written examination that consists of multipart questions
requiring a mix of short and long answers that test to varying levels of proficiency the learning
outcomes 11(a),(b),(c),(d) and 12(a),(d).
17. Implications for learning resources, including staff, library, IT and space
This module replaces MA554: no additional resources are required.
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UNIVERSITY OF KENT
18. The School recognises and has embedded the expectations of current disability equality legislation,
and supports students with a declared disability or special educational need in its teaching. Within
this module we will make reasonable adjustments wherever necessary, including additional or
substitute materials, teaching modes or assessment methods for students who have declared and
discussed their learning support needs. Arrangements for students with declared disabilities will be
made on an individual basis, in consultation with the University’s disability/dyslexia support service,
and specialist support will be provided where needed.
19. Campus where module will be delivered: Canterbury
SECTION 2: MODULE IS PART OF A PROGRAMME OF STUDY IN A UNIVERSITY SCHOOL
Statement by the School Director of Learning and Teaching/School Director of Graduate Studies
(as appropriate): "I confirm I have been consulted on the above module proposal and have given advice
on the correct procedures and required content of module proposals"
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Director of Learning and Teaching/Director of
Graduate Studies (delete as applicable)
Date
…………………………………………………
Print Name
Statement by the Head of School: "I confirm that the School has approved the introduction of the
module and, where the module is proposed by School staff, will be responsible for its resourcing"
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Head of School
Date
…………………………………………………….
Print Name
Module Specification Template
Last updated February 2013
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