MT2505 Abstract Algebra
Academic year
2025 to 2026 Semester 2
Curricular information may be subject to change
Further information on which modules are specific to your programme.
Key module information
SCOTCAT credits
15
SCQF level
SCQF level 8
Planned timetable
11.00 am Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri
Module Staff
Prof Nik Ruskuc
Module description
This main purpose of this module is to introduce the key concepts of modern abstract algebra: groups, rings and fields. Emphasis will be placed on the rigourous development of the material and the proofs of important theorems in the foundations of group theory. This module forms the prerequisite for later modules in algebra. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.
Relationship to other modules
Pre-requisites
BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED, THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS.
Assessment pattern
2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%
Re-assessment
2-hour Written Examination = 100%
Learning and teaching methods and delivery
Weekly contact
2.5 hours of lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 weeks)
Scheduled learning hours
35
Guided independent study hours
115
Intended learning outcomes
- State what is meant by a group, a ring, and a field, and to be able to verify that a particular structure satisfies one of these definitions
- Define and be able to produce theoretical arguments (proofs) using fundamental concepts of pure mathematics such as equivalence relations, equivalence classes and partitions, and such as injective, surjective and bijective functions
- Work with standard examples of groups, including those built using congruence arithmetic, matrices (such as the general linear group), permutations (such as the symmetric and alternating groups), isometries (such as dihedral groups), and the Klein 4-group
- Work with permutations, to decompose them as products of cycles, to recognise odd and even permutations
- Define what is meant by subgroups, cyclic subgroups, cosets, homomorphisms, kernels and images, normal subgroups and quotient groups, and to produce theoretical arguments to establish their properties
- State standard theorems concerning groups, including Lagrange's Theorem and the First Isomorphism Theorem, and apply them to problems in mathematics
Additional information from school
For guidance on module choice at 2000-level in Mathematics and Statistics please consult the School Handbook, at /mathematics-statistics/students/ug/module-choices-2000/
MT2505 Abstract Algebra
Academic year
2026 to 2027 Semester 2
Curricular information may be subject to change
Further information on which modules are specific to your programme.
Key module information
SCOTCAT credits
15
SCQF level
SCQF level 8
Planned timetable
11.00 am Mon (weeks 1, 3, 5, 7, 9, 12), Wed and Fri
Module Staff
TBD
Module description
This main purpose of this module is to introduce the key concepts of modern abstract algebra: groups, rings and fields. Emphasis will be placed on the rigourous development of the material and the proofs of important theorems in the foundations of group theory. This module forms the prerequisite for later modules in algebra. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.
Relationship to other modules
Pre-requisites
BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED, THEN A AT ADVANCED HIGHER MATHEMATICS, OR A AT A-LEVEL FURTHER MATHEMATICS.
Assessment pattern
2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%
Re-assessment
2-hour Written Examination = 100%
Learning and teaching methods and delivery
Weekly contact
2.5 hours of lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 weeks)
Scheduled learning hours
35
Guided independent study hours
115
Intended learning outcomes
- State what is meant by a group, a ring, and a field, and to be able to verify that a particular structure satisfies one of these definitions
- Define and be able to produce theoretical arguments (proofs) using fundamental concepts of pure mathematics such as equivalence relations, equivalence classes and partitions, and such as injective, surjective and bijective functions
- Work with standard examples of groups, including those built using congruence arithmetic, matrices (such as the general linear group), permutations (such as the symmetric and alternating groups), isometries (such as dihedral groups), and the Klein 4-group
- Work with permutations, to decompose them as products of cycles, to recognise odd and even permutations
- Define what is meant by subgroups, cyclic subgroups, cosets, homomorphisms, kernels and images, normal subgroups and quotient groups, and to produce theoretical arguments to establish their properties
- State standard theorems concerning groups, including Lagrange's Theorem and the First Isomorphism Theorem, and apply them to problems in mathematics
Additional information from school
For guidance on module choice at 2000-level in Mathematics and Statistics see our Module choices at 1000 and 2000 level page.
Syllabus
- Preliminaries and prerequisites; equivalence relations
- The definitions and familiar examples of rings and fields
- The definition of a group, Cayley tables, elementary properties of groups
- Examples of groups: modular arithmetic including the Euclidean algorithm; permutation groups and symmetries
- The order of an element, subgroups, cyclic groups, alternating groups, cosets and Lagrange’s Theorem
- Homomorphisms and isomorphisms, normal subgroups, ideals, quotient groups and rings, the First Isomorphism Theorem