University of St Andrews

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF level 8

Semester: 2

Planned timetable: 11.00 am Mon (odd weeks), Wed and Fri

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-requisite(s): If MT1002 has not been passed, then A at Advanced Higher Mathematics or A at A-level Further Mathematics.. Before taking this module you must pass MT1002

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

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 70%, Coursework = 30%

As defined by QAA
Written examinations : 70%
Practical examinations : 0%
Coursework: 30%

Re-assessment: 2-hour Written Examination = 100%

Personnel

Module coordinator: Dr M Quick
Module teaching staff: Dr Ashley Clayton
Module coordinator email mq3@st-andrews.ac.uk

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 https://www.st-andrews.ac.uk/maths/current/ug/programmes/