MT2505 Abstract Algebra

Academic year

2024 to 2025 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 8

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

11.00 am Mon (odd weeks), Wed and Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof N Ruskuc

Prof N Ruskuc
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

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

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

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 recognize 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/mathematics-statistics/students/ug/module-choices-2000/