MT4003 Groups

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 10

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.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

9.00 am Mon (even weeks), Tue and Thu

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

Module coordinator

Prof J D Mitchell

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

Module description

This module introduces students to group theory, which is one of the central fields of the 20th century mathematics. The main theme of the module is classifying groups with various additional properties, and the development of tools necessary in this classification. In particular, the students will meet the standard algebraic notions, such as substructures, homomorphisms, quotients and products, and also various concepts peculiar to groups, such as normality, conjugation and Sylow theory. The importance of groups in mathematics, arising from the fact that groups may be used to describe symmetries of any mathematical object, will be emphasised throughout the module.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2505

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks), 1 tutorial (x 10 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

  • Demonstrate an understanding of basic mathematical concepts in each of the module core topics (subgroups, generators, homomorphisms, cosets, conjugation, normal subgroups, direct products, the centre, the derived subgroup, Sylow subgroups)
  • Be familiar and able to work with concrete groups: cyclic, symmetric, alternating, dihedral, quaternions, general/special linear, etc.
  • Be able to produce theoretical arguments (proofs) which establish general properties of groups
  • Be familiar with the content of the major theorems of group theory - Lagrange's Theorem, Cayley's Theorem, three Isomorphism Theorems, Correspondence Theorem, Fundamental Theorem of Finite Abelian Groups, the Class Equation, and the Sylow Theorems - and able to use them in dealing with concrete groups
  • Apply all of the above competencies in problem solving