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• MT5864 S1- Advanced Group Theory

  MT5864 - Advanced Group Theory

  Semester 1 2023-2024

  This document is valid on: Wednesday, 02,April 2025, 07:08 PM (BST)

  Key module information

  Semester 1

  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.

  Planned timetable

  10am, Monday (odd weeks), Wednesday, Friday

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

  Module coordinator

  Dr S Harper scott.harper@st-andrews.ac.uk

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

  Relationship to other modules

  Pre-requisites

  Before taking this module you must pass MT4003

  Anti-requisites

  You cannot take this module if you take MT5824

  Groups are important mathematical objects that arise in many contexts since they encode symmetry. The aim of this module is to build on the foundations established in MT4003 and to present more advanced techniques to handle and classify groups. It will focus on the use of group actions and upon the decomposition of groups into series via the quotient group construction.

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    Module description

    Groups are important mathematical objects that arise in many contexts since they encode symmetry. The aim of this module is to build on the foundations established in MT4003 and to present more advanced techniques to handle and classify groups. It will focus on the use of group actions and upon the decomposition of groups into series via the quotient group construction.

    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 core group theory topics including actions, subgroups, quotient groups, and extensions
    • Be familiar with, and able to work with, more complicated groups than just those appearing at the 4000 level
    • Be able to produce complete theoretical arguments (proofs) which establish general properties of groups
    • Be able to state and to use some advanced theorems in group theory
    • Apply the above competencies to discern properties of given groups and to demonstrate an understanding of advanced methods by being able to apply them to discern key features of given groups
    • Obtain and be able to demonstrate a capacity in problem solving in group theory