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    Fundamental properties and foundational results of group theory and Galois theory.

    Fundamental properties and foundational results of group theory and Galois theory.

    About this paper

    Paper title Advanced Algebra
    Subject Mathematics
    EFTS 0.0833
    Points 10 points
    Teaching period Semester 1 (On campus)
    Domestic Tuition Fees ( NZD ) $620.00
    International Tuition Fees Tuition Fees for international students are elsewhere on this website.
    MATH 401-412
    Limited to
    BA(Hons), BSc(Hons), PGDipArts, PGDipSci, MA (Thesis), MSc, MAppSc, PGDipAppSc, PGCertAppSc

    Mathematics 400-level programme coordinator: Dr Fabien Montiel

    Teaching staff

    Dr Dominic Searles

    Paper Structure

    Main topics (18 lectures, 50 min each):

    Lectures 1-3

    • External and internal direct products.
    • P-groups.
    • Fundamental Theorem of Finite Abelian Groups.

    Lectures 4-5

    • Simplicity of alternating group for n at least 5.
    • (sub)normal and composition series.
    • Solvability.
    • Isomorphism theorems.

    Lectures 6-11

    • Group actions.
    • Orbit-stabiliser.
    • Class equation.
    • Enumeration under group action.
    • Polya’s theorem.

    Lectures 12-14

    • Sylow theorems and applications.

    Lectures 13-18

    • Field extensions.
    • Minimal polynomial.
    • Finite and simple extensions.
    • Splitting fields.
    • Structure of finite fields.
    • Separable/normal/Galois extensions.
    • Fundamental Theorem of Galois Theory.
    • Insolvability of general quintic equations.
    Teaching Arrangements

    18 lectures (50 minutes each).

    Tutorials: Weekly drop-in sessions for help with assignments.

    Assessment (45% of total mark): 3 written assignments.

    Final exam (55% of total mark)

    Graduate Attributes Emphasised

    Critical Thinking, Interdisciplinary Perspective, Lifelong Learning.
    View more information about Otago's graduate attributes.

    Learning Outcomes

    On completion of the study of this paper, students are expected to:

    • Understand fundamental approaches in abstract algebra.
    • Know important properties of groups and fields.
    • Understand how to rigorously prove theorems in abstract algebra.
    • Understand the power of working with general algebraic concepts and applications of these including counting with to respect to symmetry.


    Semester 1

    Teaching method
    This paper is taught On Campus
    Learning management system
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