Fundamental properties and foundational results of group theory and Galois theory.
About this paper
|Paper title||Advanced Algebra|
|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 email@example.com
- Teaching staff
- Paper Structure
Main topics (18 lectures, 50 min each):
- External and internal direct products.
- Fundamental Theorem of Finite Abelian Groups.
- Simplicity of alternating group for n at least 5.
- (sub)normal and composition series.
- Isomorphism theorems.
- Group actions.
- Class equation.
- Enumeration under group action.
- Polya’s theorem.
- Sylow theorems and applications.
- 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.