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 ) | $696.55 |
| International Tuition Fees | Tuition Fees for international students are elsewhere on this website. |
- Restriction
- MATH 401-412
- Limited to
- BA(Hons), BSc(Hons), PGDipArts, PGDipSci, MA (Thesis), MSc, MAppSc, PGDipAppSc, PGCertAppSc
- Contact
Mathematics 400-level programme co-ordinator: Dr Fabien Montiel
- Teaching staff
- 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.
- Textbooks
To be confirmed.
- 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.
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 | Tuition Fees for 2027 have not yet been set |
| International Tuition Fees | Tuition Fees for international students are elsewhere on this website. |
- Restriction
- MATH 401-412
- Limited to
- BA(Hons), BSc(Hons), PGDipArts, PGDipSci, MA (Thesis), MSc, MAppSc, PGDipAppSc, PGCertAppSc
- Contact
Mathematics 400-level programme co-ordinator: Dr Fabien Montiel
- Teaching staff
- Paper Structure
Main topics:
- Fundamental Theorem of Finite Abelian Groups
- (Sub)normal and composition series, solvability, isomorphism theorems, simplicity of alternating group for n at least 5
- Group actions, orbit-stabiliser, class equation, enumeration under group action
- Sylow theorems and applications
- Field extensions, splitting 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.
- Textbooks
Recommended texts:
- Dummit, D. S., & Foote, R. M. (2003). Abstract Algebra (3rd ed.). Wiley.
- Gallian, J. A., (2001). Contemporary Abstract Algebra (8th e.). Houghton Mifflin.
- Graduate Attributes Emphasised
- Interdisciplinary perspective, Lifelong learning, Communication.
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.