Last modified: 14 Nov 2025 12:46
Galois theory is based around a simple but ingenious idea: that we can study field extensions by instead studying the structure of certain groups associated to them. This idea can be employed to solve some problems which confounded mathematicians for centuries, including the impossibility of trisecting an angle with ruler and compass alone, and the insolubility of the general quintic equation.
| Study Type | Undergraduate | Level | 4 |
|---|---|---|---|
| Term | First Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
| Co-ordinators |
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Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback | ||||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Understand | Understand the notions of normality and separability of a field extension. |
| Factual | Remember | Remember the Fundamental Theorem of Galois Theory. |
| Procedural | Apply | Be able to calculate Galois groups of certain field extensions. |
| Procedural | Apply | Be able to calculate Galois groups of certain polynomials. |
| Procedural | Apply | Apply the Fundamental Theorem of Galois Theory to describe field extensions. |
| Assessment Type | Summative | Weighting | 70 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Students will be invited to contact Course Coordinators for feedback on the final examination. |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Analyse | Be able to determine whether a given complex number is constructible. |
| Conceptual | Understand | Understand the notions of normality and separability of a field extension. |
| Conceptual | Understand | Understand the Galois correspondence and theoretical aspects of the interplay between field theory and group theory applied to the structure theory of fields and solvability of polynomial equations. |
| Factual | Remember | Remember the Fundamental Theorem of Galois Theory. |
| Procedural | Apply | Be able to decide whether a given polynomial equation is solvable by radicals. |
| Procedural | Apply | Apply the Fundamental Theorem of Galois Theory to describe field extensions. |
| Procedural | Apply | Be able to calculate Galois groups of certain field extensions. |
| Procedural | Apply | Be able to calculate Galois groups of certain polynomials. |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback | ||||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Analyse | Be able to determine whether a given complex number is constructible. |
There are no assessments for this course.
| Assessment Type | Summative | Weighting | 100 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Best of (resit exam mark) or (resit exam mark with carried forward CA marks) |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
|
|
||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Procedural | Apply | Be able to calculate Galois groups of certain field extensions. |
| Conceptual | Analyse | Be able to determine whether a given complex number is constructible. |
| Procedural | Apply | Be able to calculate Galois groups of certain polynomials. |
| Procedural | Apply | Be able to decide whether a given polynomial equation is solvable by radicals. |
| Conceptual | Understand | Understand the Galois correspondence and theoretical aspects of the interplay between field theory and group theory applied to the structure theory of fields and solvability of polynomial equations. |
| Procedural | Apply | Apply the Fundamental Theorem of Galois Theory to describe field extensions. |
| Factual | Remember | Remember the Fundamental Theorem of Galois Theory. |
| Conceptual | Understand | Understand the notions of normality and separability of a field extension. |
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