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Curricular information is subject to change
The student is expected to develop an understanding of the following concepts:
(i) Gauss' reciprocity law and classification of conics over finite fields
(ii) Point counting over finite fields (Chevalley-Warning Theorem).
(iii) p-adic numbers, basic p-adic analysis, multiplicative structure of p-adic fields, Hensel's Lemma, conics over p-adic fields and Hilbert symbol.
(iv) Hasse-Minkowski theorem and classification of conics over number fields.
The module will cover one of the following 2 threads:
(v) An introduction to elliptic curves (group structure and Mordell-Weil theorem).
(vi) Ideal class group and the class number formula.
Gauss' reciprocity law and classification of conics over finite fields.
Point counting over finite fields.
p-adic numbers, basic p-adic analysis, multiplicative structure of p-adic fields, Hensel's Lemma.
Conics over p-adic fields and Hilbert symbol.
Hasse-Minkowski theorem and classification of conics over number fields.
An introduction to elliptic curves (group structure and Mordell-Weil theorem).
Ideal class group and the class number formula.
| Student Effort Type | Hours |
|---|---|
| Lectures | 30 |
| Tutorial | 6 |
| Specified Learning Activities | 24 |
| Autonomous Student Learning | 48 |
| Total | 108 |
MATH30400 & MATH30030, or the consent of the module coordinator.
Also advisable: MATH30090 & MATH30040.
| Description | Timing | Component Scale | % of Final Grade | ||
|---|---|---|---|---|---|
| Exam (Take-Home): Examination: Take-home final exam | Week 14 | Standard conversion grade scale 40% | No | 55 |
No |
| Exam (Online): Examination: Midterm exam | Week 6 | Standard conversion grade scale 40% | No | 20 |
No |
| Exam (Online): Examination: Midterm exam | Week 10 | Standard conversion grade scale 40% | No | 15 |
No |
| Assignment(Including Essay): Weekly assignments | Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 | Standard conversion grade scale 40% | No | 10 |
No |
| Resit In | Terminal Exam |
|---|---|
| Autumn | Yes - 2 Hour |
• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Self-assessment activities
Self-assessment activities are tentative and will be based on the following model: Students will be asked to grade their responses to midterm exams, based on a detailed solution sheet. They will prepare a detailed report on their weaknesses in key aspects of the module. Based on the accuracy of this report, their homework grades will be positively updated. The other two feedback strategies to employ (Feedback individually to students, post-assessment and Group/class feedback, post-assessment) are self-explanatory.