Eliptic Curves(MATH 517)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MATH 517 | Eliptic Curves | 2 | 3 | 0 | 0 | 3 | 7 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | English |
| Course Type | Elective |
| Course Level | Masters Degree |
| Course Instructor(s) | Ayberk ZEYTİN azeytin@gsu.edu.tr (Email) |
| Assistant | |
| Objective | Teaching the fundamental concepts of elliptic curves |
| Content |
Weeks Subjects 1 Plane curves, Bezout’s theorem, Rational points on curv es 2 Group law on cubic curves 3 Regular functions and the Riemann Roch theorem 4 Elliptic curves, torsion points and the elliptic curves over Q_p 5 Complex elliptic curves, Lattices and the Riemann surfaces 6 Group cohomology; Selmer, Tate-Schavarevich groups 7 Rank computation of E(Q) |
| Course Learning Outcomes | ÖÇ 1: Understanding the relations among the elliptic curves, Riemann surfaces and the modular forms |
| Teaching and Learning Methods | |
| References | J.S. Milne, Elliptic Curves, BookSurgeBookSurge, 2006 |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Plane curves, Bezout’s theorem, Rational points on curv es |
| 2 | Group law on cubic curves |
| 3 | Regular functions and the Riemann Roch theorem |
| 4 | Elliptic curves, torsion points and the elliptic curves over Q_p |
| 5 | Complex elliptic curves, Lattices and the Riemann surfaces |
| 6 | Group cohomology; Selmer, Tate-Schavarevich groups |
| 7 | Rank computation of E(Q) |
| 8 | Midterm exam |
| 9 | Elliptic curves over finte fields |
| 10 | Sphere packings |
| 11 | Modular forms |
| 12 | Modular forms of elliptic curves |
| 13 | Modular forms of elliptic curves |
| 14 | Fermat’s last theorem and the Wiles’s proof |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 2 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 3 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 1 | 20 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 40 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 2 | 60 |
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| 1 | 2 | 3 | 4 | 5 | ||
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| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Working Hours out of Class | 14 | 6 | 84 |
| Assignments | 1 | 20 | 20 |
| Midterm Examinations (including preparation) | 1 | 25 | 25 |
| Total Workload | 171 | ||
| Total Workload / 25 | 6.84 | ||
| Credits ECTS | 7 | ||