Despite the broad catalog blurb, this graduate course is really a focused dive into modular forms as a bridge between complex analysis and number theory, using the geometry of the modular group's action on the upper half-plane to extract arithmetic information. You'll work through fundamental domains, multiplier systems, and the valence formula, then apply Fourier expansions and theta functions to classical problems like partition identities and representations as sums of squares, with most of your time spent on weekly homework and an independent component. It sits at the entry point of a much larger landscape (L-functions, Galois representations, Iwasawa theory) that the catalog hints at, giving you the analytic toolkit needed before tackling automorphic forms or arithmetic geometry seriously.
→ STARS müfredatı (resmi syllabus)
Bilkent kataloğunda bu ders için ön koşul yazılı değil.
İzlencede önerilen kitap: Modular Forms and Functions, Robert A. Rankin, 2008/1, Cambridge University Press.
3 Bilkent kredisi, 5 AKTS.
| Kalem | Ağırlık | Notun (100 üzerinden) |
|---|---|---|
| Final: Take-home | %50 | |
| 6 homework assignments one will be dropped. | %50 |
Ağırlıklar MATH 551 izlencesinden. Hocanın bu dönemki dağılımı farklı olabilir; bağlayıcı olan ders izlencesidir. Harf notu sınırlarını hoca belirliyor, o yüzden hedefi sen giriyorsun. İzlencede FZ şartı var, sayfanın sonundaki kutuda.
Bilkent'in resmî syllabus'ünden. Sağdaki etiket o çıktının hangi değerlendirmeyle ölçüldüğünü söylüyor.
İlk dosyayı sen atarsan: not, slayt, geçmiş sınav, çözüm, cheat-sheet, ne varsa. defter ekibi öğrenci paylaşımlarından bu dersin notlarını yazar. Drive linki / PDF / ZIP, hepsi olur.
Course Learning Outcomes: Course Learning Outcome Assessment Demonstrate an understanding of modular forms via their Fourier series Final: Take-home 6 homework assignments one will be dropped. Identify the modular group the multiplier systems and use valance formula or the structure of the modular group to prove identities among modular functions Final: Take-home 6 homework assignments one will be dropped. Given a modular identity interpret it as an identity among generating functions when possible and make deductions about the relevant number theoretic functions Final: Take-home 6 homework assignments one will be dropped. Demonstrate ability to undertake independent research and communicate mathematics either in writing or by presentation Final: Take-home