- elliptic functions, Weierstrass P-function,
- complex tori,
- plane geometry and geometric construction of a group structure,
- elliptic curves,
- modular forms, modular curves, and classification theory of elliptic curves.
Elliptic Functions and Elliptic Curves (M, 3.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-40-19-M-6||Elliptic Functions and Elliptic Curves||3.0 CP (90 h)|
|CP, Effort||3.0 CP = 90 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (General)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Elliptic Functions and Elliptic Curves
|P||28 h||62 h||-||-||PL1||3.0||irreg.|
- About [MAT-40-19-K-6]: Title: "Elliptic Functions and Elliptic Curves"; Presence-Time: 28 h; Self-Study: 62 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 84151 ("Elliptic Functions and Elliptic Curves")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
Upon successful completion of this module, the students have expanded their knowledge in interdisciplinary mathematics. They have studied elliptic curves, which like a few others, is a class of mathematical objects that is relevant to almost the entire spectrum of mathematics. This ranges from number theory (e.g. Theorem of Fermat) to computational data processing (e.g. encryption algorithms). Exemplarily, the students have learnt how to approach a general problem from a priori very different specialized disciplines (here: using analytic, topological, geometric and/or algebraic methods), and to compare the results across different disciplines. They understand the proofs presented in the lecture and are able to comprehend and explain them.
- W. Fischer, I. Lieb: Funktionentheorie,
- G. Fischer: Ebene algebraische Kurven,
- J .Silverman: The Arithmetic of Elliptic Curves.
Requirements for attendance of the module (informal)
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
- [MAT-12-22-K-3] Introduction to Algebra (2V+1U, 4.5 LP)
- [MAT-12-24-K-3] Introduction to Complex Analysis (2V+1U, 4.5 LP)
Requirements for attendance of the module (formal)None
References to Module / Module Number [MAT-40-19-M-6]
|Course of Study||Section||Choice/Obligation|
|[MAT-88.105-SG] M.Sc. Mathematics||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-88.706-SG] M.Sc. Mathematics International||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-GM-MPOOL-5]||General Mathematics (Introductory Modules M.Sc.)|