2023 Students Enrolled in or before 2015 School of Science Mathematics
Advanced courses in Algebra C
- Academic unit or major
- Mathematics
- Instructor(s)
- Tadashi Ochiai
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu (M-103(H114))
- Class
- -
- Course Code
- ZUA.A333
- Number of credits
- 100
- Course offered
- 2023
- Offered quarter
- 3Q
- Syllabus updated
- Jul 8, 2025
- Language
- English
Syllabus
Course overview and goals
The theory of modular forms plays an important role in various aspects of the number theory. This course together with "Advanced Course in Algebra D1" given in 4Q forms one set of contents. In the first half "C1", we deal with the basics of the theory and we will deal with more advanced aspects of the theory in the latter half "D1".
Course description and aims
Students are expected to get familiar with the basic of the theory of modular forms and explicit examples.
Keywords
modular form, modular curve, L-function, Galois representation, automorphic representation
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Modular forms over the field of complex numbers: part 1 | Details will be provided during each class session |
| Class 2 | Modular forms over the field of complex numbers: part 2 | Details will be provided during each class session |
| Class 3 | Eichler--Shimura isomorphism | Details will be provided during each class session |
| Class 4 | Elliptic curves and modular curves: part 1 | Details will be provided during each class session |
| Class 5 | Elliptic curves and modular curves: part 2 | Details will be provided during each class session |
| Class 6 | The L-function of a modular form | Details will be provided during each class session |
| Class 7 | Algebraic definition of modular forms | Details will be provided during each class session |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to explore references provided in lectures and other materials.
Textbook(s)
None required.
Reference books, course materials, etc.
Neal Koblitz, Introduction to Elliptic Curves and Modular forms, GTM 97, Springer-Verlag, New York, 1993.
Toshitsune Miyake, Modular Forms, english ed., Springer Monographs in Mathematics, Springer-Verlag, Berlin 2006
Evaluation methods and criteria
Course scores are evaluated by homework assignments. Details will be announced during the course.
Related courses
- ZUA.A334 ： Advanced courses in Algebra D
Prerequisites
Mostly assuming only the basic knowledge of undergraduate mathematics
Other
None in particular.