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- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Ma Shohei
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- -
- Group
- -
- Course number
- MTH.A331
- Credits
- 2
- Academic year
- 2024
- Offered quarter
- 3Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
The main theme of this course is Field Theory, especially extension of fields entered around the Galois theory. This is basic when learning modern Mathematics.
Student learning outcomes
Understand various properties about filed extensions; understand the Galois correspondence; get familiar with classical examples of fields
Keywords
Fields, extension of fields, Galois groups
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Standard lecture course accompanied by discussion sessions
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Fields | Details will be provided during each class session |
| Class 2 | Extensions of fields | Details will be provided during each class session |
| Class 3 | Minimal decomposition fields, normal extensions | Details will be provided during each class session |
| Class 4 | Separable and inseparable extensions | Details will be provided during each class session |
| Class 5 | Galois extensions and Galois correspondence | Details will be provided during each class session |
| Class 6 | Calculations of various examples of Galois groups | Details will be provided during each class session |
| Class 7 | Geometry of Galois theory | Details will be provided during each class session |
| Class 8 | Finite fields | Details will be provided during each class session |
| Class 9 | Quadratic reciprocity | Details will be provided during each class session |
| Class 10 | Quadratic fields | Details will be provided during each class session |
| Class 11 | Number fields | Details will be provided during each class session |
| Class 12 | Cyclotomic fields | Details will be provided during each class session |
| Class 13 | Jugendtraum | Details will be provided during each class session |
| Class 14 | p-adic fields | Details will be provided during each class session |
Out-of-Class Study Time (Preparation and Review)
preferred, but not duty
Textbook(s)
none in particular
Reference books, course materials, etc.
Serre "A course in Arithmetic"
Assessment criteria and methods
By exams and reports. Details will be announced in the course.
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Passion for Mathematics
