2024 Faculty Courses School of Science Undergraduate major in Mathematics
Algebra III
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Shohei Ma
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue / 5-6 Fri
- Class
- -
- Course Code
- MTH.A331
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 3Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
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.
Course description and aims
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
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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 |
Study advice (preparation and review)
preferred, but not duty
Textbook(s)
none in particular
Reference books, course materials, etc.
Serre "A course in Arithmetic"
Evaluation methods and criteria
By exams and reports. Details will be announced in the course.
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
Prerequisites
Passion for Mathematics