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- Academic unit or major
- Mathematics
- Instructor(s)
- Kato Fumiharu Wakabayashi Yasuhiro
- Class Format
- Exercise (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Thr5-6(H103)
- Group
- -
- Course number
- ZUA.A302
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 1-2Q
- Syllabus updated
- 2022/3/16
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
This course is an exercise session for the lecture course "Algebra I (ZUA.A301)". The materials for exercise are chosen from that course.
Student learning outcomes
By the end of this course, students will be able to:
1) Understand the notions of (commutative) rings and modules over rings.
2) Understand tensor products and make use of them correctly.
3) Understand localization and make use of them correctly.
4) Understand the notion of Noethrian and Artinian rings, and make use of fundamental operations for them correctly.
5) Understand the notion of local rings, and make use of fundamental operations for them correctly.
6) Understand homological algebra, and make use of fundamental operations for them correctly.
Keywords
rings, ideal, residue rings, modules, tensor products, localization, Noetherian rings, Artinian rings, local rings, homological algebra
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Students are given exercise problems related to what is taught in the course "Algebra I".
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Discussion session on the following materials: Commutative rings and ideals | Details will be provided during each class session. |
| Class 2 | Discussion session on the following materials: Modules over a ring (1) | Details will be provided during each class session. |
| Class 3 | Discussion session on the following materials: Modules over a ring (2) | Details will be provided during each class session. |
| Class 4 | Discussion session on the following materials: Modules over a ring (3) | Details will be provided during each class session. |
| Class 5 | Discussion session on the following materials: Tensor products of modules (1) | Details will be provided during each class session. |
| Class 6 | Discussion session on the following materials: Tensor products of modules (2) | Details will be provided during each class session. |
| Class 7 | Discussion session on the following materials: Localization | Details will be provided during each class session. |
| Class 8 | Discussion session on the following materials: Noetherian rings and Artinian rings (1) | Details will be provided during each class session. |
| Class 9 | Discussion session on the following materials: Noetherian rings and Artinian rings (2) | Details will be provided during each class session. |
| Class 10 | Discussion session on the following materials: Local rings | Details will be provided during each class session. |
| Class 11 | Discussion session on the following materials: Homological algebra (1) | Details will be provided during each class session. |
| Class 12 | Discussion session on the following materials: Homological algebra (2) | Details will be provided during each class session. |
| Class 13 | Discussion session on the following materials: Homological algebra (3) | Details will be provided during each class session. |
| Class 14 | Discussion session on the following materials: Advanced topics | Details will be provided during each class session. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
TBA
Reference books, course materials, etc.
TBA
Assessment criteria and methods
TBA
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
- MTH.A201 ： Introduction to Algebra I
- MTH.A202 ： Introduction to Algebra II
- ZUA.A301 ： Algebra I
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students must have successfully completed [Linear Algebra I/Recitation], Linear Algebra II, Linear Algebra Recitation II, Advanced Linear Algebra I, II and Introduction to Algebra I, II, III, IV; or, they must have equivalent knowledge.
Students are strongly recommended to take ZUA.A301: Algebra I (if not passed yet) at the same time.
Other
None in particular.
