2025 (Current Year) Faculty Courses School of Science Undergraduate major in Mathematics
Algebra II
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Masatoshi Suzuki
- Class Format
- Lecture/Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Wed / 5-6 Thu
- Class
- -
- Course Code
- MTH.A302
- Number of credits
- 110
- Course offered
- 2025
- Offered quarter
- 2Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
The main topics of this course are basic topics surrounding Noetherian and Artinian rings, local rings, and homological algebra. In each class, students will complete exercises related to the course content. This course follows "Algebra I".
Homological algebra is a fundamental concept of algebra, which admits a very wide range of applications extending over both algebra and mathematics as a whole. The goal of this course is for students to become familiar with these concepts, firmly grasp their basic properties, and learn to use them correctly.
Course description and aims
By the end of this course, students will be able to:
1) Understand the notion of Noetherian and Artinian rings, and make use of fundamental operations for them correctly.
2) Understand the notion of local rings, and make use of fundamental operations for them correctly.
3) Understand homological algebra, and make use of fundamental operations for them correctly.
Keywords
Noetherian rings, Artinian rings, local rings, homological algebra
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 | Local rings | Details will be provided during each class session. |
| Class 2 | discussion session | Details will be provided during each class session. |
| Class 3 | Semi-simple rings | Details will be provided during each class session. |
| Class 4 | discussion session | Details will be provided during each class session. |
| Class 5 | Tensor product, right exactness of tensor product | Details will be provided during each class session. |
| Class 6 | discussion session | Details will be provided during each class session. |
| Class 7 | Flat modules, Projective modules, Injective modules | Details will be provided during each class session. |
| Class 8 | discussion session | Details will be provided during each class session. |
| Class 9 | Five lemma, Snake lemma | Details will be provided during each class session. |
| Class 10 | discussion session | Details will be provided during each class session. |
| Class 11 | Advanced topics | Details will be provided during each class session. |
| Class 12 | discussion session | Details will be provided during each class session. |
| Class 13 | Advanced topics | Details will be provided during each class session. |
| Class 14 | discussion session | Details will be provided during each class session. |
Study advice (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 afterward (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.
This will be announced during the lecture.
Evaluation methods and criteria
This will be announced during the lecture.
Related courses
- MTH.A201 ： Introduction to Algebra I
- MTH.A202 ： Introduction to Algebra II
- MTH.A203 ： Introduction to Algebra III
- MTH.A204 ： Introduction to Algebra IV
- MTH.A301 ： Algebra I
Prerequisites
Students are required to have successfully completed Linear Algebra I/Recitation, Linear Algebra II, Linear Algebra Recitation II, Advanced Linear Algebra I, II, Introduction to Algebra I, II, III, IV, and Algebra I; or, they must have equivalent knowledge.
Other
None in particular.