### 2022　Algebra II

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Academic unit or major
Undergraduate major in Mathematics
Instructor(s)
Kato Fumiharu  Wakabayashi Yasuhiro
Class Format
Lecture / Exercise    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Wed3-4(H103)  Thr5-6(H103)
Group
-
Course number
MTH.A302
Credits
2
2022
Offered quarter
2Q
Syllabus updated
2022/3/16
Lecture notes updated
-
Language used
Japanese
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### Course description and aims

The main topics of this course are basic topics surrounding Noetherian and Artinian rings, local rings, and homological algebras. In each class, students will complete exercises related to the course content. This course follows ""Algebra 1"".
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.

### Student learning outcomes

By the end of this course, students will be able to:
1) Understand the notion of Noethrian 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 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 session.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Noetherian rings and Artinian rings (1) Details will be provided during each class session.
Class 2 discussion session Details will be provided during each class session.
Class 3 Noetherian rings and Artinian rings (2) Details will be provided during each class session.
Class 4 discussion session Details will be provided during each class session.
Class 5 Local rings Details will be provided during each class session.
Class 6 discussion session Details will be provided during each class session.
Class 7 Homological algebra (1) Details will be provided during each class session.
Class 8 discussion session Details will be provided during each class session.
Class 9 Homological algebra (2) Details will be provided during each class session.
Class 10 discussion session Details will be provided during each class session.
Class 11 Homological algebra (3) 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.

### 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.

TBA

TBA

TBA

### 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 (i.e., required knowledge, skills, courses, etc.)

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.