2025 (Current Year) Faculty Courses School of Science Undergraduate major in Mathematics
Advanced Linear Algebra II
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Yuri Yatagawa
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Wed
- Class
- -
- Course Code
- MTH.A212
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 2Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course covers the concepts and examples of vector spaces and linear maps in linear algebra. Exercise problems will be presented in class to cement understanding. This course follows "Advanced Linear Algebra I. "
Knowledge in concrete linear algebra using matrices being assumed, this course deals with abstract theory on such subjects as dual space, bilinear form, quotient space, tensor product, etc. This is important not only in its own right but also as practical exercises for students to acquire basic skills in learning other fields of advanced mathematics.
Course description and aims
To understand important notions such as dual space, bilinear form, quotient space, tensor product, etc., and to become able to make use of them.
Keywords
dual space, bilinear form, quotient space, tensor product
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 | Dual space (1) | Details will be provided during each class session |
| Class 2 | Dual space (2) | Details will be provided during each class session |
| Class 3 | Bilinear form | Details will be provided during each class session |
| Class 4 | Symmetric bilinear form, Hermite form | Details will be provided during each class session |
| Class 5 | Quotient space | Details will be provided during each class session |
| Class 6 | Bilinear map and tensor product | Details will be provided during each class session |
| Class 7 | Tensor product of linear maps | 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 afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Takeshi Saito, ”The World of Linear Algebra”, University of Tokyo Press
Reference books, course materials, etc.
None required
Evaluation methods and criteria
To be evaluated based on the final exams and reports. Details will be announced in the course.
Related courses
- MTH.A211 ： Advanced Linear Algebra I
Prerequisites
Students are expected to have passed Advanced Linear Algebra I