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- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Mizumoto Shin-Ichiro
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(H135)
- Group
- -
- Course number
- MTH.A212
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 2Q
- Syllabus updated
- 2017/3/17
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
Students in this course will study the concept and examples of vector space in linear algebra. Exercise problems will be presented in class to cement understanding. This course follows "Advanced Linear Algebra I. "
Prior experience with linear algebra using specific matrices is assumed, and this course discusses in detail from the basics of vector space to linear mapping to eigenvalues and the like. These activities are important, also serving as practical exercises for students to acquire basic methods in learning other fields of advanced mathematics.
Student learning outcomes
Important notions are as follows:
vector space, linear span, linear map, isomorphism, commutative diagram, representation matrix, eigenvalue, eigenspace.
Keywords
linear map, dual space, quotient space
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 sessions
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Isomorphism and applications | Details will be provided during each class session |
| Class 2 | representation matrix | Details will be provided during each class session |
| Class 3 | change of basis and commutative diagram | Details will be provided during each class session |
| Class 4 | eigenvalue and eigenspace | Details will be provided during each class session |
| Class 5 | invariant subspace | Details will be provided during each class session |
| Class 6 | application of diagonalization | Details will be provided during each class session |
| Class 7 | quotient space, dual space | Details will be provided during each class session |
| Class 8 | evaluation of progress | Details will be provided during each class session |
Textbook(s)
None required
Reference books, course materials, etc.
Saito, Masahiko Introduction to Linear Algebra, University of Tokyo Press
Assessment criteria and methods
To be evaluated based on exercises in discussion sessions and the final exam as a whole. Details will be announced during the course.
Related courses
- MTH.A211 ： Advanced Linear Algebra I
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are expected to have passed Advanced Linear Algebra I
