This course covers the concept and examples of vector space in linear algebra. Exercise problems will be presented within the lectures to cement understanding. This course is followed by "Advanced Linear Algebra II".
Prior experience with linear algebra using specific matrices is assumed, and this course discusses in detail the basics of vector space and linear mapping. These activities are important, also serving as practical exercises for students to acquire basic methods in learning other fields of advanced mathematics.
The important notions are as follows:
vector space, linear span, linear map, isomorphism.
linear space, linear map, linear span, isomorphism
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Standard lecture course accompanied by discussion sessions
|Course schedule||Required learning|
|Class 1||vector space||Details will be provided during class session|
|Class 2||linearly independency||Details will be provided during class session|
|Class 3||subspace||Details will be provided during class session|
|Class 4||linear span||Details will be provided during class session|
|Class 5||basis||Details will be provided during class session|
|Class 6||properties of dimension||Details will be provided during class session|
|Class 7||sum and direct sum of linear spaces, linear map||Details will be provided during class session|
|Class 8||evaluation of progress||Details will be provided during class session|
Saito, Masahiko: Introduction to Linear Algebra, University of Tokyo Press
To be evaluated based on exercises in discussion sessions and the final exam as a whole. Details will be announced during the course.
Students are expected to have passed Linear Algebra I / Recitation and Linear Algebra II.