This is the first half of the introductory lectures on linear algebra. The second half will be heavily based on the first half.
Will be announced in the course page on UTOL.
The schedule may change.
Introductory Course in Linear Algebra.
Phenomena in natural and social sciences are usually complicated, and seldom described by linear equations. However, Linear Algebra is still powerful and effective in describing essential parts of the phenomena by linear approximation. Thus Linear Algebra has vast applications.
Linear Algebra will further provide basics for considering linear spaces that appear in quantum mechanics or Fourier analysis. The ideas in Linear Algebra are broadly utilized in sciences and engineering, including agriculture, medicine, and economy, as well as in mathematics and physics.
Although Linear Algebra is simple and clear in theory, one needs to be familiar with abstract concepts in mathematics to properly deal with it in practice. It is important for students to keep on deepening their understanding by working with exercise and related problems.
The topics listed below will be covered in the course. The items 1-5 and their applications will be treated in Mathematics II ① in 2024 A semester, and 6-10 in Mathematics II ② in 2025 S semester.
The latter half will be heavily based on the the former, especially on the concept of bases of linear spaces.