Mathematics II ① (PEAK) 2021 – 2022

Classes are organized online via ITC-LMS.

The schedule may change.

1. 2021/10/06 (Wed)  Guidance. Lecture 0: Introduction to linear algebra.
2. 2021/10/13 (Wed)  Lecture 1: Idea of sets.
3. 2021/10/20 (Wed)  Lecture 2: Concept of maps
4. 2021/10/27 (Wed)  Lecture 3: Linear transformations of coordinate plane.
5. 2021/11/03 (Wed)  Lecture 4: Geometry of coordinate spaces.
6. 2021/11/10 (Wed)  Lecture 5: Matrices and linear maps.
7. 2021/11/17 (Wed)  Lecture 6: Linear subspaces of coordinate spaces.
   2021/11/24 (Wed)  (No class)
8. 2021/12/01 (Wed)  Lecture 7: Row reduction of matrices.
9. 2021/12/08 (Wed)  Lecture 8: Inverse matrices.
10. 2021/12/15 (Wed)  Lecture 9: Bases and the ranks of matrices.
    2021/12/22 (Wed)  (cancelled)
11. 2022/01/05 (Wed)  Lecture 9 continued. Guidance for Trial Exam.
    2022/01/12 (Wed)  Trial Exam. Guidance for Final Exam. Course Evaluation Questionaire.
12. 2022/01/19 (Wed)  Lecture 10: Linear spaces and their bases.
    2022/01/26 (Wed)  Final Exam (online)  13:00～14:45
    2022/04/26 (Tue)   Make-up Exam (Online) 19:00～20:30.

• Course overview

  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.

• Course contents

  The topics listed below will be covered in the course. The items 1-4 and their applications will be treated in Mathematics II ① in A semester 2021, and 5-9 in Mathematics II ② in S semester 2022. The latter will be heavily based on the the former.

  1. Geometry of coordinate spaces
  2. Matrices and linear maps
  3. Systems of linear equations
  4. Bases of linear spaces
  5. Inner products and orthogonality
  6. Signature of quadratic forms
  7. Determinants of square matrices
  8. Eigenvalues and eigenvectors
  9. Jordan form of square matrices

• Reference Books
  In case you wish to look at related books for reference, I pick up the following although they are not in perfect match with this course:
  • S. Lipschutz and M. Lipson, Schaum's Outline of Linear algebra, McGraw-Hill.
  • G. Strang, Linear Algebra and Its Applications, 5th edition, Wellesley-Cambridge Press.