Building on elementary facts about planar and spatial vectors learned at the high-school level, this course (with recitation) focuses on higher dimensional vectors and matrices, basics and applications of determinants, and systems of linear equations.
The aim of this course is to cover the basics of linear algebra, which will be fundamental for
science and engineering.
Students are expected to understand the basics of linear algebra (such as fundamental facts about matrices and determinants) which are necessary for studying science and engineering.
Vector, matrix, determinant, system of linear equations
Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Theoretical materials are explained in lectures. A recitation class, with concrete examples and practice problems, is conducted every week.
Course schedule | Required learning | |
---|---|---|
Class 1 | Vectors, matrices, components | Understand basics of vectors and matrices. |
Class 2 | Recitation class is conducted parallel to the lectures. | Help better understand the lectures. |
Class 3 | Matrix operations | Understand various operations on matrices. |
Class 4 | Regular matrix and inverse matrix | Understand the notions of regular matrix and inverse matrix. |
Class 5 | Recitation class is conducted parallel to the lectures. | Help better understand the lectures. |
Class 6 | Systems of linear equations and the elimination method | Understand how to solve a system of linear equations. |
Class 7 | Elementary transformations and elementary matrices, rank of a matrix | Understand elementary operations on matrices and the rank of a matrix. |
Class 8 | Recitation class is conducted parallel to the lectures. | Help better understand the lectures. |
Class 9 | General method for solving a system of linear equations | Understand a more general method for solving a system of linear equations. |
Class 10 | Method of computing inverse matrices | Understand how to compute inverse matrices. |
Class 11 | Recitation class is conducted parallel to the lectures. | Help better understand the lectures. |
Class 12 | Definition of determinant up to order 3, geometric meaning of the determinant. | Understand the definition of determinant and its meaning. |
Class 13 | Definition of determinant (arbitrary order), multi-linearity, alternating property | Understand higher-order determinants. |
Class 14 | Recitation class is conducted parallel to the lectures. | Help better understand the lectures. |
Class 15 | Method of computing determinants, special determinants | Learn how to compute determinants. |
Class 16 | Expansion of determinants | Understand determinant expansions. |
Class 17 | Recitation class is conducted parallel to the lectures. | Help better understand the lectures. |
Class 18 | Determinant of transpose, multiplicativity | Understand the determinant of a transposed matrix and of a product of matrices. |
Class 19 | Cramer's formula, formula for the inverse matrix | Understand various useful formulas. |
Class 20 | Recitation class is conducted parallel to the lectures. | Help better understand the lectures. |
Class 21 | Advanced topics | Understand advanced topics in Linear Algebra. |
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.
T. Miyake, Linear Algebra, Baifukan
T. Kajiwara, Lecture on Linear Algebra, Nippon Hyoron Sha
A. Matsuo, First Steps in Mathematics, The University of Tokyo Press
Based on overall evaluation on the results of quizzes, reports, mid-term and final examinations. Details will be announced in class.
None in particular.
Resorces will be avairable via T2SCHOLA.