Linear Algebra and Its Applications

Academic unit or major

Undergraduate major in Mathematical and Computing Science

Instructor(s)

Hanna Sumita / Yu Yokoi

Class Format

Lecture/Exercise (Face-to-face)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

3-4 Tue (W8E-307(W833)) / 3-4 Fri (W8E-307(W833))

Class

-

Course Code

MCS.T203

Number of credits

110

Course offered

2025

Offered quarter

1Q

Syllabus updated

Apr 7, 2025

Language

Japanese

Syllabus

Course overview and goals

In the first part, a simple review of basic notions of linear algebra will be carried out focusing on the definitions. The comprehension of important notions such as linear independence/dependence of vectors and linear mapping will be confirmed through assignments involving their definitions. Also, some issues related to software implementations will be discussed through examples of rudimentary numerical methods to solve linear system of equations in order to understand more advanced methods of numerical analysis. In the second part, having in mind applications in engineering, development of basic notions of linear algebra to encourage better comprehension will be considered. For example, by reinterpreting the least square method using projections into vector subspaces. At the end, quadratic forms and eigenvalue problems of matrices, which are common notions always present in mathematics and computational mathematics, will be explained.

Course description and aims

Objective to attain: Master the notions of finite dimensional vector spaces, which is a basic concept in mathematics and numerical analysis, through assignments. Also comprehend the basic difficulties when applying these notions when solving linear system of equations and numerical methods involving matrices, in order to understand more advanced numerical methods.
Theme: Review the basic notions of linear algebra and to be able to not have difficulties in assignments involving them. Also, the connection to other lectures that need these notions will be considered and the attendees will be able to reinterpret these ideas in different contexts than linear algebra.

Keywords

N-dimensional Euclidean space, methods to solve linear system of equations, orthogonal projection, quadratic forms, eigenvalues and eigenvectors

Competencies

• Specialist skills
• Intercultural skills
• Communication skills
• Critical thinking skills
• Practical and/or problem-solving skills

Class flow

Definitions and theorems will be explained during the lectures according to the handouts, and assignments will be required almost at every lecture.

Course schedule/Objectives

Study advice (preparation and review)

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.

Textbook(s)

None.

Reference books, course materials, etc.

Lecture notes will be distributed when necessary. A very basic reference is "Introduction to Linear Algebra, 4th edition", G. Strang, Wellesley Cambridge Press, 2009. A more advanced level reference is "Numerical Linear Algebra", L. N. Trefethen, D. Bau, III, SIAM, 1997.

Evaluation methods and criteria

Can answer questions which involve notions of n-dimensional vector spaces and understand the basic notions of numerical methods in linear algebra. Mid-term and final exam will count 80% of the grade and the remaining 20% comes from the assignments.

Related courses

• LAS.M102 ： Linear Algebra I / Recitation
• LAS.M106 ： Linear Algebra II
• LAS.M108 ： Linear Algebra Recitation II

Prerequisites

Preferred that credits for "Linear Algebra I / Recitation'', "Linear Algebra II'', and "Linear Algebra Recitation II'' are already obtained.