授業科目名 年度 学期 開講曜日・時限 学部・研究科 全担当教員 単位数
35072:Mathematical Foundations of Computer Science(G1) 2019 秋セメスター 火4 情報理工学部 SVININ MIKHAIL 2

キャンパス

BKC

授業施設

フォレストハウス１０２号教室

授業で利用する言語

英語

授業の概要と方法

The knowledge of linear algebra is fundamental to every field of mathematics. The techniques of linear algebra are widely used in computer science, engineering, economics, natural and social sciences. In this course, students will learn the main concepts and methods in linear algebra. Typical applications of linear algebra will also be covered. Emphasis will be given to topics that are useful in other disciplines. The topics will include solving systems of linear equations, matrices and matrix operations, vector spaces, orthogonal projections and the least-square approximation of experimental data, determinants, eigenvalues and eigenvectors of matrices. The content of this course will be studied in lectures and supported by in-class and homework exercises.

受講生の到達目標

In this class the students can acquire the following knowledge and skills.
- Operate with vectors and matrices.
- Compose and solve systems of linear equations directly, by elimination and by using the matrix inverse.
- Define the rank of matrices and compute the inverse of a square matrix.
- Understand the concept of linear independence of vectors and apply it specific problems.
- Understand the concept of vector spaces and subspaces.
- Define the dimension and construct a basis of a linear subspace.
- Understand the concept (and geometric interpretation) of determinants, and apply it solving systems of linear equations.
- Learn the definition and practical skill of determining eigenvalues and eigenvectors of matrices.
- Extend the knowledge of vector and matrix quantities to those with complex numbers
- Learn practical application of matrices to different problems in science and engineering

事前に履修しておくことが望まれる科目

Pre-requisites: basic knowledge of mathematics (pre-calculus level)

授業スケジュール

授業回数/
担当教員（複数担当の場合） 		テーマ
キーワード・文献・補足事項等
1

Introduction to vectors

Cartesian coordinate systems, vectors in R^n, dot product. Equations of line and plane
2

Solving linear equation by forward elimination and back substitution.

Geometry of linear equations, basic idea of elimination.

3

Matrices and matrix operations

Matrix addition and multiplication. Laws of matrix operation. Block matrices. Elimination in the matrix language

4

Inverse and transpose matrix

Definitions and examples. Solving square linear systems by Gauss-Jordan elimination

5

Vector spaces and sub-spaces

Definitions and examples. The column space of a matrix
6

The rank of a matrix

The null space of a matrix, and the row reduced form. Solving homogeneous linear equations.

7

Complete solution to a linear system

General algorithm and geometric interpretation.
8

Linear dependence and independence of vectors

Basis and dimension of a vector space.

9

The four fundamental sub-spaces and orthogonality, .

Orthogonality, projections and least squares approximations, orthogonal matrices
10

Definition and basic properties of determinants.

Definition and examples
11

Computation of determinants and applications

Adjoint matrix, Cramer’s rule, inverses, and volumes
12

Introduction to eigenvalues and eigenvectors

Definition, examples, and basic properties
13

Diagonalizing a matrix

Algorithm and geometric interpretation
14

Applications to difference and differential equations

Solving linear systems of difference and differential equations. Non-diagonalizable matrices.
15

Symmetric and positive definite matrices. Applications to engineering problems.

Basic properties, ellipsoids in R^n, optimization problems.

授業実施形態

授業外学習の指示

Students are strongly recommended to spend at least 2 hours every week to prepare for the class. Each class’ materials (the relevant sections of the textbook, self-preparation assignments, and optional slides in the PDF format provided by the instructor) should be reviewed both before and after the class. The meaning of all English technical words should be comprehended prior to class.

成績評価方法

種別 割合(%) 評価基準等
定期試験（筆記） 70

Demonstration of the ability to state and solve differential equations.

レポート試験
（統一締切日を締切とするレポート）		 0

上記以外の試験・レポート、平常点評価
（日常的な授業における取組状況の評価）		 30

Includes evaluations of lecture quizzes, self-preparation assignments, attendance and activity in class. See also “Other Comments” below.

成績評価方法(備考)

受講および研究に関するアドバイス

We will try to follow the main textbook as closely as possible. It is important to review the textbook and the lecture notes before each lecture. As a rule, solutions to the assignment problems will be distributed in electronic form right after each class. It is highly recommended to review these solutions in order to fix possible mistakes.

教科書

書名 著者 出版社 ISBNコード 備考
Introduction to Linear Algebra (4th or 5th Edition) Gilbert Strang Cambridge Press ISBN: 978-09802327-7-6

教科書(使用頻度、その他補足)

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参考書

書名 著者 出版社 ISBNコード 備考
Schaum's Outline of Linear Algebra, (5th Edition) Seymour Lipschutz, Marc Lipson McGraw-Hill Education ISBN-10: 0071794565

参考書(使用頻度、その他補足)

参考になるwwwページ

Essence of linear algebra (Video Notes, by Grant Sanderson)
https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

Introduction to linear algebra (Viode lectures, by Gilbert Strang)
https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

授業内外における学生・教員間のコミュニケーションの方法

学生との直接対話,その他(教員より別途指示）

備考

Consultations.
Office: Creation Core, 7 fl., room no. 704.
Office Hours: By appointment
E-mail: svinin@fc.ritsumei.ac.jp
Note: Contact me if you are having any difficulties with the material. The sooner the better.

Attendance.
Students are responsible for all material covered in this class. Students must attend at least 66% of the lectures.
Professional ethics.
The behavioral and ethical standards of Ritsumeikan University will be observed in all aspects of this course. Specifically, academic dishonesty (e.g. copying assignments or the like) will result in a grade F for the corresponding assignment, and in many cases - in a failing grade (F) for the course.