Course Name Year Term Period Faculty / Graduate School All Instructors Credits
35072:Mathematical Foundations of Computer Science (G1) 2019 Fall Tue4 College of Information Science and Engineering SVININ MIKHAIL 2

Campus

BKC

Class Venue

Forest102

Language

English

Course Outline and Method

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.

Student Attainment Objectives

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

Recommended Preparatory Course

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

Course Schedule

Lecture/Instructor（When there are multiple instructors) Theme
Keyword, References and Supplementary Information
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.

Class Format

Recommendations for Private Study

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.

Grade Evaluation Method

Kind Percentage Grading Criteria etc.
Final Examination (Written) 70

Demonstration of the ability to state and solve differential equations.

Report Examination
(A report to be submitted by the unified deadline)		 0

Exams and/or Reports other than those stated above, and Continuous Assessment　
(Evaluation of Everyday Performance in Class)		 30

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

Grade Evaluation Method （Note）

Advice to Students on Study and Research Methods

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.

Textbooks

Title Author Publisher ISBN Code Comment
Introduction to Linear Algebra (4th or 5th Edition) Gilbert Strang Cambridge Press ISBN: 978-09802327-7-6

Textbooks （Frequency of Use, Note）

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Reference Books

Title Author Publisher ISBN Code Comment
Schaum's Outline of Linear Algebra, (5th Edition) Seymour Lipschutz, Marc Lipson McGraw-Hill Education ISBN-10: 0071794565

Reference Books （Frequency of Use, Note）

Web Pages for Reference

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/

How to Communicate with the Instructor In and Out of Class(Including Instructor Contact Information)

Talk with Students,Other (Separate instructions will be provided)

Other Comments

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.