Comprehensive Mathematics

Course Information

College	Toyama College	Year	2022
Course Title	Comprehensive Mathematics
Course Code	0043	Course Category	General / Elective
Class Format	Lecture	Credits	School Credit: 1
Department	Department of Applied Chemistry and Chemical Engineering	Student Grade	3rd
Term	Second Semester	Classes per Week	2
Textbook and/or Teaching Materials	"大学新入生のためのリメディアル数学 第2版 (Daigaku Shin-nyusei no Tameno Remedial Sugaku, 2nd Ed.)" (森北出版 Morikita Publ.) (written in Japanese), "新線形代数 (Shin Senkei Daisu)" (大日本図書 Dai-nippon Publ.), Lecture/exercise handouts
Instructor	Kase Junko,Kasatani Masahiro

Course Objectives

At the completion of this course, students will be able to
1) Solve standard problems picked up from contents of the first grade mathematics.
2) Solve standard problems picked up from contents of the second grade mathematics.
3) Give a presentation of solving problems in front of classmates.
4) Understand a geometric meaning of determinants, and calculate area of parallelogram or volume of parallelepiped.
5) Understand definition of linear transformation, and calculate linear transformation.

Rubric

	Ideal Level of Achievement	Standard Level of Achievement	Unacceptable Level of Achievement)
Evaluation 1	Can solve standard problems picked up from contents of the first grade mathematics quickly and almost perfectly.	Can solve standard problems picked up from contents of the first grade mathematics.	Can't solve standard problems picked up from contents of the first grade mathematics.
Evaluation 2	Can solve standard problems picked up from contents of the second grade mathematics quickly and almost perfectly.	Can solve standard problems picked up from contents of the second grade mathematics.	Can't solve standard problems picked up from contents of the second grade mathematics.
Evaluation 3	Can give a presentation of solving problems in front of classmates very positively.	Can give a presentation of solving problems in front of classmates.	Can't give a presentation of solving problems in front of classmates.
Evaluation 4	Understand a geometric meaning of determinants well, and calculate area of parallelogram and volume of parallelepiped.	Understand a geometric meaning of determinants for the most part, and can calculate area of parallelogram or volume of parallelepiped.	Don't understand a geometric meaning of determinants, and can't calculate area of parallelogram or volume of parallelepiped.
Evaluation 5	Understand definition of linear transformation well, and can calculate various linear transformation.	Understand definition of linear transformation for the most part, and can calculate elementary linear transformation.	Don't understand definition of linear transformation, and can't calculate linear transformation.

Assigned Department Objectives

ディプロマポリシー 3 （豊かな教養と倫理観を身につけ，社会に貢献できる。）

Teaching Method

Outline:

Based on the first and second grade mathematics, students will comprehensively review the fundamentals of mathematics necessary for the study of natural sciences and engineering, and will exercise standard problems.

Style:

Each class will be divided into several subclasses. One teacher will be assigned to each subclass.
Evaluations will be made comprehensively by exams (making up about 60% of the grade), by exercises and homework (making up about 40% of your grade).
Written exams will be carried out several times.

Notice:

Requisites: Attendance to lectures, exercise handouts, lesson notes, and textbooks of related subjects, (and if necessary, reference books, problem books, etc).
Please be sure to prepare complete solutions for problems before classes.

Characteristics of Class / Division in Learning

Active Learning

Aided by ICT

Applicable to Remote Class

Course Plan

			Theme	Goals
2nd Semester
	3rd Quarter
		1st	Guidance / Exercise / Review	Can solve standard problems and can give a presentation of them
		2nd	Exercise / Review	Can solve standard problems and can give a presentation of them
		3rd	Exercise / Review	Can solve standard problems and can give a presentation of them
		4th	Exercise / Review	Can solve standard problems and can give a presentation of them
		5th	Exercise / Review	Can solve standard problems and can give a presentation of them
		6th	Exercise / Review	Can solve standard problems and can give a presentation of them
		7th	Exercise / Review	Can solve standard problems and can give a presentation of them
		8th	Midterm exam
	4th Quarter
		9th	Review of midterm exam
		10th	Condition where homogeneous simultaneous linear equations have non-trivial solutions Condition where vectors are linearly independent	Can find the coefficient matrix where homogeneous simultaneous linear equations have non-trivial solutions. Can determine whether given vectors are linearly independent.
		11th	Geometric meaning of determinants Cross product	Can calculate area of parallelogram or volume of parallelepiped. Can calculate cross product of given vectors.
		12th	Definition of linear transformation	Can find matrix representing linear transformation.
		13th	Basic property of linear transformation	Can calculate image of linear transformation.
		14th	Composition, and inverse of linear transformation Rotational transformation	Can calculate matrices of composition and inverse of linear transformation. Can calculate rotation matrix.
		15th	Final exam
		16th	Review of final exam

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Other	Total
Subtotal	60	15	0	0	0	25	100
Basic Ability	60	15	0	0	0	25	100
Technical Ability	0	0	0	0	0	0	0
Interdisciplinary Ability	0	0	0	0	0	0	0