Fundamental Mathematics AⅠ

Course Information

College	Toyama College	Year	2022
Course Title	Fundamental Mathematics AⅠ
Course Code	0001	Course Category	General / Compulsory
Class Format	Lecture	Credits	School Credit: 2
Department	Department of Electrical and Control Systems Engineering	Student Grade	1st
Term	First Semester	Classes per Week	4
Textbook and/or Teaching Materials	Textbook: "Shin Kiso Sugaku Kaitei-ban(Fundamental Mathematics)" / Exercise book: "Shin Kiso Sugaku Mondai-shu Kaitei-ban", written by S. Takato et al., published by Dai-nippon Tosho (in Japanese)
Instructor	Kasatani Masahiro

Course Objectives

At the completion of this course, students will be able to
1) Calculate addition, subtraction, multiplication, division, expansion and factorization of polynomials.
2) Perform basic calculations on fractional expressions, expressions including square roots, and complex numbers.
3) Solve quadratic equations and quadratic inequalities.
4) Solve simple simultaneous equations, irrational equations, and fractional equations.
5) Factor simple higher degree polynomials using the factor theorem and solve simple higher degree equations.

Rubric

	Ideal Level of Achievement (Very Good)	Standard Level of Achievement (Good)	Unacceptable Level of Achievement (Fail)
Evaluation 1	Can calculate addition, subtraction, multiplication, division, expansion and factorization of complicated polynomials.	Can calculate addition, subtraction, multiplication, division, expansion and factorization of basic polynomials.	Can't calculate addition, subtraction, multiplication, division, expansion and factorization of basic polynomials.
Evaluation 2	Can perform complicated calculations on fractional expressions, expressions including square roots, and complex numbers.	Can perform basic calculations on fractional expressions, expressions including square roots, and complex numbers.	Can't perform basic calculations on fractional expressions, expressions including square roots, and complex numbers.
Evaluation 3	Can solve complicated quadratic equations and quadratic inequalities.	Can solve basic quadratic equations and quadratic inequalities.	Can't solve basic quadratic equations and quadratic inequalities.
Evaluation 4	Can solve complicated simultaneous equations, irrational equations, and fractional equations.	Can solve simple simultaneous equations, irrational equations, and fractional equations.	Can't solve simple simultaneous equations, irrational equations, and fractional equations.
Evaluation 5	Can factor complicated higher degree polynomials using the factor theorem and solve complicated higher degree equations.	Can factor simple higher degree polynomials using the factor theorem and solve simple higher degree equations.	Can't factor simple higher degree polynomials using the factor theorem and solve simple higher degree equations.

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:

In this course, students will learn basic mathematical concepts and mathematical skills (calculations of numbers and expressions, arithmetic operations of polynomials, factorization, the remainder theorem, calculation of fractional expressions, equations and inequalities, etc.).
Exercises are conducted in parallel with lectures to acquire mathematical and computational techniques required in engineering and other subjects.

Style:

Content of the lectures gradually increases in quantity and quality, compared to junior high school. We recommend that students prepare for each lectures.
If there is anything you do not understand in the lectures, please review it immidiately and try to understand it. Active questions are always recommended.
It is not enough to understand basic contents once. Please train repeatedly.
The lectures plan may be changed according to the student's level of understanding.

Notice:

Mini-exams will be carried out up to several times.
Evaluations will be made comprehensively by written exams (making up about 80% of the grade), by exercises and homework (making up about 20% of the grade).

Can take makeup exam in need aid up to maximum of 50 points.

Characteristics of Class / Division in Learning

Active Learning

Aided by ICT

Applicable to Remote Class

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Addition, subtraction, and multiplication of polynomials	Can calculate addition, subtraction, and multiplication of polynomials.
		2nd	Formulae for polynomial expansion, factorization of polynomials, criss-cross method factorization	Can calculate polynomial expansion and factorization of polynomials using criss-cross method.
		3rd	Long division of polynomials, the least common multiple, the greatest common divisor	Can calculate long division of polynomials. Can find the least common multiple and the greatest common divisor.
		4th	The remainder theorem, the factor theorem, factorization of higher degree polynomials	Can calculate the remainder using the remainder theorem. Can factor higher degree polynomials using the factor theorem.
		5th	Calculation of fractional expressions, lowest common denominators. Simplifying complex rational expressions.	Can calculate fractional expressions, lowest common denominators. Can Simplify complex rational expressions.
		6th	Real numbers, absolute values	Can understand composition of real numbers. Can understand number lines and calculate absolute values.
		7th	Square roots, complex numbers	Can understand and calculate square roots. Can perform arithmetic operations of complex numbers.
		8th	Mid-term exam Answers and explanations for the mid-term exam
	2nd Quarter
		9th	Quadratic equations	Can solve quadratic equations using the quadratic formula. Can understand the relationship between roots and coefficients and can apply it to factorization.
		10th	Higher degree equations	Can solve higher degree equations using the factor theorem.
		11th	Ssimultaneous equations, irrational equations, fractional equations	Can solve simple simultaneous equations, irrational equations, and fractional equations.
		12th	Identity Properties of equality Proof of equalities	Can understand the difference between equations and identities. Can prove simple equalities.
		13th	Properties of inequalities	Can solve linear and quadratic inequalities.
		14th	Proof of inequalities Sets	Can prove inequalities using the relationship between arithmetic mean and geometric mean. Can understand the basics of sets.
		15th	Final exam
		16th	Answers and explanations for the final exam Summary of the 1st semester and advise for summer vacation and the 2nd semester

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Other	Total
Subtotal	80	0	0	0	0	20	100
Basic Ability	80	0	0	0	0	20	100
Technical Ability	0	0	0	0	0	0	0
Interdisciplinary Ability	0	0	0	0	0	0	0