Advanced Mathematics Ⅰ

Course Information

College	Toyama College	Year	2020
Course Title	Advanced Mathematics Ⅰ
Course Code	0058	Course Category	General / Elective
Class Format	Lecture	Credits	Academic Credit: 1
Department	Department of Mechanical Engineering	Student Grade	4th
Term	First Semester	Classes per Week	前期:2
Textbook and/or Teaching Materials	Setsuo Takato and others "Probability and Statistics" Dainippon Tosho Publishing
Instructor	Ishida Yoshihiko

Course Objectives

•To be able to understand and calculate random variables and probability distribution.
•To be able to understand and calculate discrete/continuous probability distributions.
•To be able to understand and calculate normal distributions.
•To be able to understand and calculate statistics and sample distributions.
•To be able to understand and calculate various probability distributions.

Rubric

	Ideal Level of Achievement (Very Good)	Standard Level of Achievement (Good)	Unacceptable Level of Achievement (Fail)
Can understand and calculate discrete/continuous probability distributions.	Can understand and accurately and swiftly calculate discrete/continuous probability distributions.	Can understand and calculate discrete/continuous probability distributions.	Cannot understand or calculate discrete/continuous probability distributions.
Can understand and calculate normal distributions.	Can understand and accurately and swiftly calculate normal distributions.	Can understand and calculate normal distributions.	Cannot understand or calculate normal distributions.
Can understand and calculate statistics and sample distributions.	Can understand and accurately and swiftly calculate statistics and sample distributions.	Can understand and calculate statistics and sample distributions.	Cannot understand or calculate statistics and sample distributions.
Can understand and calculate various probability distributions.	Can understand and accurately and swiftly calculate various probability distributions.	Can understand and calculate various probability distributions.	Cannot understand or calculate various probability distributions.

Assigned Department Objectives

Learning and Educational Objectives of the “General Engineering” A-5 （工学的な諸問題に対処する際に必要な数学，自然科学及び情報の基礎的知識を理解し，それらを適切に活用することができる。）

JABEE 1(2)(c) （数学及び自然科学に関する知識とそれらを応用する能力）

Diploma policy 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:

To understand the meaning of various distributions in statistics, particularly discrete binomial distribution and continuous normal distribution.
To understand the meaning of sample distribution and population distribution.
To understand the meaning of X^2 (chi-squared) distribution, T-distribution and F-distribution, which are derived from normal distributions.
To provide students with an opportunity to make calculations through exercises and problems.

Style:

The course will be proceeded based on the premise that the students have prepared for each course. The course plan may change depending on the students' degree of preparation and understanding.

Notice:

•The lectures will follow the course materials, but students are expected to use their own spreadsheet and statistics software in order to become familiar with statistical calculations.
•Students will be able to determine the probabilities of specific problems.

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Random variables and probability distribution	Chapter 3 §1 Random variables and probability distribution §1.1 Random variables and probability distribution
		2nd	Random variables and probability distribution	§1.1 Random variables and probability distribution §1.2 Binomial distribution §1.3 Poisson distribution
		3rd	Random variables and probability distribution	§1.3 Poisson distribution §1.4 Continuous random variables
		4th	Random variables and probability distribution	§1.4 Continuous random variables §1.5 Average and variance of continuous random variables
		5th	Random variables and probability distribution	§1.5 Average and variance of continuous random variables §1.6 Normal distribution
		6th	Random variables and probability distribution	§1.6 Normal distribution §1.7 Relationship between binomial distribution and normal distribution
		7th	Random variables and probability distribution	(Exercises)
		8th	Mid-term exam	Chapter 3 §1 Random variables and probability distribution
	2nd Quarter
		9th	Statistics and sample distributions	Chapter 3 §2 Statistics and sample distributions §2.1 Function of the random variables
		10th	Statistics and sample distributions	§2.1 Function of the random variables §2.2 Population and samples
		11th	Statistics and sample distributions	§2.2 Population and samples §2.3 Statistics and sample distributions
		12th	Statistics and sample distributions	§2.3 Statistics and sample distributions §2.4 Various probability distributions
		13th	Statistics and sample distributions	§2.4 Various probability distributions
		14th	Statistics and sample distributions	(Exercises)
		15th	Final exam	Chapter 3 §2 Statistics and sample distributions
		16th	Return answers of the final exam/explanation/review	Chapter 3 §1 Random variables and probability distributions §2 Statistics and sample distributions

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