H0000000 Introduction to Mathematics

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code H0000000 Subject Classification Specialized Education

Subject Name 数学概説

Subject Name
（Katakana）スウガクガイセツ

Subject Name in
English Introduction to Mathematics

Instructor NAITO YUKI

Instructor
(Katakana) ナイトウ　ユウキ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  1Term

Days, Periods, and Classrooms (1T) Mon9-10,Weds9-10：SCI E002 AV

Lesson Style Lecture Lesson Style
(More Details) 　

Lectures on the blackboard

Credits 2.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 1 : Undergraduate Introductory

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Freshman (1st year) students

Keywords Logic, sets, functions and mappings

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Mathematics
（Knowledge and Understanding）
・Understanding classical basic theory which is a base of modern mathematics.  Being able to find and explain issues from specific events.

Physics
（Knowledge and Understanding）
・The knowledge and understanding on construction and development process and relations with culture and society of each academic discipline.

Chemistry
（Knowledge and Understanding）
・To thoroughly understand and learn knowledge of physical chemistry, inorganic chemistry and organic chemistry.
・Understanding and acquiring logical frameworks and structure of basic studying and knowledge and skills necessary for learning construction.

Biology
（Knowledge and Understanding）
・Understanding and learning basic knowledge in scientific fields.

Earth and Planetary Systems Science
（Abilities and Skills）
・Being able to understand, learn and explain logical framework and system of basic studying according to each subject and necessary knowledge and skills for constructing learning.

Earth and Planetary Systems Science
（Abilities and Skills）
・Being able to understand, learn and explain logical framework and system of basic studying according to each subject and necessary knowledge and skills for constructing learning.

Class Objectives
/Class Outline This course, Introduction to Mathematics, is provided for understanding the basic mathematics, such as logic, sets, functions and mappings.

Class Schedule Lesson1 Proposition, symbols for logic, truth table
Lesson2 Equivalent proposition, propositional laws of ``and" and ``or"
Lesson3 Converse, inverse and contraposition of proposition
Lesson4 Universal proposition and existential proposition
Lesson5 Tortology, negation of universal proposition and existential proposition
Lesson6 Notation for sets, equality of two sets, inclusion relation
Lesson7 Empty set, finite set and infinite set, intersection and union of sets, difference set and complement of a set
Lesson8 Mid-term examination
Lesson9 Direct product of sets, power set, equivalence relation and representative element
Lesson10 Quotient set, ordered set, mathematical induction
Lesson11 Function and mapping, equality of two functions (two mappings)
Lesson12 Image and inverse image
Lesson13 Injectivity and surjectivity of a mapping, inverse mapping
Lesson14 Composition of mappings, restriction of a mapping, identity mapping, quotient mapping
Lesson15 Cardinality of sets, countable set and uncountable set

Final lesson : Final examination

The proposed plan of the course may be changed in order for the students to deepen their understanding.

Text/Reference
Books,etc. Textbook:Go-o Ishikawa, ``Ronri, Shugo, Suugakugo", Kyoritsu Shuppan, 2015.

PC or AV used in
Class,etc. 　

(More Details) I will hand out some documentations if necessary.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Lesson 1--Lesson 15 Review is necessary.

Requirements

Grading Method Midterm examination and Final examination.
If I assign some quizes, these scores are also considered.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	School of Science
Lecture Code	H0000000	Subject Classification	Specialized Education
Subject Name	数学概説
Subject Name （Katakana）	スウガクガイセツ
Subject Name in English	Introduction to Mathematics
Instructor	NAITO YUKI
Instructor (Katakana)	ナイトウ　ユウキ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 1Term
Days, Periods, and Classrooms	(1T) Mon9-10,Weds9-10：SCI E002 AV
Lesson Style	Lecture	Lesson Style (More Details)
Lectures on the blackboard
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	1 : Undergraduate Introductory
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Freshman (1st year) students
Keywords	Logic, sets, functions and mappings
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Mathematics （Knowledge and Understanding）・Understanding classical basic theory which is a base of modern mathematics. Being able to find and explain issues from specific events. Physics （Knowledge and Understanding）・The knowledge and understanding on construction and development process and relations with culture and society of each academic discipline. Chemistry （Knowledge and Understanding）・To thoroughly understand and learn knowledge of physical chemistry, inorganic chemistry and organic chemistry. ・Understanding and acquiring logical frameworks and structure of basic studying and knowledge and skills necessary for learning construction. Biology （Knowledge and Understanding）・Understanding and learning basic knowledge in scientific fields. Earth and Planetary Systems Science （Abilities and Skills）・Being able to understand, learn and explain logical framework and system of basic studying according to each subject and necessary knowledge and skills for constructing learning. Earth and Planetary Systems Science （Abilities and Skills）・Being able to understand, learn and explain logical framework and system of basic studying according to each subject and necessary knowledge and skills for constructing learning.
Class Objectives /Class Outline	This course, Introduction to Mathematics, is provided for understanding the basic mathematics, such as logic, sets, functions and mappings.
Class Schedule	Lesson1 Proposition, symbols for logic, truth table Lesson2 Equivalent proposition, propositional laws of ``and" and ``or" Lesson3 Converse, inverse and contraposition of proposition Lesson4 Universal proposition and existential proposition Lesson5 Tortology, negation of universal proposition and existential proposition Lesson6 Notation for sets, equality of two sets, inclusion relation Lesson7 Empty set, finite set and infinite set, intersection and union of sets, difference set and complement of a set Lesson8 Mid-term examination Lesson9 Direct product of sets, power set, equivalence relation and representative element Lesson10 Quotient set, ordered set, mathematical induction Lesson11 Function and mapping, equality of two functions (two mappings) Lesson12 Image and inverse image Lesson13 Injectivity and surjectivity of a mapping, inverse mapping Lesson14 Composition of mappings, restriction of a mapping, identity mapping, quotient mapping Lesson15 Cardinality of sets, countable set and uncountable set Final lesson : Final examination The proposed plan of the course may be changed in order for the students to deepen their understanding.
Text/Reference Books,etc.	Textbook:Go-o Ishikawa, ``Ronri, Shugo, Suugakugo", Kyoritsu Shuppan, 2015.
PC or AV used in Class,etc.
(More Details)	I will hand out some documentations if necessary.
Learning techniques to be incorporated
Suggestions on Preparation and Review	Lesson 1--Lesson 15 Review is necessary.
Requirements
Grading Method	Midterm examination and Final examination. If I assign some quizes, these scores are also considered.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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