KA101001 Discrete Mathematics I

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Informatics and Data Science

Lecture Code KA101001 Subject Classification Specialized Education

Subject Name 離散数学I

Subject Name
（Katakana）リサンスウガク１

Subject Name in
English Discrete Mathematics I

Instructor IWAMOTO CHUZO

Instructor
(Katakana) イワモト　チュウゾウ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Mon9-10,Tues5-6：ECON B257

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture

Credits 2.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students 1st-year (School of Informatics and Data Science), 2nd-year (Electrical, Electronic and Systems Engineering)

Keywords Sets, Logic, Modular Arithmetic, Discrete Algebra, Relations, Graphs, Order

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) Integrated Arts and Sciences
（Knowledge and Understanding）
・Knowledge and understanding of the importance and characteristics of each discipline and basic theoretical framework.
（Abilities and Skills）
・The ability and skills to specify necessary theories and methods for consideration of issues.

Program of Electrical,Systems and Information Engineering
（Abilities and Skills）
・Mathematical methods required for professionals in electrical,  systems, and information engineering.

Computer Science Program
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Data Science Program
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Intelligence Science Program
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

Class Objectives
/Class Outline Discrete mathematics is a field of mathematics that deals with
discrete objects.  In this course, we will focus on concepts
such as sets, logic, modular arithmetic, discrete algebra,
relations, graphs, and order.  Through exercises, the aim is to
improve mathematical and logical reasoning skills and enhance
practical problem-solving abilities.

Class Schedule The following 8 topics will be explained in accordance with the
textbook content.  A total of 16 classes will be conducted, including
exercises and explanations of problems and implementation of quizzes.
- Discrete Sets: Power sets and set operations, inclusion-exclusion
  principle, direct sum, Cartesian product (Chapter 1).
- Logical Calculi: Propositions and logical operations, logic and
  proof (Chapter 2).
- Modulo Operations: Division theorem, congruence, roots of
  congruences, operations in modular systems (Chapter 7).
- Discrete Algebra: Properties of algebraic systems and operations,
  definitions and properties of groups, fields, and rings (Chapter 8).
- Discrete Relations: Binary relations, relation graphs and matrices,
  equivalence relations (Chapter 9).
- Discrete Graphs: Adjacency matrices, Euler's theorem (Chapter 10).
  Tree Graphs: Ordered trees, syntax trees, graph search and search
  tree properties (Chapter 11).
- Order Theory: Order relations and ordered sets, upper and lower
  bounds, logical algebra (Chapter 12).

Text/Reference
Books,etc. 近代科学社「はじめての離散数学」，小倉久和著，ISBN:9784764910546 (This book is available in both electronic and paper editions).
Class materials will be distributed on Moodle.

PC or AV used in
Class,etc. 　

(More Details)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Solve the designated exercises given in each lecture and submit them as reports.

Requirements

Grading Method Evaluation will be based on the cumulative scores of exams.

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 Informatics and Data Science
Lecture Code	KA101001	Subject Classification	Specialized Education
Subject Name	離散数学I
Subject Name （Katakana）	リサンスウガク１
Subject Name in English	Discrete Mathematics I
Instructor	IWAMOTO CHUZO
Instructor (Katakana)	イワモト　チュウゾウ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Mon9-10,Tues5-6：ECON B257
Lesson Style	Lecture	Lesson Style (More Details)
Lecture
Credits	2.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	1st-year (School of Informatics and Data Science), 2nd-year (Electrical, Electronic and Systems Engineering)
Keywords	Sets, Logic, Modular Arithmetic, Discrete Algebra, Relations, Graphs, Order
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)	Integrated Arts and Sciences （Knowledge and Understanding）・Knowledge and understanding of the importance and characteristics of each discipline and basic theoretical framework. （Abilities and Skills）・The ability and skills to specify necessary theories and methods for consideration of issues. Program of Electrical,Systems and Information Engineering （Abilities and Skills）・Mathematical methods required for professionals in electrical, systems, and information engineering. Computer Science Program （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. ・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis. Data Science Program （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. ・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis. Intelligence Science Program （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. ・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.
Class Objectives /Class Outline	Discrete mathematics is a field of mathematics that deals with discrete objects. In this course, we will focus on concepts such as sets, logic, modular arithmetic, discrete algebra, relations, graphs, and order. Through exercises, the aim is to improve mathematical and logical reasoning skills and enhance practical problem-solving abilities.
Class Schedule	The following 8 topics will be explained in accordance with the textbook content. A total of 16 classes will be conducted, including exercises and explanations of problems and implementation of quizzes. - Discrete Sets: Power sets and set operations, inclusion-exclusion principle, direct sum, Cartesian product (Chapter 1). - Logical Calculi: Propositions and logical operations, logic and proof (Chapter 2). - Modulo Operations: Division theorem, congruence, roots of congruences, operations in modular systems (Chapter 7). - Discrete Algebra: Properties of algebraic systems and operations, definitions and properties of groups, fields, and rings (Chapter 8). - Discrete Relations: Binary relations, relation graphs and matrices, equivalence relations (Chapter 9). - Discrete Graphs: Adjacency matrices, Euler's theorem (Chapter 10). Tree Graphs: Ordered trees, syntax trees, graph search and search tree properties (Chapter 11). - Order Theory: Order relations and ordered sets, upper and lower bounds, logical algebra (Chapter 12).
Text/Reference Books,etc.	近代科学社「はじめての離散数学」，小倉久和著，ISBN:9784764910546 (This book is available in both electronic and paper editions). Class materials will be distributed on Moodle.
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Solve the designated exercises given in each lecture and submit them as reports.
Requirements
Grading Method	Evaluation will be based on the cumulative scores of exams.
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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