HA135000 Exercises in Algebra II

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Science

Lecture Code HA135000 Subject Classification Specialized Education

Subject Name 代数学II演習

Subject Name
（Katakana）ダイスウガク２エンシユウ

Subject Name in
English Exercises in Algebra II

Instructor MATSUI HIROKI

Instructor
(Katakana) マツイ　ヒロキ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  Second Semester,  3Term

Days, Periods, and Classrooms (3T) Tues7-8,Fri3-4：SCI E104

Lesson Style Seminar Lesson Style
(More Details) Face-to-face

Mainly lectures.

Credits 1.0 Class Hours/Week 4 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

Keywords groups, homomorphisms, quotient groups, group actions

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.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).

Class Objectives
/Class Outline This course offers exercises on the fundamentals of group theory, aiming to develop skills in computing concrete examples, checking definitions, and producing correct proofs.

Class Schedule In coordination with Algebra II lecture, this course provides problem-solving exercises on the following topics.

Lesson1: Sets and maps
Lesson2: Division of integers
Lesson3: Definition of groups
Lesson4: Examples of groups
Lesson5: Subgroups
Lesson6: Equivalence relations and quotient sets
Lesson7: Cosets
Lesson8: Lagrange's theorem
Lesson9: Midterm Exam
Lesson10: Homomorphisms
Lesson11: Normal subgroups and quotient groups
Lesson12: Isomorphism theorems (1)
Lesson13: Isomorphism theorems (2)
Lesson14: Group actions
Lesson15: Conjugacy classes

There is a possibility of having quizzes and report assignments.

There is a possibility of having quizzes and report assignments.

Text/Reference
Books,etc. Handouts will be assigned during lectures. No specific textbook is fixed.
Any algebra textbook that includes group theory is suitable as a study-aid book.

PC or AV used in
Class,etc. Handouts, moodle

(More Details)

Learning techniques to be incorporated Quizzes/ Quiz format, Post-class Report

Suggestions on
Preparation and
Review Students are expected to work on problems that could not be covered during class.

Requirements It is recommended that students take Algebra II.

Grading Method Based on quizzes and reports.　Detailed explanations will be given in the class.

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	2026Year	School/Graduate School	School of Science
Lecture Code	HA135000	Subject Classification	Specialized Education
Subject Name	代数学II演習
Subject Name （Katakana）	ダイスウガク２エンシユウ
Subject Name in English	Exercises in Algebra II
Instructor	MATSUI HIROKI
Instructor (Katakana)	マツイ　ヒロキ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Tues7-8,Fri3-4：SCI E104
Lesson Style	Seminar	Lesson Style (More Details)	Face-to-face
Mainly lectures.
Credits	1.0	Class Hours/Week	4	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
Keywords	groups, homomorphisms, quotient groups, group actions
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. （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
Class Objectives /Class Outline	This course offers exercises on the fundamentals of group theory, aiming to develop skills in computing concrete examples, checking definitions, and producing correct proofs.
Class Schedule	In coordination with Algebra II lecture, this course provides problem-solving exercises on the following topics. Lesson1: Sets and maps Lesson2: Division of integers Lesson3: Definition of groups Lesson4: Examples of groups Lesson5: Subgroups Lesson6: Equivalence relations and quotient sets Lesson7: Cosets Lesson8: Lagrange's theorem Lesson9: Midterm Exam Lesson10: Homomorphisms Lesson11: Normal subgroups and quotient groups Lesson12: Isomorphism theorems (1) Lesson13: Isomorphism theorems (2) Lesson14: Group actions Lesson15: Conjugacy classes There is a possibility of having quizzes and report assignments. There is a possibility of having quizzes and report assignments.
Text/Reference Books,etc.	Handouts will be assigned during lectures. No specific textbook is fixed. Any algebra textbook that includes group theory is suitable as a study-aid book.
PC or AV used in Class,etc.	Handouts, moodle
(More Details)
Learning techniques to be incorporated	Quizzes/ Quiz format, Post-class Report
Suggestions on Preparation and Review	Students are expected to work on problems that could not be covered during class.
Requirements	It is recommended that students take Algebra II.
Grading Method	Based on quizzes and reports.　Detailed explanations will be given in the class.
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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