HA120000 AlgebraＩＩ

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HA120000 Subject Classification Specialized Education

Subject Name 代数学II

Subject Name
（Katakana）ダイスウガク２

Subject Name in
English AlgebraＩＩ

Instructor TAKAHASHI NOBUYOSHI

Instructor
(Katakana) タカハシ　ノブヨシ

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

Days, Periods, and Classrooms (3T) Tues7-8,Thur1-2：SCI E104

Lesson Style Lecture Lesson Style
(More Details) 　

Mainly lectures. Depending on the situation, lectures might be given online.

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

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords binary operation, algebraic system, group, homomorphism, axiom, equivalence relation

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 The basics of the group theory will be explained. The goal is to understand the basic theory of groups, to become familiar with the abstract algebra, to learn to give proofs of propositions on groups and to do calculations on concrete examples related to groups.

Class Schedule lesson1 Introduction/Sets, maps and binary operations
lesson2 Semigroups, monoids and groups
lesson3 Elementary properties of groups
lesson4 Examples of groups
lesson5 Subgroups
lesson6 Residue classes and residue sets 1
lesson7 Residue classes and residue sets 2
lesson8 A theorem of Lagrange, Fermat's little theorem
lesson9 Midterm review
lesson10 Homomorphism
lesson11 Normal subgroups and quotient groups
lesson12 Fundamental theorem on homomorphisms 1
lesson13 Fundamental theorem on homomorphisms 2
lesson14 Finitely generated abelian groups 1
lesson15 Finitely generated abelian groups 2

A final exam is planned. There might be mid-term exam. Depending on the situation, reports might be used for evaluation.

The content and schedule might change.

Text/Reference
Books,etc. Announced in the class.

PC or AV used in
Class,etc. 　

(More Details) Handouts will be distributed.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Try to understand the definitions and the statements and proofs of theorems rigorously, and to examine how they apply to concrete examples.

Requirements It is recommended that you take Exercises in Algebra II.

Grading Method Mainly based on exams and quizzes. There might be report assignments. 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	2024Year	School/Graduate School	School of Science
Lecture Code	HA120000	Subject Classification	Specialized Education
Subject Name	代数学II
Subject Name （Katakana）	ダイスウガク２
Subject Name in English	AlgebraＩＩ
Instructor	TAKAHASHI NOBUYOSHI
Instructor (Katakana)	タカハシ　ノブヨシ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Tues7-8,Thur1-2：SCI E104
Lesson Style	Lecture	Lesson Style (More Details)
Mainly lectures. Depending on the situation, lectures might be given online.
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	binary operation, algebraic system, group, homomorphism, axiom, equivalence relation
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	The basics of the group theory will be explained. The goal is to understand the basic theory of groups, to become familiar with the abstract algebra, to learn to give proofs of propositions on groups and to do calculations on concrete examples related to groups.
Class Schedule	lesson1 Introduction/Sets, maps and binary operations lesson2 Semigroups, monoids and groups lesson3 Elementary properties of groups lesson4 Examples of groups lesson5 Subgroups lesson6 Residue classes and residue sets 1 lesson7 Residue classes and residue sets 2 lesson8 A theorem of Lagrange, Fermat's little theorem lesson9 Midterm review lesson10 Homomorphism lesson11 Normal subgroups and quotient groups lesson12 Fundamental theorem on homomorphisms 1 lesson13 Fundamental theorem on homomorphisms 2 lesson14 Finitely generated abelian groups 1 lesson15 Finitely generated abelian groups 2 A final exam is planned. There might be mid-term exam. Depending on the situation, reports might be used for evaluation. The content and schedule might change.
Text/Reference Books,etc.	Announced in the class.
PC or AV used in Class,etc.
(More Details)	Handouts will be distributed.
Learning techniques to be incorporated
Suggestions on Preparation and Review	Try to understand the definitions and the statements and proofs of theorems rigorously, and to examine how they apply to concrete examples.
Requirements	It is recommended that you take Exercises in Algebra II.
Grading Method	Mainly based on exams and quizzes. There might be report assignments. 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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