ANM16001 Algebra

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Integrated Arts and Sciences Department of Integrated Arts and Sciences

Lecture Code ANM16001 Subject Classification Specialized Education

Subject Name 数理代数

Subject Name
（Katakana）スウリダイスウ

Subject Name in
English Algebra

Instructor KOTORII YUKA

Instructor
(Katakana) コトリイ　ユウカ

Campus Higashi-Hiroshima Semester/Term 3rd-Year, Second Semester, 3Term

Days, Periods, and Classrooms (3T) Fri5-8：IAS C808

Lesson Style Lecture Lesson Style
(More Details) 　

Mainly Blackboard

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

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Algebra, Group Theory, Symmetry, Permutations, Homomorphisms

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) This lecture develops knowledge and mathematical skills studied in Linear Algebra I, II, and cultivates a better understanding algebra. It will become a basis for further study of more advanced mathematics and other research areas, such as physics, chemistry or information sciences.
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.

Class Objectives
/Class Outline To learn the definitions of a group and related notions, and to understand how they are used in examples.

Class Schedule [An Example of Class Schedule]
Lesson 1: Symmetries of polyhedra
Lesson 2: Definitions of a group
Lesson 3: Group structures on numbers
Lesson 4: Dihedral groups
Lesson 5: Subgroups and generators
Lesson 6: Permutations
Lesson 7: Isomorphisms
Lesson 8: Plato's solids and Cayley's theorem
Lesson 9: Matrix groups
Lesson 10: Products of groups
Lesson 11: Lagrange's theorem
Lesson 12: Equivalence relations
Lesson 13: Conjugacy and normal subgroups
Lesson 14: Homomorphisms
Lesson 15: Summary

Text/Reference
Books,etc. To be determined

PC or AV used in
Class,etc. 　

(More Details) Blackboard, chalk, handouts

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review To understand new notions, it is important to read the definitions carefully and to try to find examples by yourself.

Requirements

Grading Method Based on the final examination, reports and exercises

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 Integrated Arts and Sciences Department of Integrated Arts and Sciences
Lecture Code	ANM16001	Subject Classification	Specialized Education
Subject Name	数理代数
Subject Name （Katakana）	スウリダイスウ
Subject Name in English	Algebra
Instructor	KOTORII YUKA
Instructor (Katakana)	コトリイ　ユウカ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Fri5-8：IAS C808
Lesson Style	Lecture	Lesson Style (More Details)
Mainly Blackboard
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Algebra, Group Theory, Symmetry, Permutations, Homomorphisms
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	This lecture develops knowledge and mathematical skills studied in Linear Algebra I, II, and cultivates a better understanding algebra. It will become a basis for further study of more advanced mathematics and other research areas, such as physics, chemistry or information sciences.
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.
Class Objectives /Class Outline	To learn the definitions of a group and related notions, and to understand how they are used in examples.
Class Schedule	[An Example of Class Schedule] Lesson 1: Symmetries of polyhedra Lesson 2: Definitions of a group Lesson 3: Group structures on numbers Lesson 4: Dihedral groups Lesson 5: Subgroups and generators Lesson 6: Permutations Lesson 7: Isomorphisms Lesson 8: Plato's solids and Cayley's theorem Lesson 9: Matrix groups Lesson 10: Products of groups Lesson 11: Lagrange's theorem Lesson 12: Equivalence relations Lesson 13: Conjugacy and normal subgroups Lesson 14: Homomorphisms Lesson 15: Summary
Text/Reference Books,etc.	To be determined
PC or AV used in Class,etc.
(More Details)	Blackboard, chalk, handouts
Learning techniques to be incorporated
Suggestions on Preparation and Review	To understand new notions, it is important to read the definitions carefully and to try to find examples by yourself.
Requirements
Grading Method	Based on the final examination, reports and exercises
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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