CC220804 Practice in Introduction to Geometry

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Education

Lecture Code CC220804 Subject Classification Specialized Education

Subject Name 代数学概論演習

Subject Name
（Katakana）ダイスウガクガイロンエンシュウ

Subject Name in
English Practice in Introduction to Geometry

Instructor KITADAI YUKINORI

Instructor
(Katakana) キタダイ　ユキノリ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  Second Semester,  4Term

Days, Periods, and Classrooms (4T) Thur1-4：EDU L104

Lesson Style Seminar Lesson Style
(More Details) 　

Lecture and exercise-oriented, note-taking, discussions, student presentations

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 Mainly for students of Program in Mathematics Education of Faculty of Education

Keywords Algebra, operations, semigroups, monoids, groups, symmetries, homomorphisms, homomorphism theorem

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) Basic specialized subject
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Secondary School Mathematics Education
（Knowledge and Understanding）
・To understand basic knowledge of teaching contents of mathematic education.
（Abilities and Skills）
・To acquire and utilize the ability to think mathematically about teaching contents of mathematic education such as algebra, geometry, statistics and computer.

Class Objectives
/Class Outline The objective of this course is to understand the contents about algebra in mathematics in secondary education and to learn the basics of a group structure which is an algebraic object defined abstractly only by conditions concerning algebraic operation.

Class Schedule Lesson 1: Find symmetries in our daily life
Lesson 2: Definitions of operations, magmas, semigroups, monoids, groups
Lesson 3: Find examples of groups
Lesson 4: Orders of groups, multiplication tables
Lesson 5: Subgroups, generators, cyclic groups, orders of elements
Lesson 6: The additive group Z and cyclic groups, homomorphisms, their kernels and images
Lesson 7: Kernels of homomorphisms and normal subgroups
Lesson 8: Congruence of integers, equivalence relations, equivalence classes, quotient sets
Lesson 9: Cosets, quotient sets
Lesson 10: Indeces, Lagrange's theorem
Lesson 11: Well-definedness, normal subgroups and quotient groups
Lesson 12: Quotient groups of integers and multiplications, multiplicative groups, primitive residue classes
Lesson 13: Fermat's little theorem, Euler's theorem
Lesson 14: Homomorphism theorem
Lesson 15: Second and third isomorphism theorem

Lesson 16: Exam

There will be several quizes and report assignments.

Text/Reference
Books,etc. No textbook.
Reference books are:
・代数入門（新装版）-- 群と加群 (数学シリーズ), 堀田良之, 裳華房, 2021年.
・代数系入門, 松坂和夫, 岩波書店, 1976年.
・代数学1 群論入門 (代数学シリーズ), 雪江明彦, 日本評論社, 2010年.
・群論, これはおもしろい -- トランプで学ぶ群 -- (数学のかんどころ 16), 飯高茂, 共立出版, 2013年.

PC or AV used in
Class,etc. 　

(More Details) Blackboard, handouts

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review When reviewing, let your brain and your hands move.  Make examples.  Ask questions.

Requirements

Grading Method exam: 70%, quizzes: 15%, reports: 15%

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 Education
Lecture Code	CC220804	Subject Classification	Specialized Education
Subject Name	代数学概論演習
Subject Name （Katakana）	ダイスウガクガイロンエンシュウ
Subject Name in English	Practice in Introduction to Geometry
Instructor	KITADAI YUKINORI
Instructor (Katakana)	キタダイ　ユキノリ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Thur1-4：EDU L104
Lesson Style	Seminar	Lesson Style (More Details)
Lecture and exercise-oriented, note-taking, discussions, student presentations
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	Mainly for students of Program in Mathematics Education of Faculty of Education
Keywords	Algebra, operations, semigroups, monoids, groups, symmetries, homomorphisms, homomorphism theorem
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	Basic specialized subject
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Secondary School Mathematics Education （Knowledge and Understanding）・To understand basic knowledge of teaching contents of mathematic education. （Abilities and Skills）・To acquire and utilize the ability to think mathematically about teaching contents of mathematic education such as algebra, geometry, statistics and computer.
Class Objectives /Class Outline	The objective of this course is to understand the contents about algebra in mathematics in secondary education and to learn the basics of a group structure which is an algebraic object defined abstractly only by conditions concerning algebraic operation.
Class Schedule	Lesson 1: Find symmetries in our daily life Lesson 2: Definitions of operations, magmas, semigroups, monoids, groups Lesson 3: Find examples of groups Lesson 4: Orders of groups, multiplication tables Lesson 5: Subgroups, generators, cyclic groups, orders of elements Lesson 6: The additive group Z and cyclic groups, homomorphisms, their kernels and images Lesson 7: Kernels of homomorphisms and normal subgroups Lesson 8: Congruence of integers, equivalence relations, equivalence classes, quotient sets Lesson 9: Cosets, quotient sets Lesson 10: Indeces, Lagrange's theorem Lesson 11: Well-definedness, normal subgroups and quotient groups Lesson 12: Quotient groups of integers and multiplications, multiplicative groups, primitive residue classes Lesson 13: Fermat's little theorem, Euler's theorem Lesson 14: Homomorphism theorem Lesson 15: Second and third isomorphism theorem Lesson 16: Exam There will be several quizes and report assignments.
Text/Reference Books,etc.	No textbook. Reference books are: ・代数入門（新装版）-- 群と加群 (数学シリーズ), 堀田良之, 裳華房, 2021年. ・代数系入門, 松坂和夫, 岩波書店, 1976年. ・代数学1 群論入門 (代数学シリーズ), 雪江明彦, 日本評論社, 2010年. ・群論, これはおもしろい -- トランプで学ぶ群 -- (数学のかんどころ 16), 飯高茂, 共立出版, 2013年.
PC or AV used in Class,etc.
(More Details)	Blackboard, handouts
Learning techniques to be incorporated
Suggestions on Preparation and Review	When reviewing, let your brain and your hands move. Make examples. Ask questions.
Requirements
Grading Method	exam: 70%, quizzes: 15%, reports: 15%
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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