HB050000 Exercises in Algebra B

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HB050000 Subject Classification Specialized Education

Subject Name 代数学Ｂ演習

Subject Name
（Katakana）ダイスウガクBエンシュウ

Subject Name in
English Exercises in Algebra B

Instructor TAKAHASHI NOBUYOSHI,KOREEDA YOSHIMUNE

Instructor
(Katakana) タカハシ　ノブヨシ,コレエダ　ヨシムネ

Campus Higashi-Hiroshima Semester/Term 3rd-Year, Second Semester, 4Term

Days, Periods, and Classrooms (4T) Tues3-4,Thur7-8：SCI B305

Lesson Style Seminar Lesson Style
(More Details) 　

Solve problems, and give presentations on the solutions with the blackboard. Depending on the situation, classes might be held online.

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 Field, Galois theory, polynomial equation, geometric problems

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) Learn Galois theory, which is one of basic theories in today's mathematics, and its application to classical or concrete problems, by solving problems.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Mathematics
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
・To acquire skills to formulate and solve mathematical questions.

Class Objectives
/Class Outline Solve problems on Galois theory and its applications, according to Algebra B.

Class Schedule According to Algebra B, solve problems about the subjects below.

lesson1 Algebraic equations and Galois theory, field theory
lesson2 Rings and fields, 1
lesson3 Rings and fields, 2
lesson4 Polynomial ring over a field, 1
lesson5 Polynomial ring over a field, 2
lesson6 Field extensions
lesson7 Characteristic, finite fields
lesson8 Irreducibility criteria for polynomials
lesson9 Summary, 1
lesson10 Galois extension and Galois group
lesson11 Examples of Galois group and Galois correspondence
lesson12 Galois groups and algebraic equations
lesson13 Proof of fundamental theorems
lesson14 Summary, 2
lesson15 Geometric problems and Galois theory, field theory

There might be quizzes and report assignments. There is a possibility of having mid-term and final exams jointly with Algebra B. Detailed explanation will be given in the class.

The contents and schedule might change.

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

PC or AV used in
Class,etc. 　

(More Details) handouts, blackboard

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Please participate actively. Read all problems and try to give answers. Examine other students' answers.

Requirements It is recommended that you take Algebra B.

Grading Method Marks will be based on presentations, reports, quizzes, and exams(if any).

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	HB050000	Subject Classification	Specialized Education
Subject Name	代数学Ｂ演習
Subject Name （Katakana）	ダイスウガクBエンシュウ
Subject Name in English	Exercises in Algebra B
Instructor	TAKAHASHI NOBUYOSHI,KOREEDA YOSHIMUNE
Instructor (Katakana)	タカハシ　ノブヨシ,コレエダ　ヨシムネ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Tues3-4,Thur7-8：SCI B305
Lesson Style	Seminar	Lesson Style (More Details)
Solve problems, and give presentations on the solutions with the blackboard. Depending on the situation, classes might be held online.
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	Field, Galois theory, polynomial equation, geometric problems
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	Learn Galois theory, which is one of basic theories in today's mathematics, and its application to classical or concrete problems, by solving problems.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Mathematics （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). ・To acquire skills to formulate and solve mathematical questions.
Class Objectives /Class Outline	Solve problems on Galois theory and its applications, according to Algebra B.
Class Schedule	According to Algebra B, solve problems about the subjects below. lesson1 Algebraic equations and Galois theory, field theory lesson2 Rings and fields, 1 lesson3 Rings and fields, 2 lesson4 Polynomial ring over a field, 1 lesson5 Polynomial ring over a field, 2 lesson6 Field extensions lesson7 Characteristic, finite fields lesson8 Irreducibility criteria for polynomials lesson9 Summary, 1 lesson10 Galois extension and Galois group lesson11 Examples of Galois group and Galois correspondence lesson12 Galois groups and algebraic equations lesson13 Proof of fundamental theorems lesson14 Summary, 2 lesson15 Geometric problems and Galois theory, field theory There might be quizzes and report assignments. There is a possibility of having mid-term and final exams jointly with Algebra B. Detailed explanation will be given in the class. The contents and schedule might change.
Text/Reference Books,etc.	Announced in the class.
PC or AV used in Class,etc.
(More Details)	handouts, blackboard
Learning techniques to be incorporated
Suggestions on Preparation and Review	Please participate actively. Read all problems and try to give answers. Examine other students' answers.
Requirements	It is recommended that you take Algebra B.
Grading Method	Marks will be based on presentations, reports, quizzes, and exams(if any).
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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