HB040000 Algebra B

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HB040000 Subject Classification Specialized Education

Subject Name 代数学Ｂ

Subject Name
（Katakana）ダイスウガクB

Subject Name in
English Algebra B

Instructor TAKAHASHI NOBUYOSHI

Instructor
(Katakana) タカハシ　ノブヨシ

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

Days, Periods, and Classrooms (4T) Tues1-2,Thur5-6：SCI B305

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 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) Understand Galois theory, which is one of basic theories in today's mathematics, and learn how it is applied to classical or concrete problems.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Mathematics
（Knowledge and Understanding）
・Understanding on primary theory of modern mathematics established on classical theory.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).

Class Objectives
/Class Outline Explain the basics of field theory, especially Galois theory. As applications, solutions to polynomial equations and geometric problems are discussed.

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

There will be a final exam. There might be quizzes and report assignments. In case of mid-semester exam, there will be an announcement. 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) Slides, videos (when necessary)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Review linear algebra, basics of group theory and ring theory. Try to examine what is told in lectures by concrete examples.

Requirements It is recommended you take Exercises in Algebra B.

Grading Method Mainly based on exams. Quizzes and reports might be considered. 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	HB040000	Subject Classification	Specialized Education
Subject Name	代数学Ｂ
Subject Name （Katakana）	ダイスウガクB
Subject Name in English	Algebra B
Instructor	TAKAHASHI NOBUYOSHI
Instructor (Katakana)	タカハシ　ノブヨシ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Tues1-2,Thur5-6：SCI B305
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	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)	Understand Galois theory, which is one of basic theories in today's mathematics, and learn how it is applied to classical or concrete problems.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Mathematics （Knowledge and Understanding）・Understanding on primary theory of modern mathematics established on classical theory. （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
Class Objectives /Class Outline	Explain the basics of field theory, especially Galois theory. As applications, solutions to polynomial equations and geometric problems are discussed.
Class Schedule	lesson1 Algebraic equations and Galois theory, field theory lesson2 Geometric problems and Galois theory, field theory lesson3 Rings and fields, 1 lesson4 Rings and fields, 2 lesson5 Polynomial ring over a field, 1 lesson6 Polynomial ring over a field, 2 lesson7 Field extensions lesson8 Characteristic, finite fields lesson9 Irreducibility criteria for polynomials lesson10 Summary, 1 lesson11 Galois extension and Galois group lesson12 Examples of Galois group and Galois correspondence lesson13 Galois groups and algebraic equations lesson14 Proof of fundamental theorems lesson15 Summary, 2 There will be a final exam. There might be quizzes and report assignments. In case of mid-semester exam, there will be an announcement. 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)	Slides, videos (when necessary)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Review linear algebra, basics of group theory and ring theory. Try to examine what is told in lectures by concrete examples.
Requirements	It is recommended you take Exercises in Algebra B.
Grading Method	Mainly based on exams. Quizzes and reports might be considered. 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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