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

EnglishAlgebra 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 OutlineExplain 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

ReviewReview 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.