Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year School of Science HB050000 Specialized Education 代数学Ｂ演習 ダイスウガクBエンシュウ Exercises in Algebra B TAKAHASHI NOBUYOSHI,KOREEDA YOSHIMUNE タカハシ　ノブヨシ,コレエダ　ヨシムネ Higashi-Hiroshima 3rd-Year,  Second Semester,  4Term (4T) Tues3-4,Thur7-8：SCI B305 Seminar Solve problems, and give presentations on the solutions with the blackboard. Depending on the situation, classes might be held online. 2.0 J : Japanese 3 : Undergraduate High-Intermediate 25 : Science and Technology 01 : Mathematics/Statistics Field, Galois theory, polynomial equation, geometric problems Learn Galois theory, which is one of basic theories in today's mathematics, and its application to classical or concrete problems, by solving problems. 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. Solve problems on Galois theory and its applications, according to Algebra B. According to Algebra B, solve problems about the subjects below. lesson1 Algebraic equations and Galois theory, field theorylesson2 Rings and fields, 1lesson3 Rings and fields, 2lesson4 Polynomial ring over a field, 1lesson5 Polynomial ring over a field, 2lesson6 Field extensionslesson7 Characteristic, finite fieldslesson8 Irreducibility criteria for polynomialslesson9 Summary, 1lesson10 Galois extension and Galois grouplesson11 Examples of Galois group and Galois correspondence lesson12 Galois groups and algebraic equationslesson13 Proof of fundamental theoremslesson14 Summary, 2lesson15 Geometric problems and Galois theory, field theoryThere 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. Announced in the class. handouts, blackboard Please participate actively. Read all problems and try to give answers. Examine other students' answers. It is recommended that you take Algebra B. Marks will be based on presentations, reports, quizzes, and exams(if any). 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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