Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year School of Science HA135000 Specialized Education 代数学II演習 ダイスウガク２エンシユウ Exercises in Algebra ＩＩ SHIMADA ICHIROU シマダ　イチロウ Higashi-Hiroshima 2nd-Year,  Second Semester,  3Term (3T) Tues9-10,Thur3-4：SCI E104 Seminar Mainly lectures. Depending on the situation, lectures might be given online. 1.0 J : Japanese 2 : Undergraduate Low-Intermediate 25 : Science and Technology 01 : Mathematics/Statistics binary operation, algebraic system, group, homomorphism, axiom, equivalence relation Mathematics（Knowledge and Understanding）・Understanding classical basic theory which is a base of modern mathematics.  Being able to find and explain issues from specific events.（Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). Solve problems on the basics of the group theory. The goal is to understand the basic theory of groups, to become familiar with the abstract algebra, to learn to give proofs of propositions on groups and to do calculations on concrete examples related to groups. lesson1 Introduction/Sets, maps and binary operationslesson2 Semigroups, monoids and groupslesson3 Elementary properties of groupslesson4 Examples of groupslesson5 Subgroupslesson6 Residue classes and residue sets 1lesson7 Residue classes and residue sets 2lesson8 A theorem of Lagrange, Fermat's little theoremlesson9 Midterm reviewlesson10 Homomorphismlesson11 Normal subgroups and quotient groupslesson12 Fundamental theorem on homomorphisms 1lesson13 Fundamental theorem on homomorphisms 2lesson14 Finitely generated abelian groups 1lesson15 Finitely generated abelian groups 2There might be a final exam, mid-term exam and quizzes. Depending on the situation, reports might be used for evaluation. The content and schedule might change. Announced in the class. Handouts will be distributed. Read and think about all problems. It is recommended that you take Algebra II. Mainly based on the answers to the problems and results of exams and quizzes. 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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