Hiroshima University Syllabus

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Academic Year 2024Year School/Graduate School School of Science
Lecture Code HA135000 Subject Classification Specialized Education
Subject Name 代数学II演習
Subject Name
Subject Name in
Exercises in Algebra II
シマダ イチロウ
Campus Higashi-Hiroshima Semester/Term 2nd-Year,  Second Semester,  3Term
Days, Periods, and Classrooms (3T) Tues9-10,Thur3-4:SCI E104
Lesson Style Seminar Lesson Style
(More Details)
Mainly lectures. Depending on the situation, lectures might be given online.  
Credits 1.0 Class Hours/Week   Language of Instruction J : Japanese
Course Level 2 : Undergraduate Low-Intermediate
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students
Keywords binary operation, algebraic system, group, homomorphism, axiom, equivalence relation 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
(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). 
Class Objectives
/Class Outline
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.  
Class Schedule lesson1 Introduction/Sets, maps and binary operations
lesson2 Semigroups, monoids and groups
lesson3 Elementary properties of groups
lesson4 Examples of groups
lesson5 Subgroups
lesson6 Residue classes and residue sets 1
lesson7 Residue classes and residue sets 2
lesson8 A theorem of Lagrange, Fermat's little theorem
lesson9 Midterm review
lesson10 Homomorphism
lesson11 Normal subgroups and quotient groups
lesson12 Fundamental theorem on homomorphisms 1
lesson13 Fundamental theorem on homomorphisms 2
lesson14 Finitely generated abelian groups 1
lesson15 Finitely generated abelian groups 2

There 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.  
PC or AV used in
(More Details) Handouts will be distributed.  
Learning techniques to be incorporated  
Suggestions on
Preparation and
Read and think about all problems.  
Requirements It is recommended that you take Algebra II.  
Grading Method Mainly based on the answers to the problems and results of exams and quizzes.  
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
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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