Hiroshima University Syllabus

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Academic Year 2024Year School/Graduate School School of Science
Lecture Code HA115000 Subject Classification Specialized Education
Subject Name 代数学I演習
Subject Name
Subject Name in
Exercises in Algebra I
タカハシ ノブヨシ,スケナガ マサユキ
Campus Higashi-Hiroshima Semester/Term 2nd-Year,  First Semester,  1Term
Days, Periods, and Classrooms (1T) Tues7-8,Thur3-4:SCI E104
Lesson Style Seminar Lesson Style
(More Details)
Solve problems. Depending on the situation, classes might be held 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 Linear space, linear map, Jordan normal form 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
(Applicable only to targeted subjects for undergraduate students)
Linear algebra is a classical and basic theory which is at the base of the modern mathematics. 
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
In association with Algebra I, learn how to solve problems related to linear algebra, Jordan normal forms and their applications.  
Class Schedule According to Algebra I, solve problems about the subjects below.

lesson1 Linear spaces: axioms and examples
lesson2 Linear combinations, basis, dimension
lesson3 Change of basis
lesson4 Linear maps, matrix representation
lesson5 Kernel, image, dimension formula
lesson6 Scalar product, metric vector space
lesson7 Quadratic forms
lesson8 Mid-semester summary
lesson9 Eigenvalues, eigenvectors, eigenspaces
lesson10 Generalized eigenspaces
lesson11 Nilpotent matrices
lesson12 Jordan normal forms, 1
lesson13 Jordan normal forms, 2
lesson14 Applications of Jordan normal forms, 1
lesson15 Applications of Jordan normal forms, 2

There is a possibility of having quizzes and report assignments. Also, there is a possibility of having a mid-term or final exam jointly with the lecture. Detailed explanation will be given in the class.

The contents and schedule might change. 
Announced in the class. 
PC or AV used in
(More Details)  
Learning techniques to be incorporated  
Suggestions on
Preparation and
Please participate actively. Read all problems and try to give answers. Examine other students' answers. 
Requirements It is recommended that you take Algebra I. 
Grading Method Based mainly on presentations, quizzes (if any), reports (if any), and examinations (if any).  
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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