| 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
（Katakana） |
ダイスウガク１エンシユウ |
Subject Name in
English |
Exercises in Algebra I |
| Instructor |
TAKAHASHI NOBUYOSHI,SUKENAGA MASAYUKI |
Instructor
(Katakana) |
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
Program
(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
Evaluation
(Applicable only to targeted subjects for undergraduate students) | 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). |
|---|
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. |
Text/Reference
Books,etc. |
Announced in the class. |
PC or AV used in
Class,etc. |
|
| (More Details) |
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
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 |
|
| 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. |