| Academic Year |
2024Year |
School/Graduate School |
School of Science |
| Lecture Code |
HA100000 |
Subject Classification |
Specialized Education |
| Subject Name |
代数学I |
Subject Name
（Katakana） |
ダイスウガク１ |
Subject Name in
English |
Algebra I |
| Instructor |
TAKAHASHI NOBUYOSHI |
Instructor
(Katakana) |
タカハシ ノブヨシ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
2nd-Year, First Semester, 1Term |
| Days, Periods, and Classrooms |
(1T) Tues3-4：SCI E104, (1T) Thur1-2：SCI E209 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
|
| Mainly lectures. Depending on the situation, lectures might be given online. |
| Credits |
2.0 |
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 |
As a continuation of Linear Algebra I and II, the theory of linear spaces will be explained. Jordan normal forms will be discussed. |
| Class Schedule |
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-term examination
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
A final exam is planned. There might be a mid-term exam and quizzes. Depending on the situation, reports might be used for evaluation.
The content and schedule might change. |
Text/Reference
Books,etc. |
Announced in the class. |
PC or AV used in
Class,etc. |
|
| (More Details) |
Slides, videos (when necessary) |
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
Read definitions, propositions and theorems(statements and proof) etc. carefully, and try to think how they apply to examples. |
| Requirements |
It is recommended that you take Excersises in Algebra I. |
| Grading Method |
Mainly based on exams. There might be quizzes and report assignments. Detailed explanations will be given in the class. |
| 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. |