Course Objectives
Learning purposes: 1. To acquire basic knowledge about algebra, which is the basis of modern mathematics.
2. To understand the basic properties of one complex and quaternion.
3. To acquire basic knowledge about group theory.
4. To acquire basic knowledge about abstract vector spaces.
Rubric
| Excellent | Good | Acceptable | Unacceptable Level |
| Achievement 1 | Has good understanding of quaternions and the rotation of space. | Understands about 70% of quaternions and the rotation of space. | Understands about 60% of quaternions and the rotation of space. | Doesn't understand about 60% of quaternions and the rotation of space. |
| Achievement 2 | Has a good understanding of groups and linear expressions. | Understands about 70% of groups and linear expressions. | Understands about 60% of groups and linear expressions. | Doesn't understand about 60% of groups and linear expressions. |
| Achievement 3 | Fully understands the idea of abstract vector space and the idea of linear expression. | Understands about 70% of content on abstract vector space and linear expressions. | Understands about 60% of content on abstract vector space and linear expressions. | Doesn't understand about 60% of abstract vector space and linear expressions. |
Assigned Department Objectives
Teaching Method
Outline:
General or Specialized : Specialized
Field of learning : Mathematics / Physics (Specialized Subjects)
Required, Elective: Elective must complete subjects
Foundational academic disciplines : Mathematical science / Mathematics / Basic analysis
Relationship with Educational Objectives : This class is equivalent to "(3) Acquire deep foundation knowledge of the major subject ares
Relationship with JABEE programs : The main goals of this are "(A) , A-1.
Class outline: The basics of algebra. The theory of complex numbers and quaternions, the basic theory of group theory, and the basic theory of abstract vector spaces are explained.
Style:
Course method : In addition to lectures, practice in group discussions to learn the basics of algebra.
Grade evaluation method : Evaluation is based on the results of two regular examinations (50%) and the exercise report (50%). In addition, depending on the grade, an additional report may be assigned.
Notice:
Course Plan
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Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Definition of complex numbers, body structure and rotation of two-dimensional space |
Understand what a complex number field is
|
| 2nd |
Definition of quaternion and body structure |
Understand what a quaternion is
|
| 3rd |
Quaternion and rotation of 3D space |
Understand the benefits of rotating 3D space with quaternions
|
| 4th |
Group definition and replacement |
Understand what a group is
|
| 5th |
Symmetric groups and subgroups |
Understand the structure of symmetric groups and their subgroups
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| 6th |
Homomorphism theorem and its application |
Understand what homomorphisms are
|
| 7th |
First term midterm exam |
Comprehensive understanding of the basics of complex fields, quaternions, and group theory
|
| 8th |
Definition of abstract vector space and subspace |
Understand what an abstract vector space is
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| 2nd Quarter |
| 9th |
Sum and scalar times of linear map |
Understand what a linear map is
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| 10th |
Cartesian product and direct sum |
Understand the difference between direct sum and direct sum
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| 11th |
Matrix space and linear map space |
Understand concrete examples of vector spaces
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| 12th |
Dual space |
Understand what is dual space
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| 13th |
Equivalence relations and quotient sets |
Understand what is equivalent and what is split by equivalent
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| 14th |
Commercial space |
Understand the commercial space
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| 15th |
Last term exam |
Comprehensive understanding of the basics of abstract vector spaces
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| 16th |
Answers and explanations for the final exam |
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| 2nd Semester |
| 3rd Quarter |
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| 8th |
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| 4th Quarter |
| 9th |
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| 16th |
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Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
| Subtotal | 50 | 0 | 0 | 0 | 0 | 50 | 100 |
| Basic Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Specialized Proficiency | 50 | 0 | 0 | 0 | 0 | 50 | 100 |
| Cross Area Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |