Course Objectives
Learning purposes : Learn geometry, especially topology.
Course Objectives :
1. To understand topology, sets, and Euler's theorem.
2. To understand metric and topological spaces, continuity, closed surfaces, and groups.
Rubric
| Excellent | Good | Acceptable | Not acceptable |
| Achievement 1 | Fully understands the concepts of Topology, Sets, and Euler's theorem. | Understands the concepts of Topology, Sets, and Euler's theorem. | Understands the basic concepts of Topology, Sets, and Euler's theorem. | Insufficient understanding of Topologies, Sets, and Euler's theorem. |
| Achievement 2 | Fully understands the concept of Metric Space and Topological Space, Continuity, closed surface, and group. | Understands the concept of Metric Spaces and Topological Spaces, Continuity, closed surfaces, and groups. | Understands the basic concepts of Metric and Topological Spaces, Continuity, closed surfaces, and groups. | Insufficient understanding of Metric and Topological Spaces, Continuity, closed surfaces, and groups. |
Assigned Department Objectives
Teaching Method
Outline:
General or Specialized : Specialized
Field of learning : Mathematics / Physics
Foundational academic disciplines : Algebra, Geometry and Related fields / Geometry Related
Relationship with Educational Objectives : This class is equivalent to "(3) Acquire deep foundational knowledge of the major subject area".
Relationship with JABEE programs : The main goals of learning / education in this class are "(A), A-1".
Course outline : The rudimentary part of topology is an area that can be understood without any prior knowledge of mathematics. There are many parts of this field that lead to results by logical manipulation using the definitions, and learning this field is good training for thinking logically through appropriate mathematical thinking. Looking at the beautiful mathematical world and understanding its structure indirectly helps us to understand many mathematical phenomena around us.
Style:
Course method : Classes will be centered on board writing, but at the same time, as much exercise time as possible will be provided so that students can understand the content of the lecture more deeply and acquire the ability to solve problems on their own.
Grade evaluation method : Evaluate the total of two regular exams (60% evaluated equally) and other exams, exercises, reports, and lesson approaches (40%). Depending on the grades, etc., a re-examination may be conducted (report submission is required). The retest will be evaluated in the same way as the main test, with an upper limit of 80 points.
Notice:
Precautions on the enrollment : Students must take this class (no more than one-third of the required number of class hours missed) in order to complete the 5th year course.
Course advice : It is important to make sure to prepare and review, and to understand the lecture contents more deeply by solving the exercises on your own.
Foundational subjects : Fundamental Mathematics (1st year), Fundamental Mathematics Practice (1st), Differential and Integral Ⅰ(2nd), Fundamental Linear Algebra (2nd), Integrated Science and Technology Practice (2nd), Differential and Integral Ⅱ (3rd), Basic Calculus (3rd), Mathematics for General Education (3rd), Integrated Mathematics Practice (3rd), Applied Mathematics Ⅰ (4th), Applied Mathematics Ⅱ (4th), Set Theory and General Topology (4th)
Related subjects : Mathematics in general
Attendance advice : It is important to understand the content of the lecture well and solve the problem by yourself. I want you to value finding a solution on your own. If you are late a lot, you may be treated as absent after giving a warning.
Characteristics of Class / Division in Learning
Course Plan
|
|
|
Theme |
Goals |
| 1st Semester |
| 1st Quarter |
| 1st |
Guidance, What is topology? |
Understand the expansion and contraction of figures and the extraction of features of figures.
|
| 2nd |
The set and the world that spreads from it
Learning content outside class hours: Report assignment (1) "The set and the world that spreads from it" |
Understand what a set is.
|
| 3rd |
The set and the world that spreads from it
Learning content outside class hours: Report assignment (1) "The set and the world that spreads from it" |
Understand relationships, mappings and transformations.
|
| 4th |
Euler's theorem
Learning content outside class hours: Report assignment (2) "Euler's theorem" |
Understand the relationship between points, sides, and faces of plane figures and solid figures.
|
| 5th |
Euler's theorem
Learning content outside class hours: Report assignment (2) "Euler's theorem" |
Examine the type of regular polyhedron.
|
| 6th |
Metric space and topological space
Learning content outside class hours: Report assignment (3) "Metric space and topological space" |
Understand the neighborhoods and general topological spaces in Euclidean space and Euclidean space.
|
| 7th |
1st semester mid-term exam |
|
| 8th |
Return and commentary of exam answers |
|
| 2nd Quarter |
| 9th |
What does it mean to change smoothly-continuity-
Learning content outside class hours: Report assignment (4) "What does it mean to change smoothly-continuity-" |
Understand the "continuity" of functions.
|
| 10th |
What does it mean to change smoothly-continuity-
Learning content outside class hours: Report assignment (4) "What does it mean to change smoothly-continuity-" |
Understanding the "continuity", discontinuous mapping, and homeomorphism of topological to topological maps
|
| 11th |
Thinking with a development view-the world of closed surfaces-
Learning content outside of class hours: Report assignment (5) "Thinking with a development view-a world of closed surfaces-" |
Understand the development of cubes and "glue".
|
| 12th |
Thinking with a development view-the world of closed surfaces-
Learning content outside of class hours: Report assignment (5) "Thinking with a development view-a world of closed surfaces-" |
Understand the projective plane and its properties.
|
| 13th |
Consider the algebraic structure of a group
Learning content outside class hours: Report assignment (6) "Thinking about the algebraic structure of groups" |
Understand the definition of groups and examples.
|
| 14th |
Consider the algebraic structure of a group
Learning content outside class hours: Report assignment (6) "Thinking about the algebraic structure of groups" |
Understand the generator of groups, the fundamental theorem on homomorphism with normal subgroups, and the commutative group with commutators.
|
| 15th |
(1st semester final exam) |
|
| 16th |
Return and commentary of exam answers |
|
Evaluation Method and Weight (%)
| Examination | Presentation | Mutual Evaluations between students | Behavior | Portfolio | Other | Total |
| Subtotal | 60 | 0 | 0 | 0 | 0 | 40 | 100 |
| Basic Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| Specialized Proficiency | 60 | 0 | 0 | 0 | 0 | 40 | 100 |
| Cross Area Proficiency | 0 | 0 | 0 | 0 | 0 | 0 | 0 |