The goal of the course is for students to learn deep learning and how to present their learning by investigating, thinking, and understanding each topic of topology and geometry on their own under the advice of the instructor.
Outline:
Students will select a topic they wish to study more deeply from among the topological and geometric topics studied in Liberal Arts Seminar 1, and conduct group study activities on the same topic.
Through group study activities and presentations, students will learn how to write and present their research results, which can be applied to their graduation research in the fifth year.
Style:
Students will be divided into groups to present their studies on several themes related to topology and geometry.
Students will prepare to present the results of their group study at symposiums and other venues.
Students are evaluated comprehensively on their class attitude, the content of their presentations, and their learning products.
Notice:
This course is a full-year course.
This course is also offered to other colleges of NIT.
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Theme |
Goals |
| 2nd Semester |
| 3rd Quarter |
| 1st |
Guidance |
The instructor will give an overview of the content of the course so that students can get an idea of what they will be studying on their own or in groups in this course.
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| 2nd |
Thematic Development Activities (1) |
Students will understand the meaning of homeomorphism and can calculate Euler numbers.
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| 3rd |
Thematic Development Activities (2) |
Students will understand the concepts of congruence and knots, as well as understand how to derive the tricolorability which is one of knot invariants and can calculate it.
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| 4th |
Thematic Development Activities (3) |
Students will understand how to derive the Goeritz invariant which is one of the knot invariants and can calculate it.
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| 5th |
Thematic Development Activities (4) |
As an extension of the vector space studied in the third year, students will learn the definition of a group and its examples to understand the concept.
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| 6th |
Presentation of studies by groups (1) |
Students will study topics of interest from those studied in the four lectures and present their findings.
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| 7th |
Thematic Development Activities (5) |
Students will understand the derivation and the calculation method of fundamental groups obtained by classifying sets consisting of loops from the closed interval [0, 1] to a figure by a certain equivalence relation.
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| 8th |
Thematic Development Activities (6) |
Student will understand the concept of the L-S category, which is the minimum number to cover a figure with a contractible open set, and how to compute it.
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| 4th Quarter |
| 9th |
Thematic Development Activities (7) |
Student will understand the concept of curvature determined for curves in planes and space and can calculate it.
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| 10th |
Thematic Development Activities (8) |
Students will understand the concept of torsion determined for curves in space and can calculate it.
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| 11th |
Presentation of studies by groups (2) |
Students will study topics of interest from those studied in the four lectures and present their findings.
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| 12th |
Thematic Development Activities (9) |
Students will understand the parametric equation for various surfaces.
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| 13th |
Thematic Development Activities (10) |
Students will understand the concept of curvature for surfaces and can calculate it.
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| 14th |
Thematic Development Activities (11) |
Students will understand the concept of the simplicial complex and its properties.
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| 15th |
Thematic Development Activities (12) |
Students will understand the concept of homology groups determined for simplicial complexes and can calculate several homology groups.
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| 16th |
Presentation of studies by groups (3) |
Students will study topics of interest from those studied in the four lectures and present their findings.
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