Liberal Arts Seminar 1 (Topology and Geometry)

Course Information

College	Kurume College	Year	2024
Course Title	Liberal Arts Seminar 1 (Topology and Geometry)
Course Code	4AR09	Course Category	General / Compulsory
Class Format	Lecture	Credits	School Credit: 1
Department	Department of Mechanical Engineering	Student Grade	4th
Term	First Semester	Classes per Week	2
Textbook and/or Teaching Materials	Reference book: Osami YAMAMOTO, Yokuwakaru Topology, Morikita Publishing Co (in Japanese)
Instructor	酒井道宏

Course Objectives

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.

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Achievement 1	Students can engage in independent learning activities without the advice of faculty members.	Students can engage in independent learning activities under the advice of faculty members.	Students cannot engage in independent learning activities even if the faculty members advise them to do so.
Achievement 2	Students can think logically without the advice of faculty members.	Students can think logically under the advice of faculty members.	Students cannot think logically even if the faculty members advise them to do so.
Achievement 3	Students can present the results of their studies without the advice of faculty members.	Students can present the results of their studies under the advice of faculty members.	Students can present the results of their studies even if the faculty members advise them to do so.

Assigned Department Objectives

4 See

Teaching Method

Outline:

In topology, students will study classification of figures using topological invariants such as Euler numbers, classification of knots using knot invariants, and homology groups and their computation methods as an application of linear algebra. In geometry, students will study curvature and torsion of curves and curvature of surfaces.
Students will give presentations on the topics they have studied in order to prepare for group study in the second semester and to learn presentation methods that can be applied to their graduation research in the fifth year.

Style:

Lectures will be given on various topics related to topology and geometry.
Students will give presentations on topics of interest and study in each of the four lectures.
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.
Students from other colleges of NIT may take this course for a half year.

Characteristics of Class / Division in Learning

Active Learning	Aided by ICT	Applicable to Remote Class	Instructor Professionally Experienced

Course Plan

			Theme	Goals
1st Semester
	1st 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.
		2nd	Classification of figures and its applications	Students will understand the meaning of homeomorphism and can calculate Euler numbers.
		3rd	Congruence and its applications	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.
		4th	Goeritz invariant and its applications	Students will understand how to derive the Goeritz invariant which is one of the knot invariants and can calculate it.
		5th	Group	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.
		6th	Presentation of study	Students will study topics of interest from those studied in the four lectures and present their findings.
		7th	Fundamental group	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.
		8th	L-S category	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.
	2nd Quarter
		9th	Curvature of curves	Student will understand the concept of curvature determined for curves in planes and space and can calculate it.
		10th	Torsion of space curves	Students will understand the concept of torsion determined for curves in space and can calculate it.
		11th	Presentation of study	Students will study topics of interest from those studied in the four lectures and present their findings.
		12th	Parametric equation of surfaces	Students will understand the parametric equation for various surfaces.
		13th	Curvature of surfaces	Students will understand the concept of curvature for surfaces and can calculate it.
		14th	Simplicial complex	Students will understand the concept of the simplicial complex and its properties.
		15th	Homology group	Students will understand the concept of homology groups determined for simplicial complexes and can calculate several homology groups.
		16th	Presentation of study	Students will study topics of interest from those studied in the four lectures and present their findings.

Evaluation Method and Weight (%)

	Test	Presentation	Peer review	Class attitude	Self-assessment	Learning products	Total
Subtotal	0	50	10	10	10	20	100
Basic Proficiency	0	50	10	10	10	20	100
Specialized Proficiency	0	0	0	0	0	0	0
Cross Area Proficiency	0	0	0	0	0	0	0