学部・大学院区分
Undergraduate / Graduate		多・博前
時間割コード
Registration Code		3211002
科目区分
Course Category		Ａ類Ⅰ（基礎科目）
Category A-1
科目名　【日本語】
Course Title		数理科学展望Ⅱ
科目名　【英語】
Course Title		Perspectives in Mathematical Science II
コースナンバリングコード
Course Numbering Code
担当教員　【日本語】
Instructor		永尾　太郎 ○ 中西　知樹 石井　亮
担当教員　【英語】
Instructor		NAGAO Taro ○ NAKANISHI Tomoki ISHII Akira
単位数
Credits		2
開講期・開講時間帯
Term / Day / Period		秋 火曜日 ３時限
Fall Tue 3
授業形態
Course style
学科・専攻
Department / Program
多元数理科学専攻
必修・選択
Required / Selected
選択


授業の目的　【日本語】
Goals of the Course(JPN)
授業の目的　【英語】
Goals of the Course
The purpose of this course is to introduce and explain various concepts and methods in mathematical sciences. This year, the course is provided by three instructors.

Part I (ISHII Akira) Kleinian singularities and their resolutions

Part II (NAGAO Taro) Introduction to the theory of orthogonal polynomials

Part III (NAKANISHI Tomoki) Mysterious dilogarithm
到達目標　【日本語】
Objectives of the Course(JPN))
到達目標　【英語】
Objectives of the Course
Part I (ISHII Akira) Students should learn some basic ideas of algebraic geometry through examples of Kleinian singularities and their resolutions.

Part II (NAGAO Taro) Students should become familiar with basic concepts of orthogonal polynomials, and ready to apply them to scientific problems.

Part III (NAKANISHI Tomoki) Students should open their eyes for dilogarithm identities and their hidden algebraic perspective.
授業の内容や構成
Course Content / Plan
Part I (ISHII Akira) I explain finite subgroups of SL(2,C), invariant rings, quotient singularities and their resolutions. If time permits, I will discuss the McKay correspondence.

Part II (NAGAO Taro) In this part of the lecture, basic properties of orthogonal polynomial, such as recurrence relations, are given and well-known examples are introduced.

Part III (NAKANISHI Tomoki) I explain dilogarithm identities and their relation to root systems, Y-systems, and cluster algebras.
履修条件
Course Prerequisites
Part I (ISHII Akira) Undergraduate linear algebra and algebra

Part II (NAGAO Taro) Undergraduate linear algebra, calculus and complex analysis

Part III (NAKANISHI Tomoki) Nothing other than basic undergraduate calculus
関連する科目
Related Courses
Part I (ISHII Akira) Undergraduate linear algebra, algebra and complex analysis

Part II (NAGAO Taro) Undergraduate linear algebra, calculus and complex analysis

Part III (NAKANISHI Tomoki) Undergraduate calculus
成績評価の方法と基準
Course Evaluation Method and Criteria
In each part, the instructor will determine the grade in the following way.

Part I (ISHII Akira) Grading is based on report.

Part II (NAGAO Taro) Grading is based on a report (or reports).

Part III (NAKANISHI Tomoki) Grading is based on a report (or possibly an exam in the last lecture).

At the end of the semester, by using the grades of the instructors, the final grade of the course will be determined.
教科書・テキスト
Textbook
Part I (ISHII Akira) Textbooks will not be used.

Part II (NAGAO Taro) Textbooks will not be used.

Part III (NAKANISHI Tomoki) Textbooks will not be used.
参考書
Reference Book
Part I (ISHII Akira) Recommended books will be introduced in the lecture.

Part II (NAGAO Taro) Recommended books will be introduced in the lecture.

Part III (NAKANISHI Tomoki) Recommended books will be introduced in the lecture.
課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours)
Part I (ISHII Akira) Students are encouraged to compute examples.

Part II (NAGAO Taro) Students are recommended to study concrete examples.

Part III (NAKANISHI Tomoki) Some exercises are given.
注意事項
Notice for Students
If necessary, NUCT will be used to make announcements.
他学科聴講の可否
Propriety of Other department student's attendance
他学科聴講の条件
Conditions of Other department student's attendance
レベル
Level
2
キーワード
Keyword
Part I (ISHII Akira) invariant rings, resolutions of quotient singularities

Part II (NAGAO Taro) orthogonal polynomials, recurrence relations

Part III (NAKANISHI Tomoki) dilogarithm, root system, Y-system, cluster algebra
履修の際のアドバイス
Advice
授業開講形態等
Lecture format, etc.
Part I (ISHII Akira) Face-to-face lecture (+ NUCT when necessary)

Part II (NAGAO Taro) Face-to-face lecture (+ NUCT when necessary)

Part III (NAKANISHI Tomoki) Face-to-face lecture (+ NUCT when necessary)
遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class)