
住所: 〒464-8602 愛知県名古屋市千種区不老町

ファイル更新日：2024年03月06日

教育・就職

■少人数クラスシラバス■

●S. リシャール

学部・大学院区分 Undergraduate / Graduate	多・博前
時間割コード Registration Code
科目区分 Course Category	B類(講究) C類(実習)/Category B Category C
科目名【日本語】 Course Title	関数解析講究1 関数解析講究2 関数解析講究3 関数解析講究4 関数解析実習1 関数解析実習2 関数解析実習3 関数解析実習4
科目名【英語】 Course Title	Seminar on Functional Analysis 1 Seminar on Functional Analysis 2 Seminar on Functional Analysis 3 Seminar on Functional Analysis 4 Practical Class on Functional Analysis 1 Practical Class on Functional Analysis 2 Practical Class on Functional Analysis 3 Practical Class on Functional Analysis 4
コースナンバリングコード Course Numbering Code
担当教員【日本語】 Instructor	リシャールセルジュ
担当教員【英語】 Instructor	Serge RICHARD
単位数 Credit	B類4単位 C類1単位
開講期・開講時間帯 Term / Day / Period	Determined with students
授業形態 Course style	セミナー
学科・専攻 Department / Program	多元数理科学研究科
必修・選択 Compulsory / Selected	選択必修

授業の目的【日本語】 Goals of the Course(JPN)
授業の目的【英語】 Goals of the Course	Develop the ability to read, understand, and communicate scientific material of any kind: books, papers, videos, etc. Acquire a solid knowledge in one specialized field, but extend the interest and understanding on various topics. Become an independent thinker and researcher.
到達目標【日本語】 Objectives of the Course(JPN)
到達目標【英語】 Objectives of the Course	The following two independent subjects are proposed: 1) Functional analysis: The aim is study functional analysis with a special emphasis on spectral theory. Scattering theory, index theory for $C^{*}$-algebras, non-commutative topology, are some of the possible topics studied during this seminar. 2) Data assimilation: The aim is to study various tools of data assimilation, and to work on some concrete problems. Once a sufficient understanding is reached, interactions with the data assimilation research team from RIKEN will be possible.
授業の内容や構成 Course Content / Plan	The seminar consists in regular meetings and oral presentations made by students. Each participant is working on a different subject and with a different support (book or articles). Everybody can benefit from the work of the other students though the presentations and the explanations provided. The seminars and the interactions are taking place in English.
履修条件 Course Prerequisites	1) Standard undergraduate courses of calculus and functional analysis. 2) Basic programming skill, or a strong motivation for studying realistic applications.
関連する科目 Related Courses	1) The master course provided each spring semester on a topic related to this seminar, as for example "$C^{}$-algebraic methods in spectral theory" (Spring 2022 & 2014), "$K$-theory for $C^{}$-algebras, and beyond" (Spring 2020 & 2015), "Introduction to functional analysis" (Spring 2019), "Scattering theory" (Spring 2018), "Dixmier traces" (Spring 2017), "Hilbert space methods for quantum mechanics" (Spring 2016). 2) The course "Introduction to data assimilation" (Spring 2022). See the following link for the corresponding lecture notes: http://www.math.nagoya-u.ac.jp/?richard/lecture_notes.html
成績評価の方法と基準 Course Evaluation Method and Criteria	Grade based on attendance, oral presentations, independent work, and a written report.
教科書・テキスト Textbook	As a starter, some of the lecture notes available on http://www.math.nagoya-u.ac.jp/~richard/lecture_notes.html
参考書 Reference Book	According to the interest of the students, several possible books will be proposed, as for example: - Hilbert space methods in quantum mechanics, Amrein, 2009 - $C^{}$-algebras and operator theory, Murphy, 1990 - An introduction to $K$-theory for $C^{}$-algebras, Rordam, Larsen, Laustsen, 2000 - Mathematical scattering theory: general theory, Yafaev, 1991 - Basic noncommutative geometry, Khalkhali, 2010 - Data Assimilation, a mathematical introduction, Law, Stuart, Zygalakis, 2014 - Probabilistic Forecasting and Bayesian Data Assimilation, Reich, Cotter, 2015
課外学習等 (授業時間外学習の指示) Study Load(Self-directed Learning Outside Course Hours)	Most of the work consists in reading, understanding, and sharing knowledge. Applications will depend on the interest of the students.
注意事項 Notice for Students	It is certainly easier to improve your English skill in the quiet environment of a seminar rather than later in a busy life.
質問への対応方法 How to Ask Questions	By email
他学科聴講の可否 Propriety of Other department student’s attendance
他学科聴講の条件 Conditions for Other department student’s attendance	This seminar is intended for master students from the graduate school of mathematics, but any motivated student can also attend it.
レベル Level
キーワード Keyword	Spectral theory, scattering theory, $C^{*}$-algebras, index theorems, data assimilation
履修の際のアドバイス Advice
授業開講形態等 Lecture format, etc.	This will be decided according to the students attending the seminar. In person meetings will be prefered, and online meetings will be chosen 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)	If necessary, some meetings will take place through Zoom.