授業の目的 【日本語】
Goals of the Course(JPN) | | |
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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.
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到達目標 【日本語】
Objectives of the Course(JPN)) | | |
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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.
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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.
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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.
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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
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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.
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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
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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
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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.
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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.
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他学科聴講の可否
Propriety of Other department student's attendance | | |
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他学科聴講の条件
Conditions of 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.
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レベル
Level | | |
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キーワード
Keyword | | Spectral theory, scattering theory, C*-algebras, index theorems, data assimilation
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履修の際のアドバイス
Advice | | |
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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 preferred, and online meetings will be chosen when necessary.
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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) | | 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.
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