授業の目的 【日本語】
Goals of the Course(JPN) | | この講義は講師三人によるオムニバス形式の英語講義である.
内容は英文を参照すること.
See English text. |
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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 (KASUYA Hisashi) Connections and Curvatures in differential geometry
Part II (SUGIMOTO Mitsuru) Fourier analysis and its applications
Part III (HAYASHI Masahito) Information-theoretic security |
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到達目標 【日本語】
Objectives of the Course(JPN)) | | 各講師ごとに与えられたテーマに則した問題について考察し, レポートを作成, 提出することによってテーマの理解を深める. 各テーマの内容は英文を参照すること.
See English text. |
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到達目標 【英語】
Objectives of the Course | | Part I (KASUYA Hisashi) Students should understand the importance of connections and curvatures in studying differential geometry.
Part II (SUGIMOTO Mitsuru) Students should understand how Fourier analysis is applied to various problems of mathematics.
Part III (HAYASHI Masahito) Understanding the basics of information-theoretical security. |
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授業の内容や構成
Course Content / Plan | | Part I (KASUYA Hisashi) In this part of the lecture, the role of connections and curvatures in geometry is explained.
Part II (SUGIMOTO Mitsuru) In this part of the lecture, the basic theory of Fourier analysis is introduced.
Part III (HAYASHI Masahito) Information theoretical security (Hayashi) Lecture 1. Notations on probability theory Lecture 2. Introduction of Information measure Lecture 3. Security measure Lecture 4. Hash function Lecture 5. Leftover hashing lemma |
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履修条件
Course Prerequisites | | Part I (KASUYA Hisashi) Undergraduate linear algebra, calculus and topology.
Part II (SUGIMOTO Mitsuru) Undergraduate calculus
Part III (HAYASHI Masahito) Undergraduate calculus and linear algebra. |
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関連する科目
Related Courses | | Part I (KASUYA Hisashi) Undergraduate linear algebra, calculus and topology
Part II (SUGIMOTO Mitsuru) Undergraduate calculus
Part III (HAYASHI Masahito) Undergraduate linear algebra, Undergraduate calculus, Undergraduate probability |
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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 (KASUYA Hisashi) Grading is based on reports.
Part II (HAYASHI Masahito) Grading is based on reports.
Part III (SUGIMOTO Mitsuru) Grading is based on a report that will be assigned at the end of the part.
At the end of the semester, by using the grades of the instructors, the final grade of the course will be determined. |
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教科書・テキスト
Textbook | | Part I (KASUYA Hisashi) Textbooks will not be used.
Part II (SUGIMOTO Mitsuru) Textbooks will not be used.
Part III (HAYASHI Masahito) |
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参考書
Reference Book | | Part I (KASUYA Hisashi) Recommended books will be introduced in the lecture.
Part II (SUGIMOTO Mitsuru) E. M. Stein & R. Shakarchi, Fourier Analysis: An Introduction, Princeton Lectures in Analysis
Part III (HAYASHI Masahito) Textbooks will not be used. |
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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) | | Part I (KASUYA Hisashi) Students are recommended to study by themselves the references given during the lecture.
Part II (SUGIMOTO Mitsuru) Students are recommended to study by themselves the references given above.
Part III (HAYASHI Masahito) Students are recommended to study by themselves the references given during the lecture. |
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注意事項
Notice for Students | | | If necessary, TACT will be used to make announcements. |
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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 | | |
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レベル
Level | | |
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キーワード
Keyword | | Part I (KASUYA Hisashi) Connection, curvature, differential geometry
Part II (SUGIMOTO Mitsuru) Fourier series, Fourier transformation
Part III (HAYASHI Masahito) Information Theory, Security, Independence |
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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. | | Part I (KASUYA Hisashi) Face-to-face lecture (+ TACT when necessary)
Part II (SUGIMOTO Mitsuru) Face-to-face lecture (+ TACT when necessary)
Part III (HAYASHI Masahito) Face-to-face lecture (+ TACT 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) | | |
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