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授業の目的 【英語】
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【Standardized across all programs】 In a global and interconnected society, mathematics play a central role. They are at the root of all communications tools, and serve as a universal language for natural and social sciences. All current technological developments are based on them. Mathematics can also be learned, enjoyed, and shared by everybody. Studying mathematics is also learning humility, tolerance, and diversity.
The aim of these Special Mathematics Lectures is to provide a solid knowledge on various mathematical topics. Concomitantly, students will develop a rigorous argumentation and a critical thinking. Each semester, a new subject is proposed, and these lectures are accessible to all students of Nagoya University, independently of their major and of their academic age. These special lectures also offer a unique opportunity to study in an international, transdisciplinary, and friendly environment.
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授業の達成目標 【英語】
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Differential geometry plays a central role in many physical theory, as for example in classical mechanics, in solid states physics or in general relativity. During this one semester course, many essential notions will be introduced, among them the definitions of a manifold, of the curvature, of the parallel transport, of the holonomy, etc. By attending this course, students will get familiar with these notions, and will master the fundamental difference between extrinsic and intrinsic geometrical properties.
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授業の内容や構成
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The following subjects will be studied during this course (tentative program)
I) Differentiable manifolds
II) Tensors, tensor fields and differential forms
III) Integration on manifolds
IV) Riemannian manifolds
V) Curvature
VI) General relativity
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履修条件・関連する科目
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Basic knowledge on calculus and linear algebra, as provided in Calculus I & II and in Linear algebra I & II. Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.
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成績評価の方法と基準
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The final grade will be based on the active participation during the lectures and on some written reports. Students will be encouraged to work on applications related to their major during the semester. Students need to notify the course withdrawal to the instructor when they have no intention of finishing the course during the semester.
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教科書
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Free textbooks will be provided during the lectures
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参考書
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Free reference books will be provided during the lectures
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課外学修等
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Students are expected to read their notes, and to be familiar with the content of the previous lectures before each new lecture.
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注意事項
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It is expected that the students will show a certain maturity in studying independently and in choosing some exercises and problems to solve. Study sessions might be organized on a weekly basis.
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本授業に関するWebページ
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担当教員からのメッセージ
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実務経験のある教員等による授業科目（大学等における修学の支援に関する法律施行規則に基づくもの）
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授業開講形態等
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B-3）Face-to-face course（both simultaneous interactive and on-demand methods will be provided when necessary)
対面授業の場合の講義室は、時間割B表（名大ポータル>教養教育院ページ掲載）を確認すること。
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