授業の目的 【英語】
Goals of the Course [ENG] | | 【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】
Objectives of the Course [ENG] | | | To acquire basic knowledge of topological spaces and their properties by studying a variety of examples. Students will also obtain an elementary understanding of homotopy theory as a gateway to further studies in algebraic topology. |
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授業の内容や構成
Course Content or Plan | | The topic will be an introduction to topology, which is a mathematical framework to understand continuity and equivalence in much more general settings. We will also give a basic overview of homotopy theory, which is one example of the interaction of topology with abstract algebra.
Planned content (tentative):
Metric spaces
- open/closed sets
- continuity and completeness
- compactness
Topological spaces
- open/closed sets, bases, separation axioms
- continuous maps and homeomorphisms
- subspaces and quotient spaces
- compactness and connectedness
Homotopy
- homotopic paths and the fundamental group
- covering spaces
- higher dimensional homotopy
この科目は英語で行います．
内容は位相空間（あるいはトポロジー）の入門です．位相空間を用い，より一般の設定において関数の連続性や空間の同型を定義できます．また代数的位相幾何学の例として，ホモトピーの基礎を紹介します． |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | A working knowledge of calculus (such as that obtained from the Calculus I and II courses) will be expected. Some knowledge of linear algebra and group theory will also be helpful, but is not required.
Motivated 1st year students can also attend without these prerequisites but after a discussion with the instructor.
微分積分の知識を期待しますが，やる気であれば，誰でも受講する可能です．線形代数学か群論を勉強したことが役に立ちますが，必要ではありません．1年生も担当者と相談後，履修は可能です． |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | The grade will be determined by exercises and homework questions submitted by students throughout the semester. Achievement of the objectives stated in the [Objectives of the Course] section will be considered the criterion for passing the course.
Students who wish to withdraw from the topic are asked to inform the instructor. |
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教科書
Textbook | | Theodore W. Gamelin and Robert E. Greene, Introduction to Topology (2nd edition), Dover Publications, 1999
It is not necessary to purchase this textbook.
Lecture summary notes and other references will also be distriubuted. |
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参考書
Reference Book | | Martin D. Crossley, Essential Topology, Springer, 2005
James R. Munkres, Topology, Prentice Hall, 2000 |
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課外学修等
Study Load (Self-directed Learning Outside Course Hours) | | | Exercises and homework questions will be given to students. 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
Notice for Students | | | 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 semi-regular basis. |
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本授業に関するWebページ
Reference website for this Course | | |
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担当教員からのメッセージ
Message from the Instructor | | The course is a great opportunity to learn mathematics in an international environment.
日本人が含まれる一般プログラムの学生へ:
授業の参加・受講は大歓迎です！NU-EMIプロジェクトのおかげで，留学生のチューターによるサポートが無料で提供されています． |
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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）
Courses taught by Instructors with practical experience | | |
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授業開講形態等
Lecture format, etc | | B-3）Face-to-face course （both simultaneous interactive and on-demand methods will be provided when necessary)
* The classroom for face-to-face classes is listed in Timetable B on the ILAS website. |
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