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] | | | Probability is playing an essential role in many research fields, and in particular for describing complex systems. Our goal is to provide the necessary background information for understanding the use and the power of probability. Thus, we shall study the basic abstract theory of probability, and discuss some applications according to the interest and to the motivation of the students. The presentation will be accessible to all students, independently of their major. |
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授業の内容や構成
Course Content or Plan | | The main topics covered will be (tentative program)
1) Events and probabilities
2) Discrete valued random variables
3) Multivariate discrete distributions
4) Probability generating function
5) Distribution function and density function
6) Multivariate distributions and independence
7) Moments and moment generating functions
8) The main limit theorems
9) Branching processes
10) Random walk (1D)
11) Random process in continuous time |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | | 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 need an approval from the instructor. |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | | 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. Achievement of the objectives stated in the [Objectives of the Course] section will be considered the criterion for passing the course. 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
Textbook | | | Free textbooks will be provided during the lectures |
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参考書
Reference Book | | | Free reference books will be provided during the lectures. Lecture notes will also be available. |
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課外学修等
Study Load (Self-directed Learning Outside Course Hours) | | | 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 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
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 | | |
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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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