まず離散確率変数の場合に，確率論の基礎的な概念を復習し，大数の法則，中心極限定理，ポアソンの少数の法則など基本的な定理を述べることから始める。マルコフ連鎖，ランダムウォーク，統計力学への応用など幅広い話題にも触れる予定である。その後，ルベーグ積分論による確率論の基礎づけを行う。離散から連続へと自然に確率論の理解を深めていくことを目指す。確率論の多様な基礎科学への応用を知るとともに，現代確率論の考え方の基礎を身につけることが目標である。

By the end of the course, students will be able to: 1.　Identify how language ideologies shape social interactions. 2.　Analyze identity construction through discourse using sociolinguistic tools. 3.　Critically examine everyday, media, and institutional discourse for power dynamics. 4.　Reflect on their own linguistic positioning in multilingual, transnational contexts.

By the end of the course, students will be able to: 1.　Identify how language ideologies shape social interactions. 2.　Analyze identity construction through discourse using sociolinguistic tools. 3.　Critically examine everyday, media, and institutional discourse for power dynamics. 4.　Reflect on their own linguistic positioning in multilingual, transnational contexts.

連続時間ランダムウォークとしてのレヴィ過程、レヴィ過程に関する確率積分、確率微分方程式(SDE)に関する入門事項から入る。その後で、レヴィ駆動型SDEモデルの統計推測に関するいくつかのトピックを扱う。その背後にある汎用的な理論も解説する。計算機を用いたシミュレーションデモも実施する予定である（RパッケージYUIMA）。 We begin by introducing Lévy processes as continuous-time random walks, followed by an overview of stochastic integration and stochastic differential equations (SDEs). Subsequently, we present statistical inference theory for Lévy-driven SDE models, alongside the relevant general asymptotic theory. We also plan to conduct simulation demonstrations using a computer (R package YUIMA).

銀行や証券会社などの金融機関では、デリバティブと呼ばれる金融商品が取り扱われている。これらの商品の妥当な価格は、それに関連する株価や為替、金利などの市場変動に確率モデルを仮定することで、算出されている。 本講義ではまず、ポートフォリオ，デリバティブ等の金融用語の説明をはじめ，ファイナンスにおける基本的事項について解説する．そのうえで、デリバティブ価格を求めるための確率モデルが満たすべき性質、価格導出の原理などを考察する。これにより、新しい金融商品を考案したり、それを評価するための確率モデルを立て、価格を導出する上で必要となる基本事項を習得することを目標とする。 なお、デリバティブの価格付けの原理を理解することを主目的とするため，離散時間モデルにおける説明を丁寧に行い，連続時間モデルについてはモデルの考え方の説明と主たる結果の紹介にとどめる． Financial institutions such as banks and securities companies handle financial products called derivatives. Reasonable prices for these products are obtained by assuming a stochastic model for market fluctuations in underlying asset prices. In this lecture, after explaining the basic matters in finance, we will explain the properties that should be satisfied by the stochastic model for obtaining the price of derivatives and the principle of price derivation. The purpose of this lecture is to correctly understand the principle of pricing. The theorems are carefully proved in the framework of the discrete-time model which is easy to understan

測度論的確率論・確率過程論の基礎を理解する。/ The goal of the course is to understand the basics of measure-theoretic probability and stochastic processes.

基本的な確率過程の一つであるランダムウォークの性質に関連した性質を理解する。

連続時間ランダムウォークとしてのレヴィ過程、レヴィ過程に関する確率積分、確率微分方程式(SDE)に関する入門事項から入る。その後で、レヴィ駆動型SDEモデルの統計推測に関するいくつかのトピックを扱う。その背後にある汎用的な理論も解説する。計算機を用いたシミュレーションデモも実施する予定である（RパッケージYUIMA）。 We begin by introducing Lévy processes as continuous-time random walks, followed by an overview of stochastic integration and stochastic differential equations (SDEs). Subsequently, we present statistical inference theory for Lévy-driven SDE models, alongside the relevant general asymptotic theory. We also plan to conduct simulation demonstrations using a computer (R package YUIMA).

独立観測モデルを主対象として、漸近推測理論の基礎概念を解説する。確率統計学I等で学んだ大数の法則や中心極限定理を使って理論体系を構成する。 This lecture introduces the basic ideas of asymptotic inference theory, mostly focusing on the independent observation model. The theoretical system is based on the law of large numbers and the central limit theorem learned in Probability Statistics I and other courses.

This course explores the culture, industry, and politics of the piano through interdisciplinary approaches and active learning. The piano is a musical instrument that originated in Europe and developed into its modern form through the technological innovations in the Industrial Revolution. The instrument has not only occupied a central place in the history of Western music but also played a critical role in the shaping of class, gender, racial/ethnic/national consciousness, identities, and practices around the world. In the second half of the twentieth century, East Asian nations of Japan, South Korea, and China have become major producers and consumers of the piano, and many of the world’s most acclaimed pianists in genres ranging from classical to jazz and electronic are Asian. In this course, we will examine the diverse meanings of the piano and its music for peoples and societies around the world, especially in Europe, the United States, and Asia. The topics include: technology, industry, and business of piano manufacturing and sales; evolution of piano performance and pedagogy; notions of pianistic virtuosity and (dis)ability; class, gender, and family formation through piano lessons; piano and its music as a tool of nationalism and imperialism; globalization and cultural hybridity of the piano; representations of the piano across cultural genres; piano and its music in the digital age. Through the course, students will: - learn to think of piano not only as a musical but also a social instrument - understand historical, political, and economic factors that shape the music industry and musical practice - understand various forms of empowerment and mobilization as well as exclusion, marginalization, and exploitation through musical practice - learn interdisciplinary approaches to the study of music, including American studies, cultural studies, disability studies, ethnography, ethnomusicology, history, law, musicology, and sociology The course will address the following themes of Sustainable Development Goals (SDGs): Goal 4: Quality education Goal 5: Gender equality Goal 8: Decent work and economic growth Goal 9: Industry, innovation and infrastructure Goal 10: Reduced inequalities Goal 12: Responsible consumption and production