This is an introductory course on mathematical methods for public policy analysis, designed for GraSPP students without a strong background in mathematics. Students from non-economics, non-engineering, or non-science majors are especially welcomed. The course helps students develop a solid mathematical foundation, enabling them to apply essential mathematical techniques to public policy issues. It is structured into four parts: 1. differential calculus, 2. linear algebra, 3. multivariate calculus and constrained static optimization, 4. dynamic optimization and linear dynamic systems.

The objective of this course is to brush up the mathematical skills required in advanced mechanical engineering through solving the example problems. Besides, solutions of partial differential equations are explained with the emphasis of the related physics. The methods using Green’s functions for nonhomogeneous differential equations are explained. Singular perturbation problems and renormalization technique are also explained as tools to obtain the approximate solutions. Furthermore, homogenization method, optimal design, structural optimization and sensitivity analysis are explained.

広く産学官にわたってグローバルに活躍するために必要な「俯瞰力」を養成することを目指す。物質科学の各分野について最先端の知識を修得し、自分の専門分野と周辺分野がどのように関連するか、あるいはし得るか、について深く考察するために、第一線で活躍する講師の方々にその分野の最前線を概観していただく。さらに、それらの講義を通して異分野間のコミュニケーションを円滑に進めるための具体的方法論を学ぶ。 This survey course is designed to enable students to develop the broad perspective that is required of global leaders working in and across industry, academia, and government. Students will gain knowledge and insight on advancements in each field of materials science research, given by leading researchers working on the frontline in those fields. This will allow students to consider how peripheral fields are related to their own area of expertise, and to consider the potential for forging bridges between related fields in the future. In addition, students will learn specific methodologies designed to facilitate smooth communication among different disciplines.

本授業では、現代物理学において重要な役割を果たしている可積分系と呼ばれる数理モデルを題材に、複雑な多体系の振る舞いを数理的に理解するための基本的な考え方を学ぶ。 非線形な古典力学系や量子多体系において厳密に解ける構造がどのように現れるかに着目し、その数理的背景と物理的意味を直感的に解説する。また、可積分性が統計力学的性質や物理現象の理解にどのようにつながるかを説明する。 本講義は複数の教員によるオムニバス形式で行う。

Through this course, you will explore education not simply as schooling, but as a lifelong and socially embedded process through which knowledge is created, shared, challenged, and transformed. Rather than asking only what people should learn, we will ask deeper questions about whose knowledge is valued, how learning occurs, and how education can contribute to more just, inclusive, and sustainable futures. We will examine diverse educational approaches across cultures and contexts through comparative education, educational innovation, Open Education, learning ecologies, artificial intelligence, decolonial perspectives, and international case studies. Through collaborative inquiry and project-based learning, you will design innovative educational responses to real-world global challenges. Ultimately, the course aims to help you become thoughtful global citizens who can critically evaluate knowledge, appreciate multiple ways of learning, and imagine new educational possibilities for a rapidly changing world. By the end of this course, students will be able to: (1) Explain key concepts related to education, knowledge, and global change from diverse cultural and international perspectives. (2) Analyze critically contemporary educational issues, including the roles of technology, artificial intelligence, equity, and social justice in shaping learning. (3) Communicate and collaborate effectively with peers from diverse disciplinary and cultural backgrounds to discuss educational challenges and solutions. (4) Design an evidence-informed educational innovation that addresses a contemporary global challenge by integrating insights from comparative education and multiple knowledge traditions.

Through this course, you will explore education not simply as schooling, but as a lifelong and socially embedded process through which knowledge is created, shared, challenged, and transformed. Rather than asking only what people should learn, we will ask deeper questions about whose knowledge is valued, how learning occurs, and how education can contribute to more just, inclusive, and sustainable futures. We will examine diverse educational approaches across cultures and contexts through comparative education, educational innovation, Open Education, learning ecologies, artificial intelligence, decolonial perspectives, and international case studies. Through collaborative inquiry and project-based learning, you will design innovative educational responses to real-world global challenges. Ultimately, the course aims to help you become thoughtful global citizens who can critically evaluate knowledge, appreciate multiple ways of learning, and imagine new educational possibilities for a rapidly changing world. By the end of this course, students will be able to: (1) Explain key concepts related to education, knowledge, and global change from diverse cultural and international perspectives. (2) Analyze critically contemporary educational issues, including the roles of technology, artificial intelligence, equity, and social justice in shaping learning. (3) Communicate and collaborate effectively with peers from diverse disciplinary and cultural backgrounds to discuss educational challenges and solutions. (4) Design an evidence-informed educational innovation that addresses a contemporary global challenge by integrating insights from comparative education and multiple knowledge traditions.

工学全分野で必要不可欠な道具である、常微分方程式、ベクトル解析、変分法について学ぶ。実践的な理解を目指す。

Cities are facing complex sustainability challenges shaped by the interactions between environmental, social, and economic systems. This course introduces key concepts of urban sustainability, discusses major urban challenges and potential responses, and considers trade-offs associated with different interventions. Topics include health and wellbeing in urban settings, energy consumption, climate change and the urban heat island effect, green infrastructure, and issues of access and equity. Through these themes, the course aims to develop an understanding of urban sustainability challenges and the ability to critically evaluate possible responses from multiple perspectives. For the final project, students will choose an urban sustainability topic of interest and connect course concepts with real-world issues that matter to them. By the end of this course, students will be able to: •Explain major sustainability challenges facing urban areas and their connections to the Sustainable Development Goals (SDGs). •Understand relationships between urban form, climate, resilience, and society. •Identify potential benefits, limitations, and unintended consequences of sustainability interventions. •Communicate sustainability issues across disciplinary boundaries

Cities are facing complex sustainability challenges shaped by the interactions between environmental, social, and economic systems. This course introduces key concepts of urban sustainability, discusses major urban challenges and potential responses, and considers trade-offs associated with different interventions. Topics include health and wellbeing in urban settings, energy consumption, climate change and the urban heat island effect, green infrastructure, and issues of access and equity. Through these themes, the course aims to develop an understanding of urban sustainability challenges and the ability to critically evaluate possible responses from multiple perspectives. For the final project, students will choose an urban sustainability topic of interest and connect course concepts with real-world issues that matter to them. By the end of this course, students will be able to: •Explain major sustainability challenges facing urban areas and their connections to the Sustainable Development Goals (SDGs). •Understand relationships between urban form, climate, resilience, and society. •Identify potential benefits, limitations, and unintended consequences of sustainability interventions. •Communicate sustainability issues across disciplinary boundaries

人間が行う知識や情報の処理をコンピュータで再現しようとする試みは、古くから続けられてきました。その成果として、線形分離に優れたサポートベクトルマシンや、現在さまざまな分野で活用されている深層学習が挙げられます。これらのアルゴリズムでは、たとえば0と1のような単純な出力しか持たないモデルを複数組み合わせることで、より複雑な情報の記憶や処理が可能になります。この講義では、コンピュータが知識や情報をどのように処理しているかを可視化しながら学び、機械学習の本質を理解することを目指します。