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.

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.

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.

The course will involve a series of discussions among students following specified formats intended to maximize participants’ ability to learn and apply the following: -Skills for pragmatic, practical, intersectional approaches and multilateral solutions to global issues and challenges, especially in devising and evaluating policy proposals and alternatives. -Ability to assess, discuss, and debate global issues by leveraging multidisciplinary perspectives across public policy, economics, politics, ethics, security, international governance, and law. In addition to discussions, students will also develop skills in policy analysis, discussion, consensus building, effective presentation, and policy brief writing. The following is a list of themes: -Decarbonization, energy security and geopolitics, and the role of nuclear -The role of leading institutions and fair competition in global education in the era of digitalization -Challenges in progressing gender equality against the context of varying social vulnerabilities and inequalities across the globe -International leadership and the future role of international organizations

２人の教員がオムニバス形式で様々な分野における自然現象を記述する数理モデルやセルオートマトンの構成法及び，それらの数理的モデルの解析について講義する． 今年度予定されるトピックは，可解格子模型、離散数理モデルと離散可積分系の数理的記述などである．

Aims 1. To introduce students to the history of the lands that now make up most of Poland, Lithuania, Belarus, and Ukraine, from the sixteenth century until the 1930s. 2. To consider civic and ethno-linguistic concepts of ‘nation’ and ‘nationalism’ within this historical context. 3. To enhance the ability to understand and to appreciate how people have existed, acted and thought in the past in the context of the complexity and diversity of historical situations, events and intellectual outlooks. In particular, students should consider how people in the past have evaluated the times in which they were living. 4. To enhance the ability to use and evaluate texts and other source materials both critically and empathetically, as well as appreciating the limits and challenges of the extant record. The critical evaluation of texts should include an understanding of the questions which historians ask and why they do so. By the end of the course students will have read a wide selection of historical works. 5. To enhance the ability to frame and sustain an argument. Arguments should be structured, coherent, relevant, and concise, and should take into account all aspects of a given problem. Objectives By the end of the course, students should have acquired: 1. Enhanced generic skills: these may be defined as -- (i)self-direction and self-discipline; (ii)independence of mind and initiative; (iii) the ability to work with others and to have respect for the reasoned views of others; (iv)the ability to identify, gather, deploy and organize evidence, data, and information; and familiarity with appropriate means of achieving this; (v)analytical ability and the capacity to consider and solve problems, including complex problems; (vi)structure, clarity and fluency of expression; (vii)intellectual maturity and integrity; (viii)empathy and imaginative insight; (ix)ability to organize time, work, and personal resources to optimal effect. 2. A body of historical knowledge relating to the Polish-Lithuanian Commonwealth to 1795 as well as the territories that formerly constituted it, from the partitions until the 1930s.

Aims 1. To introduce students to the history of the lands that now make up most of Poland, Lithuania, Belarus, and Ukraine, from the sixteenth century until the 1930s. 2. To consider civic and ethno-linguistic concepts of ‘nation’ and ‘nationalism’ within this historical context. 3. To enhance the ability to understand and to appreciate how people have existed, acted and thought in the past in the context of the complexity and diversity of historical situations, events and intellectual outlooks. In particular, students should consider how people in the past have evaluated the times in which they were living. 4. To enhance the ability to use and evaluate texts and other source materials both critically and empathetically, as well as appreciating the limits and challenges of the extant record. The critical evaluation of texts should include an understanding of the questions which historians ask and why they do so. By the end of the course students will have read a wide selection of historical works. 5. To enhance the ability to frame and sustain an argument. Arguments should be structured, coherent, relevant, and concise, and should take into account all aspects of a given problem. Objectives By the end of the course, students should have acquired: 1. Enhanced generic skills: these may be defined as -- (i)self-direction and self-discipline; (ii)independence of mind and initiative; (iii) the ability to work with others and to have respect for the reasoned views of others; (iv)the ability to identify, gather, deploy and organize evidence, data, and information; and familiarity with appropriate means of achieving this; (v)analytical ability and the capacity to consider and solve problems, including complex problems; (vi)structure, clarity and fluency of expression; (vii)intellectual maturity and integrity; (viii)empathy and imaginative insight; (ix)ability to organize time, work, and personal resources to optimal effect. 2. A body of historical knowledge relating to the Polish-Lithuanian Commonwealth to 1795 as well as the territories that formerly constituted it, from the partitions until the 1930s.

The course will take an intersectional approach to why we commonly find an underrepresentation of women in the Science, Technology, Engineering and Mathematics (STEM) fields. The course will begin by addressing our own unconscious biases and stereotypes, and question the research behind male and female differences. We will cover the brief history of the underrepresentation of minorities and explore research articles on why and how women and other minorities have been excluded from STEM fields. Students will be expected to read scientific articles, discuss them, and apply those concepts to examine their own social environments.

The course will take an intersectional approach to why we commonly find an underrepresentation of women in the Science, Technology, Engineering and Mathematics (STEM) fields. The course will begin by addressing our own unconscious biases and stereotypes, and question the research behind male and female differences. We will cover the brief history of the underrepresentation of minorities and explore research articles on why and how women and other minorities have been excluded from STEM fields. Students will be expected to read scientific articles, discuss them, and apply those concepts to examine their own social environments.