情報科学の基礎となる数学のうち,集合,関係,束,情報理論,代数系(群,環,体),およびその情報的応用(符合,暗号,乱数等)を扱う.
Study basic mathematics for information science; set, relation, lattice, abstract algebra (group, ring, field), information theory, coding theory, cryptography and random numbers.
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.
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FEN-MX5b23L3
FEN-MX5b23L3
機械系応用数学(Applied Mathematics for Mechanical Engineering)
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.
新規医療療法を患者の手元に提供する為には、臨床試験を実施しデータ収集が求められている。集積されたデータより、医療療法の有効性、安全性を確認する為には統計解析結果が求められる。本講義を通して、臨床試験について、構成、デザイン、統計解析方法、統計学的検定、を理解し、収集されたデータ解析に直面する数理的考察を議論する。特に、Sセメスターでは、抗がん剤の臨床試験に焦点をあて、データ解析実施の際の数理的課題を掌握し、解決方法について考察を行う。
It is required to conduct clinical trials to obtain clinical data. The reason required to conduct clinical trials is to show efficacy and safety of the medical therapies based on the results derived from statistical analyses for the clinical data. The lectures will focus on design, statistical analyses, statistical inference on the data analyses of clinical trial data. Specially mathematical statistical analyses on the clinical trials of oncology therapies will be reviewed and discuss the related issues.