学部前期課程
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最終更新日：2026年10月16日
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最終更新日：2026年10月16日
授業計画や教室は変更となる可能性があるため、必ずUTASで最新の情報を確認して下さい。
UTASにアクセスできない方は、担当教員または部局教務へお問い合わせ下さい。
自然科学ゼミナール(PEAK)
Applications of Mathematics in the Sciences
This course is designed to demonstrate how mathematical concepts that U. Tokyo students have learned in their pure mathematics classes are used and applied in advanced studies in the natural and social sciences. Understanding applications of mathematics in the sciences allows students to understand what they have learned more deeply, and helps them to realize the importance of mathematics for their advanced studies in the Senior Division programs.
The course is delivered by three instructors from different fields of expertise, presenting three stories of the use of mathematics. Each part focuses on particular mathematical ideas and methods and gives examples of where they can be applied. The fields of academic discipline and topics are the following:
Part I (physics / chemistry). The mathematical description of quantum mechanics: Complex linear vector spaces and bra-ket notation and their application in describing the fundamental property of spin.
Part II (mathematical economics). Dynamic optimization and economic decision: Finding optimal lifelong consumption-savings plan.
Part III (chemical and environmental engineering). Process modeling and control: Mathematical modelling and control systems related to industrial and environmental processes.
The course is delivered by three instructors from different fields of expertise, presenting three stories of the use of mathematics. Each part focuses on particular mathematical ideas and methods and gives examples of where they can be applied. The fields of academic discipline and topics are the following:
Part I (physics / chemistry). The mathematical description of quantum mechanics: Complex linear vector spaces and bra-ket notation and their application in describing the fundamental property of spin.
Part II (mathematical economics). Dynamic optimization and economic decision: Finding optimal lifelong consumption-savings plan.
Part III (chemical and environmental engineering). Process modeling and control: Mathematical modelling and control systems related to industrial and environmental processes.
時間割／共通科目コード
コース名
教員
学期
時限
50114
CAS-PI2200S3
自然科学ゼミナール(PEAK)
前田 章
月曜3限
マイリストに追加
マイリストから削除
講義使用言語
英語
単位
2
実務経験のある教員による授業科目
NO
他学部履修
不可
開講所属
教養学部（前期課程）
50120
CAS-PI2200S3
自然科学ゼミナール(PEAK)
前田 章
月曜3限
マイリストに追加
マイリストから削除
講義使用言語
英語
単位
2
実務経験のある教員による授業科目
NO
他学部履修
不可
開講所属
教養学部（前期課程）
授業計画
Lectures 1-4 (Prof. Jonathan R. Woodward)
Part I: The mathematical description of quantum mechanics
This part serves as an introduction to the commonly used model for describing quantum mechanics known as bra-ket notation, introduced by the British physicist Paul Dirac. It relies on key ideas from linear algebra and describes the states of quantum systems as complex vectors and observable properties as complex matrices.
Lectures 5-8 (Prof. Akira Maeda)
Part II: Dynamic optimization and economic decision
This part discusses the concept of dynamic optimization and its application to individual’s economic decision, in particular lifelong planning.
Lectures 9-12 (Prof. Yasuki Kansha)
Part III: Process modeling and control
This part discusses an introduction of modeling methods through mathematical calculations such as creating way of balance equations, linearization and transformations. In addition, the effect of these calculations to controller design is discussed.
授業の方法
Each part will be taught by the following method.
Part I: Combination of conventional lectures and interactive group work
Part II: Conventional lectures
Part III: Combination of conventional lectures, and interactive work
成績評価方法
Grading for this course is based on those of three parts.
Part I: Assignments, quizzes, attendance and participation
Part II: In-class quizzes and attendance
Part III: Assignments, attendance and participation
履修上の注意
There will be no formal textbook required. Lecture notes or handouts will be distributed. In addition, in Part I, Paul Dirac’s original text entitled, “The Principles of Quantum Mechanics” will be used as a reference text and distributed electronically (as it is in the public domain).
