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- 工学院，物質理工学院，環境・社会理工学院共通科目
- Liberal arts and basic science courses
- First-Year Courses
- School of Science
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School of Environment and Society
- Department of Architecture and Building Engineering
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- Department of Innovation Science
- Graduate major in Technology and Innovation Management
- Common courses
- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Artificial Intelligence
- Instructor(s)
- Takayasu Misako Takayasu Hideki
- Class Format
- Lecture (HyFlex)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue7-8(G1-103 (G114)) Fri7-8(G1-103 (G114))
- Group
- -
- Course number
- ART.T468
- Credits
- 2
- Academic year
- 2023
- Offered quarter
- 2Q
- Syllabus updated
- 2023/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
In order to understand phenomena that are difficult to describe from first principles because they involve uncertainty or are highly complex, the task of "modeling" to formulate them as mathematical problems is particularly important. In this lecture, students will learn the basic mathematics required for modeling, using examples of typical phenomena involving stochastic elements and nonlinearity.
Student learning outcomes
Through learning basic mathematical models of phenomena, including stochastic elements and nonlinear dynamics, students will acquire a foundation for advanced modeling of more complex phenomena.
Keywords
Stochastic variables, probability distributions, correlations, diffusion phenomena, Brownian motion, branching processes, phase transition phenomena, transport phenomena, complex networks
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
| ✔ Students learn the fundamentals of mathematical modeling of unknown phenomena | ||||
Class flow
Lectures will be given face-to-face. For each lecture content, specific phenomena will be presented and mathematical description will be given.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | What is modeling | Learn about observation, model building, analysis, and model evaluation. |
| Class 2 | Observation of Phenomena and Basic Models 1 | Learn basic distributions such as exponential and normal distributions and the mathematical models behind them. |
| Class 3 | Observation of Phenomena and Basic Models 2 | Learn about the power law distributions and the mathematical model behind them. |
| Class 4 | Observation of Phenomena and Basic Models 3 | Learn about nonlinear dynamics and basic mathematical models. |
| Class 5 | Modeling of Diffusion Phenomena 1 | Learn the diffusion equation as a macroscopic irreversible phenomenon. |
| Class 6 | Modeling Diffusion Phenomena 2 | Derive the characteristics of diffusion phenomena from random walks. |
| Class 7 | Application of Diffusion Phenomena Modeling 1 | Learn time series models of price fluctuations in financial markets. |
| Class 8 | Application of Diffusion Phenomena Modeling 2 | Learn how to model financial markets from a microscopic perspective. |
| Class 9 | Modeling of Branching and Aggregation Phenomena 1 | Learn about modeling of branching processes in various systems. |
| Class 10 | Modeling of Branching and Aggregation Phenomena 2 | Learn about modeling of aggregation processes. |
| Class 11 | Modeling of Phase Transition Phenomena 1 | Learn the properties of basic models of phase transition phenomena and their theoretical solutions. |
| Class 12 | Modeling Phase Transition Phenomena 2 | Learn about models of congestion and phase transitions in transport phenomena. |
| Class 13 | Modeling of Phase Transition Phenomena 3 | Learn about self-organized critical phenomena and their models. |
| Class 14 | Modeling Complex Network Phenomena | Learn about characterization of complex network structures and their models. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None in particular.
Reference books, course materials, etc.
Other reference materials will be announced during the lecture. Lecture notes will be downloadable.
Assessment criteria and methods
The level of understanding of the lecture content will be evaluated based on the report assignment.
Related courses
- MCS.T211 ： Applied Calculus
- MCS.T203 ： Linear Algebra and Its Applications
- MCS.T223 ： Mathematical Statistics
- MCS.T212 ： Fundamentals of Probability
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students should have basic knowledge and skills in linear algebra, calculus, and probability/statistics.
