2024 Faculty Courses School of Computing Department of Computer Science Graduate major in Artificial Intelligence
Mathematical Modeling
- Academic unit or major
- Graduate major in Artificial Intelligence
- Instructor(s)
- Misako Takayasu / Hideki Takayasu
- Class Format
- Lecture (HyFlex)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Tue / 7-8 Fri
- Class
- -
- Course Code
- ART.T468
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
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.
Course description and aims
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
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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. |
Study advice (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.
Evaluation methods and criteria
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
Students should have basic knowledge and skills in linear algebra, calculus, and probability/statistics.
Other
The first lecture will be held in room G1-103 on Friday, June 14.