2022 Faculty Courses School of Computing Undergraduate major in Mathematical and Computing Science
Mathematical Modeling
- Academic unit or major
- Undergraduate major in Mathematical and Computing Science
- Instructor(s)
- Misako Takayasu / Hideki Takayasu
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Mon (W834) / 7-8 Thu (W834)
- Class
- -
- Course Code
- MCS.T315
- Number of credits
- 200
- Course offered
- 2022
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
For understanding uncertain and/or complex phenomena that are difficult to describe from the first principle, it is particularly important to appropriately formulate them as mathematical problems. This task is often termed "modeling". This course shows elementary mathematical techniques that are necessary for the modeling, illustrating representative probabilistic and/or nonlinear phenomena.
Course description and aims
The goal is to acquire basic skills for engaging in advanced modeling of more complex phenomena by learning elementary mathematical models for probabilistic and/or nolinear dynamical phenomena.
Keywords
Random variable, probability distribution, correlation, diffusion phenomena, Brownian motion, branching process, phase transition, transport phenomena, complex network
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
- Learn the basics of mathematical modeling of unknown phenomena
Class flow
For each topic, we first show concrete target phenomena, and introduce how they are formulated as mathematical problems.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Introduction to modeling | General introduction to observation, modeling, analysis and evaluation |
| Class 2 | Observation of phenomena and basic models 1 | Basic distributions such as exponential distribution and the normal distributions and corresponding mathematical models |
| Class 3 | Observation of phenomena and basic models 2 | Power law distributions and corresponding mathematical models |
| Class 4 | Observation of phenomena and basic models 3 | Nonlinear dynamics and corresponding mathematical models |
| Class 5 | Modeling of diffusion phenomena 1 | Macroscopic irreversibility of diffusion phenomenon, and derivation of diffusion equation |
| Class 6 | Modeling of diffusion phenomena 2 | Microscopic view of diffusion phenomenon and Brownian motion |
| Class 7 | Modeling of diffusion phenomena: Application 1 | Models of financial time series are introduced as an application of diffusion |
| Class 8 | Modeling of diffusion phenomena: Application 2 | Microscopic agent-based models of financial markets are introduced as an application of diffusion |
| Class 9 | Modeling of branching and aggregation phenomena 1 | Branching process and its modeling |
| Class 10 | Modeling of branching and aggregation phenomena2 | Aggregation process and its modeling |
| Class 11 | Modeling of phase transition phenomena 1 | Basic models of phase transition, basic properties and theoretical solutions |
| Class 12 | Modeling of phase transition phenomena 2 | Transport phenomena and congestion phase transition, and related models |
| Class 13 | Modeling of phase transition phenomena 3 | Self-organized criticality and related models |
| Class 14 | Modeling of complex networks | Complex networks and related 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.
Reference books, course materials, etc.
To be distributed electronically when needed.
Evaluation methods and criteria
Students' understanding will be assessed by reports.
Related courses
- MCS.T211 ： Applied Calculus
- MCS.T203 ： Linear Algebra and Its Applications
- MCS.T223 ： Mathematical Statistics
- MCS.T212 ： Fundamentals of Probability
Prerequisites
Basic knowledge and skills about linear algebra, calculus, probability theory, and statistics are required.