Dear students,
This repository contains the training material for mathematical modeling. The material is based on each topics I consider important for mathematical modeling. The material is organized in the following way:
Apart from the above topics, I will also include some examples and exercises for each topic. The examples and exercises are designed to help you understand the concepts and techniques in mathematical modeling. Furthermore, after all these topics, I will also include some case studies and projects for you to work on. The case studies and projects are designed to help you apply the concepts and techniques you have learned in mathematical modeling to real-world problems.
Moreover, I will also include some useful resources for mathematical modeling. The resources include books, papers, and software. The following textbooks are some of the books I recommend for mathematical modeling:
For the preparation of mathematical modeling competitions, I have conducted some materials for the competitions. The materials are based on some common mathematical models and techniques used in mathematical modeling competitions. The materials are organized in the following way:
| Supplementary Materials | Files(English) | Files(Chinese) |
|---|---|---|
| Interpolation and Curve Fitting | English | Chinese |
| Unconstrained Optimization | English | Chinese |
| Constrained Optimization | English | Chinese |
| Decision Theory | English | Chinese |
Moreover, followings are the beamer slides I have prepared for the mathematical modeling competitions:
| Beamer Slides | Files |
|---|---|
| Chapter 1 Mathematical Prerequisites | Beamer |
| Chapter 2 Introduction to Mathematical Modeling | Beamer |
| Chapter 3 Graphs of Functions as Models | Beamer |
| Chapter 4 Model Fitting and Data Analysis | Beamer |
| Chapter 5 Experimental Modeling | Beamer |
| Chapter 6 Simulation Modeling | Beamer |
| Chapter 7 Discrete Probabilistic Modeling | Beamer |
| Chapter 8 Mathematical Frameworks for Optimal Decision Making | Beamer |
| Chapter 9 Decision Theory and Game Theory | Beamer |
For one may be interested, followings are my approaches for the mathematical modeling competitions:
| Competitions | Files |
|---|---|
| HiMCM | 2019 Problem B |
| HiMCM | 2021 Problem A |
| HiMCM | 2022 Problem B |
| HiMCM | 2023 Problem B |
| HiMCM | 2024 Problem B |
| MCM | 1986 Problem (I personally think this is beginner level, but it might be difficult to solve back in 1986) |
| MCM | 2023 Problem A |
| IMMC | 2024 Autumn Problem A (I have not write a blog post for this yet) |
| IMMC | 2025 Autumn Problem A |
| IMMC | 2025 Autumn Problem B |
| IMMC | 2025 Autumn Problem C |
The above competitions are mostly written on my blog. For one may be interested, you can visit my blog.
Now I have been working on a new project, which is to write a book about mathematical modeling. The book will be based on the material in this repository, but it will be more comprehensive and detailed. You may read it here. The book is still under construction, but I will update it regularly. If you have any suggestions or comments, please feel free to contact me.
In order to know more about practical mathematical modeling competitions, you can visit the following websites:
Hope you enjoy the material and find it useful for your competition or other projects. If you have any questions or suggestions, please feel free to contact me. I will be happy to help you.
Yours sincerely,
S.K. Cheng