Untitled Quiz

Introduction

• Models are used in various disciplines (biology, engineering, computer science, psychology, sociology, and marketing).
• Mathematical models can be used to find patterns in life.
• Defining the problem is critical in modeling.
• Assumptions help simplify complex problems by focusing on key variables.
• Defining variables is essential for understanding the problem and forming equations.
• Building a solution involves using appropriate mathematical tools.
• Analysis and assessment involve evaluating results and identifying potential improvements.
• Reporting results involves clearly explaining the model's findings.

Defining the Problem

• Mathematical models answer open-ended questions.
• Problems can be approached in several ways.

Making Assumptions

• Assumptions simplify problems by reducing the number of variables to consider.
• Assumptions are used to make research easier and focus on essential aspects of the problem.

Defining Variables

• Defining variables helps in identifying all factors involved in the equation.
• Understanding the problem is key to defining variables correctly.
• Correct variable definitions are crucial for a good model.

Building a Solution

• Finding the solution involves using the tools and methods in the mathematical toolbox.
• Various mathematical models can be used to solve problems.
• Advanced computer software can be used to solve complex computations.

Analysis and Assessment

• Evaluating the model's theoretical value for practical application is important.
• Improvements to the model based on its evaluation should be noted.
• The model's results are crucial for understanding the context of the problem.

Reporting Results

• Clearly explaining the model is the last step in the process.
• The process and results must be explained in detail for other people to understand.
• The explanation must be free of technical jargon.

Defining Problem (Part 2)

• The United Nations Sustainable Development Goals (SDGs) aim to solve major problems like poverty, hunger, and inequality.
• Improving people's lives is based on 17 interconnected global goals.
• Protecting the environment is a key goal, including having clean water, affordable energy, and addressing climate change.

Make Assumptions (Part 3)

• Population growth in a country is the result of births and immigration exceeding deaths and emigration.
• Birth rate, death rate, immigration, and emigration are factors influencing population growth.
• Factors like healthcare, lifestyle, and economic conditions impact population growth.

Define Variables (Part 4)

• Mathematical model predicts Thailand’s population in 2030.
• Independent variable (x) is time.
• Dependent variable (y) is population.

Build Solutions (Part 5)

• Data on Thailand’s population from 2000 to 2021 is collected.
• A scatter plot is created in Desmos to understand population trends.
• Regression analysis using various functions (quadratic, cubic, exponential, logarithmic) determines the best fit for the data.

Analysis and Assessment (Part 6)

• The model's prediction for Thailand’s population in 2030 is calculated using the chosen function (cubic).
• The prediction is compared with similar predictions for other advanced economies (G7 countries).
• The number of teachers in Thailand in 2030 was predicted using a similar methodology (scatter plot of number of teachers over the 2000-2015 data).
• Also, the obtained result is compared with the average number of teachers per 1000 people in G7 countries.

References

• Various references on mathematical modeling, solutions, and the UN's Sustainable Development Goals are listed.