Mathematics is not just a series of abstract symbols and formulas, it is a language, a tool, and a way of thinking. It plays a vital role in modern society, from financial analysis to engineering design, from medical research to artificial intelligence, mathematics is everywhere. Mathematics provides a precise and rigorous way of expression to help us understand complex systems and problems. It is closely related to other disciplines, such as physics relies on mathematics to describe the laws of natural phenomena, economics uses mathematical models to predict market trends and computer science uses mathematical theories to optimize algorithms and design software. The logic and universality of mathematics make it a bridge connecting different disciplines and promoting the progress of science and technology. Through mathematics, we can explore the world more deeply, solve practical problems, and constantly push the boundaries of knowledge forward. How to find a suitable mathematical research focus for high school students? As the cornerstone of the scientific field, mathematics provides a variety of exploration paths, allowing you to choose a variety of different paths in the mathematics passion project. Think about which mathematical topics can inspire your passion. Maybe you are curious about the application of mathematics in sports data analysis, or you want to explore how mathematics can help solve environmental problems, or you are interested in the role of mathematics in astronomy. Once you have identified your area of interest, you can start exploring it in depth.

Keep in mind that different passion projects may require different levels of technical skills, such as mastering programming skills, while some projects may involve more exploration of theoretical concepts. Which direction you choose depends entirely on your interests and what you feel comfortable with. If you don't have certain technologies yet, don't worry, this is a good opportunity to learn new skills. You can think of the process of participating in the project as a dual journey of improving your technical capabilities and deepening your understanding of the topic of interest.

What are some good math research ideas?

1. Global Tourism Flow Interconnection System

In the context of the interconnected global economy, the cross-border spread of COVID-19 is uneven. We model the global tourism flow interconnection system as a complex network with countries as nodes and tourism connections between countries as edges. This study will explore related questions and try to provide answers.

2. Aerodynamics of Frisbee Sports

Currently, millions of people around the world use Frisbees as a daily outdoor recreational activity. Frisbees can travel long distances when they are thrown, but the physics behind the trajectory of Frisbees is not clear, and the trajectory of Frisbees cannot be quickly predicted. This project uses computational fluid dynamics to study the physical principles of Frisbee during flight.

3. Racing tail design and aerodynamic analysis

This project uses computational fluid dynamics to study the impact of racing tails on racing aerodynamics. First, a simplified three-dimensional physical model is established based on the appearance characteristics of classic racing cars. Then, a simulation model is established in the computational fluid dynamics software, and simulation calculations are performed. Finally, the developed computational fluid dynamics model is used to design the best racing tail to achieve minimum drag and minimum lift.

4. Physical and mental health issues of left-behind teenagers

In this project, researchers will analyze the impact of personal factors, family factors, and school factors on the physical and mental health of left-behind teenagers. After collecting the questionnaires, the questionnaires will be sorted and the data will be analyzed. The main research tool is the data analysis software SPSS. Through these analyses, researchers will initially know which factors have a greater impact on the physical and mental health of left-behind teenagers.

5. World Happiness Index

What affects a country's happiness index? What kind of country has the highest people's happiness index? How to improve the residents' happiness index? We will use statistical methods to analyze the above problems based on existing data. This project is suitable for students who are interested in applied statistics.

6. Venture capital and innovation and entrepreneurship: Evidence from the Belt and Road Initiative

This topic is expected to use venture capital data from Qingke Private Equity, as well as regional economic development, patents, and other data, to identify the effect of the Belt and Road Initiative in guiding venture capital and promoting innovation and entrepreneurship, and further study its positive role in connecting the economy, eliminating trade barriers, and reducing regional imbalances.

7. Consumer behavior prediction

The purpose of this topic is to shape the understanding of the process of marketing science from the birth of data to productization. Students will learn to transform business problems into data science problems, cultivate students' understanding of big data, and then guide students to pre-process real data and perform machine learning on existing data to predict consumer behavior or classify users.

8. The impact of parents' educational background on children's academic performance

Does parents' educational background affect children's academic performance? Based on existing data, we will use statistical methods to analyze the correlation between parents' educational background and children's academic performance, and will also establish a regression model in statistics to predict and determine which factors will affect children's academic performance.

9. Research on factors affecting China's marriage market

The equilibrium of the marriage market affects population growth and the investment and accumulation of human capital. Using data from the Chinese census and household surveys, this research project aims to analyze the impact of demographic policies, socioeconomic factors, etc. on marriage market outcomes. This project examines the impact of the marriage market on economic development, human capital improvement, and a series of measures of economic and social development levels.

10. Circuit breakers and information cascades in financial markets

Information cascades occur when people make decisions based solely on historical information about previous behavior and ignore their private information. It has been widely used in social learning models, where inefficient equilibria may occur. This project will conduct both theoretical analysis and empirical testing, the latter of which will be carried out on stock data, especially in the period after the circuit breaker occurs.

11. Numerical simulation of flow around sailing boat wings

In this project, first, a simplified three-dimensional physical model is established based on the shape characteristics of the sailing boat. Secondly, a computational fluid dynamics model is established and simulated. Finally, the developed computational fluid dynamics model is used to infer the influence of key parameters on the force of the sailing boat and find the optimal operation suggestions.

12. Applied statistics and causal reasoning: taking data from international trade as the research object

Social science research is becoming more and more data-based, which is an excellent opportunity for researchers. In the course, we will use a series of commonly used real data in the field of trade, including micro-trading behavior of enterprises, supply chain, and questionnaire data on trade tendencies.

13. Weibo forwarding chain of traffic stars

In this project, we will use tools such as text mining, semantic clustering, and sentiment analysis to explore the fan portraits behind traffic stars!

14. Machine learning prediction of people at high risk of heart disease

What characteristics would put people at high risk of heart attack? Based on the existing data, we will use the classic classification algorithm in machine learning to model and predict who is at high risk of heart disease. This project is suitable for students who are interested in applied statistics and machine learning.

15. Quantum Information - Quantum Separability Problem

This project will introduce the background of quantum information, mathematical foundations including matrices and semi-positive matrices, the mathematical definition of density matrices as quantum states, the definition and tasks of quantum separability problems, and the understanding and application of quantum entanglement.

16. Measurement of nonlinear response curves of SLR cameras and conversion to HDR images

This study aims to first measure the nonlinear response curves of SLR cameras, then perform mathematical analysis on them and propose fitting functions. The results will be compared with those reported in the literature, and conclusions will be drawn subsequently. In addition, the response curves will be used to construct the corresponding high dynamic range (HDR) radiation images. The algorithm will also be compared with previous methods and commercial HDR converter software.

17. London Underground Passenger Flow Prediction Based on Graph Neural Networks

The subway plays an important role in modern transportation networks, especially in London, where it is almost everyone's first choice for travel. The goal of this project is to use neural network graphs to predict the passenger volume of the London Underground.

18. Global Tourism Mobility Interconnection System

What is the relationship between the spread of the epidemic and the position of countries in the network? Which network characteristics are most related to the spread of the epidemic? How to build a reasonable epidemic prevention and control plan based on the understanding of the global tourism network (GTN)? This study will explore the above questions and try to give answers.

19. Density functional theory calculation of high refractive index polymer development

In this project, to explore a large number of polymers with different chemical structures, save experimental workload, and quickly determine the structure of the most suitable compound, we will focus on studying high refractive index polymers through density functional theory calculation methods.

20. Algorithm implementation and theoretical analysis of interactive search

This topic will explore and prove the theoretical lower bound of the number of problems of the optimal algorithm in the worst case and the theoretical upper bound of the number of problems of the proposed algorithm. To prove that the proposed algorithm is theoretically close to the optimal algorithm. In addition to the theoretical guarantee of the effect, the topic also needs to analyze and optimize the algorithm from the efficiency to ensure the efficiency of the algorithm.

How to show my mathematical research results?

After completing a mathematical project, it is also crucial to effectively show your results. You may notice that many mathematical project ideas revolve around a clear theme, but the ways to show these results are diverse. You can choose different ways to present your work, such as writing a research paper, making a podcast to tell your story, or designing infographics to visually display your findings.

It is important to find a way to not only fully present your mathematical project but also to attract your audience and make them interested in your work. Whether it is through text, sound, images, or interactive experiences, finding the presentation method that best suits your project topic and audience will help your results be more widely recognized and understood.

In addition, you can also continue to improve your research project and participate in some mathematical research competitions, such as the International Science and Engineering Fair, Mathematics and Statistics Research Competition, and The Siemens Competition in Math, Science, and Technology. Participating in these competitions can not only gain new inspiration in the process of communicating with peers but also get close to experts in the field of mathematics.

How can I get guidance and support for my mathematical research ?

If you have a strong interest in mathematics, or are eager to explore mathematical concepts in depth, and are interested in starting a passionate project, Embark will provide you with an ideal starting point. You will have the opportunity to connect with a professional mathematical research mentor and receive personalized guidance through one-on-one online communication. In these virtual mentoring sessions, your mentor will help you master new mathematical concepts, solve difficult problems encountered during project implementation, and discuss with you how to best present your passion project.

Through these courses, you will not only gain a deeper understanding of mathematics but also learn how to effectively communicate and present your research results. Your mentor will be your guide to explore the world of mathematics, help you turn your curiosity into concrete project results, and take solid steps on the road of mathematics. Click here to get in touch with Embark's mentors.