TEACHING APPLIED MATHEMATICS WITH PRACTICAL ECONOMIC PROBLEMS TO ECONOMICS STUDENTS

ABSTRACT

The article "Teaching Applied Mathematics with Practical Economic Problems to Economics Students" explores the integration of applied mathematics in economics education. It emphasizes the significance of incorporating real-world economic problems into the curriculum to enhance students' understanding of mathematical concepts and their applications in economic analysis. The article discusses various teaching strategies, including case studies, project-based learning, and the use of software tools, to effectively engage students in applying mathematical techniques to practical economic issues.

АННОТАЦИЯ

В статье «Преподавание прикладной математики с практическими экономическими задачами студентам-экономистам» исследуется интеграция прикладной математики в экономическое образование. Он подчеркивает важность включения реальных экономических проблем в учебную программу для улучшения понимания студентами математических концепций и их применения в экономическом анализе. В статье обсуждаются различные стратегии обучения, включая тематические исследования, проектное обучение и использование программных инструментов, чтобы эффективно вовлекать студентов в применение математических методов к практическим экономическим вопросам.

Keywords: Applied Mathematics. Economics Education. Practical Economic

Ключевые слова: Прикладная математика. Экономическое образование. Practical economic problems.

In the rapidly evolving landscape of modern economics, the integration of applied mathematics has become increasingly critical. As economic models grow more complex and data-driven, the need for economics students to possess strong mathematical skills is more pronounced than ever. This article explores the importance of teaching applied mathematics through practical economic problems and discusses effective strategies for implementing this approach in the curriculum.

Informing Economic Policy. The insights gained from mathematical models and empirical analysis are instrumental in informing economic policy. Policymakers rely on these tools to evaluate the potential impacts of their decisions and to design effective strategies for achieving economic objectives. For instance, mathematical models can simulate the effects of different fiscal or monetary policies, providing guidance on the best course of action to stabilize the economy or promote growth [1].

Advancing Financial Economics. In the realm of financial economics, applied mathematics plays a critical role in the valuation of financial instruments, risk management, and portfolio optimization. Concepts from stochastic calculus and probability theory are used to model the behavior of asset prices and to assess the risks associated with various investment strategies. This mathematical rigor is essential for the functioning of modern financial markets and the development of innovative financial products.

Addressing Complex Systems and Global Challenges. As economic systems become increasingly complex and interconnected, applied mathematics offers powerful tools for understanding and addressing global challenges. Network theory is used to analyze the interconnectedness of financial institutions and assess systemic risk. Game theory provides insights into strategic interactions in various economic contexts, from competitive markets to international trade negotiations.

The role of applied mathematics in economics is both profound and pervasive. It provides the language and framework for expressing economic concepts, the tools for analyzing data, and the foundation for making informed decisions. As the economic landscape continues to evolve, the importance of applied mathematics in shaping our understanding of economic phenomena and guiding policy decisions will only grow.

Integrating Practical Economic Problems into the Curriculum. To effectively teach applied mathematics to economics students, educators should focus on integrating practical economic problems into the curriculum. This can be achieved through various methods:

Case Studies. Incorporating case studies that require mathematical analysis can provide students with a concrete context for applying their skills. For example, a case study on optimizing production in a factory can illustrate the application of linear programming, while an analysis of historical stock market data can demonstrate the use of statistical methods in finance.

Project-Based Learning. Engaging students in project-based learning allows them to tackle complex economic problems in a collaborative and hands-on manner. Projects can range from developing models to predict inflation rates to creating simulations of market dynamics. This approach encourages critical thinking, problem-solving, and the application of mathematical concepts in a real-world setting [2].

Software and Technology. Integrating software tools commonly used in economic analysis, such as MATLAB, R, or Python, can enhance students' computational skills and their ability to handle large datasets. By learning to use these tools in conjunction with mathematical techniques, students can better understand the practical applications of their studies.

Interdisciplinary Collaboration. Encouraging collaboration between economics and mathematics departments can foster a more holistic understanding of applied mathematics in economics. Joint seminars, workshops, and courses can provide students with diverse perspectives and a more comprehensive education.

Example: Simulating the Cobweb Model in Python

The Cobweb Model is a classic example used in economics to illustrate how price and quantity adjust over time in markets with delayed supply responses, such as agricultural markets.

 Mathematical Formulation:

1. Demand Function:

- Where  is the quantity demanded,  is the price, and  and  are constants.

2. Supply Function:

- Where  is the quantity supplied,  is the price in the previous period, and  and  are constants.

3. Equilibrium Condition: In equilibrium,

 Python Simulation:

Picture 1. Python Simulation

Diagram:

The resulting plot from the Python code will show the oscillations in price and quantity over time, characteristic of the Cobweb Model. Here's a conceptual diagram illustrating the dynamics:

Picture 2.  Conceptual diagram illustrating the dynamics

In this diagram, the lines represent the oscillating paths of price and quantity over time. The exact shape and stability of these oscillations depend on the parameters of the demand and supply functions [3].

This simulation demonstrates how software applications can be used to model and visualize complex market dynamics, providing valuable insights into economic phenomena.

Conclusion

Teaching applied mathematics with practical economic problems is essential for preparing economics students for the complexities of the modern economic landscape. By integrating real-world applications into the curriculum, educators can enhance students' analytical skills, deepen their understanding of economic theory, and equip them with the tools necessary for success in their future careers.

References:

1. Arrow, K. J., & Intriligator, M. D. (Eds.). (1981). Handbook of mathematical economics (Vol. 1). North-Holland.
2. Blaug, M. (1997). Economic theory in retrospect. Cambridge University Press.
3. Chiang, A. C., & Wainwright, K. (2005). Fundamental methods of mathematical economics (4th ed.). McGraw-Hill.