Welcome to the Mathematical Modelling website for Mathematical Science at Osaka University!
This course consists of two laboratories that, using the power of mathematics, research mathematical principles for various real-world phenomena, including natural phenomena such as fluids, heat, and quanta, as well as social phenomena such as medicine, AI, and network dynamics.
In order to seamlessly manage today's complex society, we must be able to predict and control various real-world phenomena. In traditional societies, prediction and control sometimes relied on the intuition of experienced individuals, whereas in today’s modern society, this process relies on a process of (1) establishing mathematical models of phenomenon, (2) analyzing these models using the power of mathematics, and (3) applying the results of these analyses to actual phenomena. Over the past 300 years, efforts have confirmed in all countries that these mathematical methods, which originated in Western Europe in the 17th century, are far more powerful than methods relying on experience and intuition.
For example, it is well known that calculus-based Newtonian mechanics provides extremely accurate predictions for macro-scale phenomena. Approaches to “predicting phenomena using mathematical methods” have been developed in various fields, for example, in the form of vector analysis for electromagnetism, Riemannian geometry for relativity, functional analysis for quantum mechanics, and probability analysis for financial engineering. The mathematical modelling based prediction and control method referred to as “Mathematical X” (where X is the name of the phenomena to be studied) has been widely used as part of the intellectual infrastructure available for and actually applied when developing many important phenomena models in today’s complex society.
On the other hand, the importation of the Western European system of learning into Japan during the Meiji Restoration some 150 years ago, at which time science was already becoming classified into different subjects, has also meant that Japanese students, including those studying in Japan’s universities even today, have encountered science as independent subjects such as mathematics, science, and sociology. For this reason, Japanese students may not be familiar with real mathematical science as a means of tackling real-world problems.
In this course, students engage in research and receive education regarding mathematical science based on the latest modern mathematics from a consistent perspective of tackling real-world phenomena, and take care not to fall into the trap of studying application for the sake of application.
Takayuki Kobayashi, Professor, Differential Equation Group
Michinori Ishiwata, Professor, Applied Analysis Group
Students in the Mathematical Modelling course conduct research on and study approaches to analyzing natural and social phenomena using the power of mathematics. “Mathematics” includes both pure mathematics and applied mathematics such as control theory, optimization, and inverse problems.
The Mathematical Modelling course consists of the Differential Equation Group and the Applied Analysis Group. Since modern mathematical methods are essential as the basis for mathematically analyzing phenomena, they are studied by students in both Groups.