Mathematical science is the science in which mathematical and statistical models are constructed, developed mathematically and diagnosed empirically in order to understand practical phenomena which occur in the fields of natural science, social science, technology, biology and so forth. For the purpose, one needs to utilize computers with advanced levels to make computer simulations, computer graphics and to develop algorithms, among others. This area consists of two large groups. One is a group of applied mathematics and the other a group of statistical science, each having two smaller subgroups. In this area, emphasis is placed on research and education of differential equations, mathematical physics, statistical analysis and data science.

**Laboratories**

**Area of Mathematical Modelling**

The Area of Mathematical Modelling comprised of the following two research groups is concerned with research and education of mathematical theory and applications on modelling phenomena occurred in several fields of natural science, social science and engineering.

**Differential Equation Group**

■ Prof.: Takayuki KOBAYASHI

■ Assoc.Prof.: Satoshi MASAKI

■ Assis.Prof.: Hajime KOBA

Here we study nonlinear partial differential equations appearing in the various fields of Mathematical Sciences. For example, we are focusing on the following topics:

- LASER beam propagation in a nonlinear medium.
- Bifurcation analysis to infinite dimensional dynamical systems and its application to pattern formation problem.
- Development of computational topology methods applied to dynamical system theories.

**Applied Analysis Group**

■ Prof.: Michinori ISHIWATA

■ Assis.Prof.: Hajime KOBA

This group is engaged in the following study and education.

- Mathematical formulation of problems in natural science, engineering,economics,and medical science based on physical principle and phenomena.
- Numerical simulation, numerical scheme, and mathematical analysis based on the theory of partial differential equations and nonlinear functional analysis.
- Investigation of mathematical structure for self-interacting particles and biological functions such as the kinetic equation,system of chemotaxis, and tumour growth model.

**Area of Statistical Science**

**Statistical Analysis Group **

■ Prof.: Joe SUZUKI

■ Assoc.Prof.: Fuyuhiko TANAKA

■ Assis.Prof.: Kosuke MORIKAWA

(Sorry, under preparation)

**Data Science Research Group**

■ Prof.: Yutaka KANO

■ Assoc.Prof.: Etsuo HAMADA

■ Assis.Prof.: Kosuke MORIKAWA

An important purpose of multivariate analysis is to identify any relations among many variables based on statistical data. The recent topics in this field are new modeling and statistical causal inference. In this research group, we apply mathematics and computers extensively to study structural equation modeling,graphical modeling,and independent component analysis as well as survival analysis in biostatistics. Our research includes methodological and application aspects.