# Master's Program in Mathematics

See Also→ Department of Mathematics [Master's Course]

Mathematics is the foundation of natural sciences and is applied in various facets of human life. Master course students study analysis of various natural and social phenomena, and construction of mathematical theory by searching the mathematical structures lying in this analysis. Students can learn mathematical capabilities and knowledge through these types of research.

### Introduction of Department

Mathematics is a reliable foundation of natural science and offers applications to various aspects of human life. In our department we are making our effort to develop mathematical theories through analyzing various phenomena which appear not only in mathematics but also in natural and social sciences and through studying the mathematical structures which underlie those phenomena. Through these studies and researches, our graduate students will be able to acquire good ability in knowledge of Mathematics.

Educational Philosophy

The study of mathematics endeavors to examine and clarify the mathematical structures and principles that lie in the core of occurrences in the natural world, as well as in human activities and in a wide range of other phenomena.

The mathematics can provide methods for analyzing many forms of structures and phenomena as well as for making predictions about related events.

The aim of the education of Department of Mathematics is to provide students who have already studied the basics and methods of modern mathematics with deeper and wider understandings of these mathematical theories.

Expectations of Students

Based on the above philosophy, the character that Department of Mathematics expects to the students is as follows.

Students applying to this Department are expected to have a particular interest in enjoying mathematics, in finding principles hidden behind the innumerable natural and social phenomena in the world, and in conducting an in-depth pursuit of those principles.

### Curriculum

Complex Structure

Topology

Analysis and number theory

Theory of Manifolds

Phase topology in low dimensional space

Topology in three dimensional space

Mathematics of symmetries

Filels and Galois theory

Functional Equations

Functional Analysis

Probability Theory

Stochastic Differential Equation

General Theory of Modern Mathematics

### The Course of Theory of Mathematical Structures

In this course, we deal with various mathematical structures: arithmetic structure, algebraic structure, topological structure, geometric structure, and complex structure. The purpose of our research is to understand mathematical structures of the objects as a whole. We study what kinds of structures exist in the objects and how they are related. In fact, these structures are closely related to each other, and one of the main interest of our research is concerned with the interactions between them. Nowadays, mathematical structures are becoming more and more unified. Though individual research is based on individual mathematical structures, we must study the objects from many different viewpoints. Thus, our aim in the course on Theory of Mathematical Structures is to widen and enrich perspectives of Mathematics through new developments.

### The Course of Mathematical Analysis of Phenomena

In this course, we deal with the following subjects: nonlinear analysis, analytical theory of global phenomena, theory of classical differential equations, probability theory, and Fourier analysis. We concentrate our attention on "movements" in various phenomena to carry out research on these subjects and we study their mechanisms by using infinitesimal analysis. Note that kinds of analysis are already found and developed. However, in this course, we will not only succeed to classical research, but also make new models of phenomena and recognize universality through bird's eye view. Then we will break the old frameworks of these fields of research and rearrange them organically. Thus, our aim is to achieve many fruitful developments in Mathematical Analysis of Phenomena.