# Introduction

A basic idea of "mathematical sciences" is a combination of broad ranged research areas holding a central position in fundamental sciences. Although they include traditional pure mathematics as a core, mathematical sciences indeed expand toward applied sciences which plays roles for development of sciences and technologies as well as structural reorganization of our society.

In the "Division of Mathematical Sciences," we will cultivate students' basic abilities of logical thinking, scientific analysis, and creative conception through the process to generalize and abstract concepts of numbers, expressions, and shapes. Additionally, we will foster the spirit of scientific reasoning to see phenomena and judge circumstances in the real world. We will raise people who have those abilities summed up and merged. They would play a leading role in various areas in our society as experts with high skills and proper judgment.

In general, mathematics or mathematical sciences are expected to be a foundation for all kinds of sciences. That may be true. However, we would like the students to realize that they have a comprehensive structure built by huge amount of results from the past and expanding now for the future. We will strongly make it emphatic that mathematics or mathematical sciences are themselves interesting objects for an extensive investigation.

**Let us explain briefly our undergraduate program and research activity.**

## DP (Diploma Policy)

The Division of Mathematical Sciences will confer the degree, Bachelor of Science and Technology, on a person who is considered to have obtained the following.

(1) Common sense and mature thought as an ordinary person.

(2) Grounding and responsibility as a person in a society.

(3) Special knowledge and application skills in mathematical sciences suitably used depending on circumstances.

## AP (Admission Policy)

The Division of Mathematical Sciences will seek a person who is interested in mathematics, and feels it attractive to try to find a solution for a problem to develop science and technology from a mathematical point of view.

## CP (Curriculum Policy)

The Division of Mathematical Sciences offers an educational opportunities equally to all students. Our program proceeds on the following lines.

(1) Students should learn every fundamental subject from each of the six main fields (algebra, geometry, analysis, applied mathematics, statistical science, information science) which we consider constitute mathematical sciences together. Moreover, they should try to understand interaction between them. Active learning is necessary for a student to use obtained knowledge effectively.

(2) We have two classes a week for core subjects to make and keep the foundation firm. One is a lecture class. We teach only a small number of important facts in order for students to acquire basic knowledge certainly and extend it freely by themselves. Another is a combined class of exercise sessions, supplementary lessons, and lectures of advanced topics. We place emphasis on how to apply knowledge rather than knowledge itself.

(3) Students are expected to look at mathematical sciences as an academic specialty. We will cultivate ability to feel the high dimensional spread of the areas and their change over time. By interaction between the existing ones, we will fix our eyes on both creation of a new research area and accommodation to problems of the real world. Students will be encouraged to have the second and third fields in addition to the current major of study, which help them broaden their scientific view.

## People and Research Fields

The Division of Mathematical Sciences has twelve faculty members together with several part-time teachers. The research objects of the faculty's interest are distributed in the six main fields. As a map shows below, each of them has such a broad range that they overlap each other to keep a room for a new notion or a generalized concept.

**Algebra**: Investigating to find structural properties of sets and mappings equipped with concrete or abstract operations.

This includes group theory, commutative algebra, algebraic geometry, number theory, representation theory,

covered mainly by Kiyoshi Baba, Yasuhiko Tanaka, Nobuhiro Terai.

**Geometry**: Investigating to find invariant properties of figures under transformation and generalized concept of far and near.

This includes set theory, topology, algebraic curves,

covered mainly by Nobuyuki Kemoto, Nobuhiro Terai.

**Analysis**: Investigating to find properties of functions and their variation by differentiation and integration.

This includes functional analysis, nonlinear analysis, partial differential equations, probability theory, measure theory,

covered mainly by Ryoji Fukuda, Shuji Yoshikawa, Hiroshi Watanabe.

**Applied Mathematics**: Investigating various kinds of problems over a broader range of science from a mathematical point of view.

This includes numerical analysis, linear programming, operations research, optimization theory,

covered mainly by Shuji Yoshikawa, Tsuneshi Obata.

**Statistical Science**: Investigating to extract essential properties of a group by suitable sampling from huge amount of data.

This includes data science, discrete data analysis, multivariate analysis,

covered mainly by Yoshimichi Ochi, Takahiko Hara.

**Information Science**: Investigating how to use computers effectively to mathematical problems related to the real world.

This includes computer science, data mining, discrete mathematics, parallel distributed processing,

covered mainly by Yoshimichi Ochi, Hitomi Okuma.