# Division of Mathematics and Mathematical Sciences

Department of Mathematics

## Introduction & Policy Outline

Mathematics is an academic field revealing abstract relations between numbers, shapes, and other quantities. Although in its long history mathematics has established solid and lasting logical methodologies, countless new problems keep arising not only from within mathematics itself but also through the influence of other fields, such as physics, biology and economics, among others. New mathematical theories are being actively created one after another in order to deal with these new problems. In addition, owing to its power of abstraction and universal nature, mathematics finds many unexpected applications in various fields, including information science, economics, as well as the natural sciences.

Numerous highly recognized mathematicians including two distinguished Fields Medalists, Dr. Heisuke Hironaka and Dr. Shigefumi Mori, are graduates of our department. Building on these precious assets in the spirit of "academic freedom" fostered by Kyoto University, the department of Mathematics has always been at the forefront of mathematical research worldwide.

In our graduate course, the education of young world-leading mathematicians successfully thrives on its rich traditions. After graduating from our program, graduates either pursue mathematical research, or play another active role in our society. In order to provide such graduate students with advanced expertise in mathematics, we created, amongst others, a cooperative course of Actuarial Mathematics. It is also our mission to train excellent junior and senior high school teachers of mathematics.

The research fields covered at the department of Mathematics are listed below.

**Research Fields:**

Algebraic Geometry / Number Theory / Differential Geometry / Differential Topology / Algebraic Topology / Representation Theory / Complex Geometry / Complex Analysis / Theory of Differential Equations / Operator Algebra / Functional Analysis / Probability Theory / Dynamical Systems / Algebraic Analysis and Mathematical Physics / Applied Mathematics / Computer Science / Actuarial Mathematics

The Division of Mathematics & Mathematical Sciences consists of two courses; on the one hand it is the program in mathematics offered by the faculty of the Department of Mathematics at the Graduate School of Science, and on the other hand it is the program in mathematical sciences provided by the faculty of the Research Institute for Mathematical Sciences (RIMS).

Our undergraduate program offers the fundamental courses of algebra, geometry and analysis that were established in the first half of the 20th century, toward the understanding of modern mathematics. In addition, the department of Mathematics is responsible for general mathematics education for all undergraduate programs in Kyoto University. This includes in particular basic mathematics courses such as Calculus or Linear Algebra.

Department of Mathematics(external link)