## Research Areas at the Department of Mathematics

Mathematics is often described as the foundation of various scientific studies.
Because of its traditional and fundamental nature familiar to us,
mathematical study is usually considered
as an academic discipline based on the past achievements. Indeed,
mathematics does have a long rich history.
At the same time, however, it continues to grow rapidly.
A number of academic journals are published and
revamped every year, and research conferences and seminars
are regularly held to bring together researchers
from all around the world.

With rapid advancements witnessed in various
fields of science,
the scientific community is always pursuing new types of
mathematics.
Breakthroughs in mathematics, on the other hand, are also contributing to new
perspectives on other scientific disciplines. Many new fields of
mathematics have been born from attempts to solve particular
phenomena by formalizing
them with mathematical expressions.
This dynamics is exemplified in the relationship between the evolution
of Modern Physics and the emergence of new mathematical approaches,
such as Functional Analysis, Differential Geometry, Differential Equations,
Topology, Algebraic Geometry, Algebraic Analysis, Probability Theory,
and Dynamical Systems. In their early forms, such new approaches are
largely unsophisticated; however, the very efforts to seek greater
sophistication and define essential elements through
formalization have led to the overall progress in
mathematics.

The Department of Mathematics at
Hokkaido University preserves this spirit, covering a wide range of research areas
--- from theory-driven approaches that mainly seek to achieve theoretical sophistication,
such as Number Theory, to more practical approaches that employ computers
for calculations of various phenomena.
Our diverse curriculum also includes what is known as Mathematical Sciences.