Mathematics is the foundation of all natural science.
By representing the universe in mathematical form, you can resolve the most basic problems.
And that leads directly to the "search for truth."
The Department of Mathematics does not stop at pure mathematics, but fosters a high level of mathematical perception that contributes to resolving all sorts of natural and social phenomena and putting them into theoretical frameworks.
Q. Professor, I understand your specialty is “non-linear differential equations.” What does that mean?
Today, this approach is used in forecasting the weather. However, a wide variety of factors other than wind force and direction, such as heat and the rotation of the earth, make simple, linear representations of weather impossible; the motion is very complex. The equations used to represent such motion are non-linear differential equations.
Mathematicians like myself do not think of events in physical terms, but understand them in terms of expressions. Mathematicians therefore tackle fundamental problems, starting with whether or not an expression has a solution, and if so, how that solution can be expressed as a function, and if not, whether an approximation can be obtained.
For example, from Galois theory we know that it is not possible to obtain solutions for fifth or higher degree polynomial equations, and sometimes it is also not possible to obtain solutions for non-linear differential equations. Even if a solution is known to exist, it doesn’t follow that a function to express it can be readily found. Between these two there is a gap.
Mathematics is intensive thought training in the “search for truth”
Q. What sort of requirements are there for people undertaking fundamental problems in the Department of Mathematics?
Studies focused on skills or qualifications tests can only increase knowledge in a specific field. However, those who build their thinking power with mathematics, the foundation of all sorts of scholarship, can contribute to all aspects of human prosperity. This is because greater thinking power makes it possible to study, talk about, and understand even fields that are unfamiliar.
In striving to increase our thinking power, what we are doing is participating in the “search for truth.” There are some who express doubts about the usefulness of such a quest, but I am certain of its value.
For example, in information engineering, the theory of cryptography is a development of algebra. Financial engineering also includes elements of differential equations. In physics, the fundamental question “what is the smallest unit of matter?” has brought us to fundamental particles, and these fundamental particles are making contributions to nuclear energy research.
The mind is trained in a different way, so there is no need to worry about academic paths.
Q. Since mathematics is a fundamental subject, some students may wonder whether it will help them find employment.
* Actuaries are people who engage in the profession of analyzing the cost of uncertainty and future risk. Also referred to as “statisticians.”