What is Mathematical Science?

Welcome to the Department of Mathematics

Understanding from the Basics is the Real Power

What’s considered trendy today will most likely be old-fashioned in 10 years. However, studying in the Department of Mathematics is not one of them. Mathematics theorems retain the same value today as they were proven over 2,000 years ago. Some theorems have even increased their values thanks to the development of new science and technology. The basics of information technology are supported by number theory and discrete mathematics, and the knowledge of statistical science and probability theory is indispensable for analyzing massive amounts of data.
By learning such universally valuable studies, you can build a solid foundation of your perspective and worldview. This foundation includes many seeds of ideas that can be useful in society. We welcome not only those who want to pursue mathematics as an academic study but also those who wish to apply mathematical thought in society. What you earn here is highly valued in various fields of society.

The Very First "Mathematical Science" Department in Japan

There are various universities, including national universities, with a Department about Mathematical sciences today, but Keio University was the first in Japan to establish this department. Mathematical sciences refer to a wide range of academic fields from so-called pure mathematics to academic fields that apply mathematics. We carry out various fields of educational research in order to cultivate students who apply such skills to a wide range of fields. For example, we are well known for the fields of differential equation theory, geometry, probability and ergodic theory, number theory, discrete mathematics, computational mathematics, and statistical sciences. Furthermore, our department is distinct in that these various studies are organically linked.

It’s Important to Think by Yourself

Have you ever spent a long time trying to solve a math problem? If you could luckily solve it, the joy you felt must have been exceptional. Real math is neither memorizing formulas nor memorizing problem patterns. It's important to take your time and think through it. The time you spend while being stuck on a problem will not be wasted, and the learning you gain only through this process will become a great asset to you. If you are one who likes to ponder over things until you are fully satisfied or one who loses track of time when sitting in front of a computer, you are a good candidate for the Department of Mathematics. Also, there is a diverse pool of students in our department. This diversity is necessary, because mathematical sciences is the science that studies mathematical nature, which is as diverse as ordinary nature.


What you can learn in Department of Mathematics,
Mr. Naoto Dainobu(a Ph.D. student, Kurihara Laboratory)

When I talk with my friends in other departments, they sometimes tell me that the mathematics in the Department of Mathematics is different and awful.
I guess they want to say that the mathematics I'm studying is difficult. I don’t think that their impression is completely correct, but I certainly feel that mathematics learned in the Department of Mathematics is different from mathematics learned in other departments. For example, while my friends in other departments were calculating Fourier series expansions, I was learning what kind of functions could be expanded into Fourier series. So, I have the impression that in our department one can learn fundamental theories which are much deeper than the mathematics for mere theory users. In that sense, our department provides the best environment for those who want to understand the principles and the reasoning of things.

In our department, we have many opportunities to present and explain our ideas in front of people. For example, in a seminar which is regularly held, we have to present what we have studied in front of an audience including supervisors in the 4th year. Through these seminars and discussions with various people, the students can acquire the ability to explain things logically and concisely. You may think that is not much, but this ability one can get in our department is extremely valuable. Because this ability is obtained through the trainings of the talk in front of senior students and professors. Having only a rough understanding of the text is not at all enough. One has to study the text fully and completely before the seminar. The skill you obtained will be useful, not only inside the Department of Mathematics, but also outside of our department throughout your life.

You might think that it is hard to study in our department, but we have a system that many people help you when you need it. I also received a lot of help from my classmates, senior students, and professors. Let's study together in the Department of Mathematics.

Theme Park named Mathematics Mr. Hikaru Matsumoto(Completed a Master’s degree in March 2021, Ota Laboratory)

Are you interested in the Department of Mathematics but hesitate to pursue it because mathematics seems like a small world, and you are worried about keeping up with the studies? I thought that too when I was choosing a department. But I chose the Department of Mathematics thinking I could work it out somehow once I jumped in.
As I studied mathematics, I realized the breadth and scope of mathematics as a field of study. The world of mathematics, which once seemed like a narrow straight road, now feels like a vast theme park. Mathematics covers a variety of subjects from pure mathematics to statistics, which shares the same concept of using numbers to express ideas under strict logic. This is my current image of mathematics, which overlaps with my image of the Departments of Mathematics, where people with a wide variety of specialities and interests come together to pursue the same academic subject.
It’s up to you how you spend your time and what you enjoy at this theme park. From those who are eager to start studying to those who don’t quite have the confidence in pursuing mathematics yet, as long as you have the desire to understand and enjoy mathematics, you can eventually find an attraction that suits you and that you enjoy.
You may sometimes get stuck because you cannot understand the classes or your research doesn't progress well. Even in these times, you will have friends that help you and professors to show you the right path. The Department of Mathematics provides opportunities for discussion and social gatherings both inside and outside the classroom for that reason. Many people think that studying mathematics on their own is not easy, but you will be able to move forward when you have friends and professors to talk to. I believe this is the real value in studying mathematics at a university.
Instead of worrying, I believe there is something fun waiting for you if you take a step forward. I hope that you will have a good relationship with mathematics.

What it means to study statistics Dr. Tomoshige Nakamura(Completed a Doctorate degree in March 2021, Minami Laboratory)

Statistics is the study of various "data" such as the population of countries, the collection of GDP of the world, fluctuations in stock prices, and sales. Specifically, we study methods related to the processes of those data collection, organization, analysis, and interpretation of analytical findings. One of our motivations for studying statistics is to discover some kind of regularity in phenomena that look random. Fluctuations in stock prices and fish catches seem to fluctuate randomly on a daily basis, but they are actually ruled by regularity. The discovery of these rules leads not only to understand phenomena themselves but also to support our daily decision-making.
Today, various things are converted into data, and the range of application of statistics continues to expand. Even in fields such as sports, education, and healthcare, where experience has traditionally been valued, the increase in available data is allowing more accurate analysis to become possible. Through these analyses, there have been cases where actions being done with an expected result actually had “no effect” from a statistical viewpoint.

Of course, statistics is an intriguing academic discipline but its appeal is not limited to research. Statistics is increasingly being recognized as a tool for understanding things and supporting appropriate decision-making in a society where the amount of data keeps increasing. In other words, statistics is starting to show its value by being applied to the real world. As we go out into the world, it is impossible to live without data. I believe that studying statistics in our department will definitely lead to acquiring a skill that will arm you to survive the future. Why don’t you study statistics with us?