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## Doctoral Long-term Internship Program

#### Background and Objectives

In 2006, the Kyushu University Graduate School of Mathematics began a long-term (three months or more) internship program for Ph. D. students in the Functional Mathematics Course of the doctoral course. A total of 60 students have so far completed this program, in this decade.

In general, an internship is a system that enables students to experience corporate research and business practices as an intern. In the School of Engineering, they have had an internship program in which third-year undergraduate students and first-year master's course students become interns for a period of two weeks to one month during their summer holidays. In contrast, students in mathematics have usually been indifferent to corporate internships until just 10 years ago, but in recent years, the demand for mathematicians in the world of manufacturing, information communications, and finance has been increasing, and when a short-term internships for job hunting was even included, many students completing the Master of Mathematics course now came to experience employment in the private sector.

For example, at the research institute of the company they solve mathematic problems by simulation (high calculation software), but, it is not unusual to take one day for one calculation. When the calculation result does not meet the performance that they expected, they change parameters and repeat calculations. Because improvement of the calculation efficiency leads to large shortening of the research and development period, mathematically trained professionals who can get inside the inner structure of simulators which became black-box is demanded. The expectation to mathematically trained professionals increases rapidly for control of the automatic driving in car companies. In the insurance industry, the risk management to perform the prediction and the risk evaluation of the payment detailed money corresponding to the insurance accident becomes the important problem, in addition to conventional duties such as the product development and the profit management, and statistics and mathematics are essential for these.

Students of the Functional Mathematics course devote themselves to their studies to acquire the compatibility to the real world through this internship program in addition to developing a sense of the universality of mathematics and a robust and logical way of thinking through their math courses in order to meet such the social request. Furthermore, by viewing mathematics from a real-world perspective, it is anticipated that interns will come to appreciate the value of mathematics and that of studying mathematics and will reflect their real-world insights in later research.

#### Preparations

Taking sports as an example, a student who is good at mathematics might be compared to a fast athlete. However, while the ability to move fast gives the athlete an edge in just about any kind of competition, mathematics by itself is not sufficient in the real world. Thus, to help students recognize what is lacking before they set out on an internship, people from the corporate world are invited to talk about the role of mathematics in business and industry and the frame of mind that an intern should adopt. Communication skills are also a requirement considering that problem solving in the corporate world is usually carried out by teams. Accordingly, interns are required to have a good command of presentation, spreadsheet, and word-processing software in addition to programming skills such as Python and the C language.

In a company, specialists in various fields work together to solve problems.

#### Results

Participating companies have been summarized below. As well as students who are specialized in statistics, optimazation, numerical analysis and computer science, a lot of students who are specialized in pure mathematics such as algebra, geometry, the analysis, participate in Doctoral Long-term Internship Program.

NTT Group, SUMITOMO GROUP, TOSHIBA Group, Nippon Steel Group, HITACHI Group, Panasonic Group, FUJITSU Group, MITSUBISHI GROUP, ING Insurance, Ube Industries, Kankyo Technos, CATALER, National Institute of Information and Communications Technology, Zetta Technology, DIC, Technos, DENSO, NISSAN, Nisshin Fire & Marine Insurance, IBM Japan, HUMAN TECHNO SYSTEM, MAZDA, MITSUI E&S, Roland |

#### The specialty of Interns

Students who specialize in statistics, numerical analysis and computational theory can work on problems using their specialty. Cryptography is the ideal theme for students who specialize in algebra. Data compression is also the theme for which their specialty can be utilized. Image recognition and image processing are themes for which many students of mathematics are prepared. University supports students who work on themes different from subject of study during internship, by providing the place for consultation by mathematical experts. As a result, several students achieved results such as coauthored academic papers and patent applications. In addition, several collaborative researches began with the internship. About half of the 37 people with doctoral degree in the Functional Mathematics course find employment in companies, and 14 have postdoctoral and assistant professor positions.

#### Impressions of Interns and Mentors

The following are typical of comments made by interns and mentors in the internship program.

- My outlook broadened by interacting with people that I had never come in contact with before in the world of mathematics and by encountering research fields I would have never known about. This has become a big asset for me.
- It hit me how useful mathematics could be in the real world.
- I realized that being comfortable around formulas as opposed to resisting them is the strength of true mathematicians. I also found out that without skills to explain mathematics and get others to understand its effect, it probably would not be accepted in the corporate world.
- I felt a sense of solidarity with the people around me and a sense of responsibility in my work that I could never feel in everyday life. This was a great experience for me.
- I admired the tenacity and organizing power that drove the experiments and data analysis in the company.

- I admired the intern's positive attitude in trying to understand the essence of a problem even in areas outside of his specialty. I was also surprised at the interns' highly intuitive ability toward formulas and numbers.
- The intern's ability to comprehend and discern was superb enabling him to complete the internship project quickly and correctly. His explanations were also very easy to understand, which was much appreciated.
- I came to realize that basic skills in mathematics will be even more of a necessity for developing advanced technology in the years to come. That is, I came to realize again the importance of mathematics in technology development.

In addition to these impressions, the optimistic, cheery attitude of the interns reveals a high level of satisfaction and self-confidence. Even greater results can be expected if an intern works on improving programming and presentation skills. In 2008, a student skilled in statistics passed a one-hour-plus telephone interview in English after doing a half-year internship in English at a foreign-affiliated enterprise. The need for mathematics education that can contribute to industry is beginning to be realized in Europe as well, and an international conference in this regard is being held this year in Portugal. Developments such as these reflect the dramatic changes taking place in the world of mathematics. It's the Graduate School of Mathematics at Kyushu University that is quickly responding and adapting to these changes.

There are 8 successful students who have conducted internship overseas at the Kyushu University Leading Graduate Program.