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▼2014 早春号

A WASEDA Miscellany


GUEST Martin

International Education in Mathematics

GUEST Martin
Professor, Department of Mathematics, Faculty of Science and Engineering

Waseda University is justifiably famous for educating many foreign students, so I would like to offer some personal views on the future of international education in my own subject, mathematics. I came to Waseda quite recently, after working at Tokyo Metropolitan University for 15 years. Before that I worked in the USA, and before that I studied in England. Thus, my views are influenced mainly by universities in the UK, USA, and Japan. But I have also experienced study and research in Germany, as I shall explain later.

There is a worldwide trend to conducting university education in English, but I do not entirely agree with this. For basic mathematics and science (which is already difficult enough!) I believe that students must study in their native language, until they have reached a certain level of proficiency. On the other hand, for more advanced mathematics courses, it is feasible to have some courses in English. Mathematics is very suitable for this, because statements like 2(a+b) = 2a+2b or (d/dx) sin x = cos x are the same in every country of the world. If Japanese students know the basic concepts (from calculus and linear algebra), and if they know some common vocabulary (such as "it follows that" and "without loss of generality"), then they can understand lectures in English.

I would like to relate a personal experience of this kind. When I was a graduate student at Oxford University, I spent a year as a foreign student at the University of Bonn, in Germany. I attended a course given by Professor Friedrich Hirzebruch, one of the foremost mathematicians of the last century. He spoke in English, as there were some foreign students (like me) in the audience. But sometimes a German student would ask a question, and Professor Hirzebruch would reply in German. Then he would continue to give the lecture in German (until he remembered to switch back to English). To my great surprise, I could still understand him, even though my knowledge of German was poor. This greatly increased my self-confidence! Afterwards, I was not afraid to attend a lecture on mathematics in German, and I felt more at ease talking to German students and lecturers.

In the same vein, I believe that foreign students at Waseda must be encouraged to attend lectures in Japanese. I am sure that many of them will enjoy the experience and gain confidence, just as I did in Germany. There are other important reasons for doing this. One is that Waseda has many excellent Japanese students, and foreign students will benefit from interacting with them. Another is that Waseda has many excellent Japanese teachers and researchers, and foreign students should not be isolated from them either. Indeed, it is common sense that foreign students should not be segregated; otherwise, what is the point of them coming to Japan at all?

In order to understand a mathematics lecture in Japanese, a foreign student must have a good command of the basics (calculus and linear algebra). It is necessary to know some basic Japanese mathematical vocabulary (expressions like "kono toki", "gyaku ni" and "hitsuyo jubun joken"). My lectures might be a good starting point for Waseda students, as my Japanese sentences are always very simple!

For graduate courses, it is probably desirable to have several mathematics courses in English. The reason for this is that all current mathematics research literature is in English. From a cultural point of view, this may be unfortunate, but it is a fact. On the other hand it means that Japanese universities with mathematics graduate courses in English would have a good chance to attract excellent students from abroad. In other subjects, the question of internationalization is quite delicate. However, because of its universal logic and symbolism, mathematics can be at the forefront of university internationalization in Japan.


ゲスト マーティン

Photo of the discussion held on Nishi-Waseda Campus, showing the author together with his research partner Professor Lin Chang-Shou (National Taiwan University)
最近の共同研究者の一人、国立大学台湾のLin Chang-Shou 教授と。西早稲田キャンパスで行われたディスカッションでの1枚


 大学の講義を英語で行うことが世界的な流れになっていますが、私は全面的には賛成しません。数学と科学の基礎については、学生はある程度のレベルに到達するまで母国語で学ぶべきだと思います(どちらも基礎の時点で十分難しいです!)。一方、更に高度な数学の講義は英語で行うのに適していると思います。数学は英語で学ぶのに最も適した科目です。なぜなら、2(a+b) = 2a+2b や (d/dx) sin x = cos xといった表記は全世界共通だからです。基本的な考え方(微積分や線形代数など)を理解し、常識的な語彙(「it follows that(〜という結果になる)」や「without loss of generality(一般性を失うことなく)」など)をいくつか理解していれば、日本人の学生でも英語の授業を理解することができます。