Campus Now
Early Spring Issue (Apr. 2014)
 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 selfconfidence! 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.