Q&A

 Q1 What is the difference between mathematics studied at the Mathematical Institute and mathematics studied in high school?

 Ａ： Consider the following infinite sum. 　S = 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + ．．． Group it with parentheses as 　S = (1 - 1) + (1 - 1) + (1 - 1) + ．．．= 0 + 0 + 0 + ．．．= 0 　S = 1 + (- 1 + 1) + (- 1 + 1) + (- 1 + 1) + ．．．= 1 + 0 + 0 + 0 + ．．．= and + 1　も　- 1 Since there are infinitely many +1’s and -1’s, 　S = (1 + 1 - 1) + (1 + 1 - 1) + (1 + 1 - 1) + ．．．= 1 + 1 + 1 + ．．．= ∞ 　S = (1 - 1 - 1) + (1 - 1 - 1) + (1 - 1 - 1) + ．．．= -1- 1- 1 - ．．．= - ∞ Students at the university mathematics department can explain why this happens easily, but other students probably can not. 　Mathematics includes many difficult and delicate matters, in fact. However, high school education and interdisciplinary education at a university do not usually involve such difficulty. They teach only one aspect of mathematics, which everyone might need to know in daily life. On the other hand, true mathematics is taught at the university mathematics department. You are seldom taught in high school mathematics why a formula is correct. A university mathematics department lets you understand everything by yourself, including the terms under which a formula holds.