Q1What is the difference between mathematics studied at the Mathematical Institute and mathematics studied in high school?

Q2 How do I study in the Mathematical Institute? What is the merit of studying at the Mathematical Institute in graduate studies?

Q3 What subjects do I study at the university mathematics department?

Q4 In what order will I study mathematics courses at the university mathematics department?

Q5 What is interdisciplinary education?

Q6 What is a seminar?

Q7 I got better grades in high school mathematics than other students. Can I learn mathematics well in the university mathematics department?

Q8 What is important for studying at the Mathematical Institute?

Q9 What should I do when I am lost in mathematics?

Q10 What kinds of jobs are available after graduation from the Mathematical Institute?

Q11 How can I carry out a job search at the Mathematical Institute?

Q12 How much does it cost to enter Tohoku University?

Q13 How much does it cost to rent an apartment in Sendai?

Q14 How is mathematics useful to society?

Q15 Please give me some examples of how mathematics is useful for the outside world.

Q16 Will mathematicians' research truly contribute to society?

Q17 How can I solve problems in study or private life?

Q18 What should I do if I cannot get along with my instructor?



Q4 In what order will I study mathematics courses at the university mathematics department?

A: Calculation of expressions, properties of figures and shapes, and differentiation and integration are studied in high school mathematics. University mathematics expands on the study of these subjects.

In the first year at university, more advanced calculus and matrix theory (linear algebra) are studied than in high school mathematics. In interdisciplinary education, one studies how to solve a differential equation, mathematical statistics as an introduction to probability and statistics, and theory of functions of complex numbers as variables

  One starts to study true mathematics during the second semester of the first year.

The present mathematics is described using the language of set theory. Therefore, students learn first about sets with infinitely numerous elements. For example, the sets of natural numbers, rational numbers, real numbers, and complex numbers have infinitely many elements. It turns out that the set N of natural numbers and the set Q of rational numbers have the same degree of infinite elements, as do the set R of real numbers and set C of complex numbers. However, it turns out that each of R and C has far more elements than N either or Q.

Convergence and continuity of a sequence are explained intuitively in high school mathematics or liberal arts education at a university, but one is at a loss to explain why the following strange things
0 = 0 + 0 + 0 + . . . = (1 - 1) + (1 - 1) + (1 - 1) + . . .=
1 +(- 1 + 1) + (- 1 + 1) + (- 1 + 1) + . . . = 1+ 0 + 0 + 0 + . . . = 1
happen in such a manner Therefore, (1) What is convergence? and (2) What is continuity? are studied next. These issues, first discovered at the beginning of the 19th century, are taught as the theory of topological spaces in the Mathematical Institute in Semesters 2?3, from the second semester of the first year to the first semester of the second year.

Once you understand them, you can study modern mathematics. Then, students study algebra, geometry, and analysis in detail.

TOHOKU UNIVERSITY Graduate School of Science and Faculty of Science,
Tohoku University
Division of Mathematics
Graduate School of Information Science
Tohoku University