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?



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

A: Mathematics subjects currently studied at university mathematics department are roughly classified as algebra, geometry, and analysis.

Algebra is an advanced form of polynomial calculation learned in high school mathematics. Number theory includes studies of the properties of integers, e.g. what kind of distribution do prime numbers take on a number line?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, ・・・

A set of all the zeros of some polynomials such as the following equation is designated as an algebraic variety.
y2 = x3 + a x + b (where a and b are constant)

Algebraic geometry
is the study of geometric properties of an algebraic variety. A set with a well-behaved product, such as all the maps from a cube to a cube, or all the 2 × 2 invertible matrices, is designated as a group. The group theory, which studies various properties of a group, is also an important field of algebra.
is a discipline including the study of properties of figures and shapes. It includes topology, in which one studies invariant properties of a figure in continuous deformation, and differential geometry, in which one studies invariant properties of a figure in smooth deformation
No two-dimensional, closed, and curved surface lacks a boundary, other than a spherical surface and a curved surface some holes like a ring buoy. That is one of the simplest results of topology. A bubble forms a curved surface called a minimal surface. Its study is an important theme of differential geometry.

is an advanced form of calculus studied in high school mathematics. For example, using Euler equation: e^iz = cos z+i sin z, exponential function e^z can be extended to a complex valued function of a complex variable. It demonstrates that the exponential function and trigonometric functions are functions of the same kind. Analysis includes function theory, in which one studies properties of such functions of complex variables. In Fourier analysis, one studies properties of periodic functions, expressing them as sums of sine and cosine functions. In the theory of differential equations, one studies solutions of differential equation such as y"+ a(x) y'+ b(x) = 0. In functional analysis, one studies properties of infinite dimensional vector spaces such as the space C (R) all the continuous functions on the real axis. Probability theory is used for studies of regular and complicated matter like a fractal. For example, a differential equation describing the properties of fluids has a well-behaved solution. This is a prevailing research theme of analysis.

Other subjects of mathematics include foundations of mathematics in which one studies properties of mathematical logics and axioms.
TOHOKU UNIVERSITY Graduate School of Science and Faculty of Science,
Tohoku University
Division of Mathematics
Graduate School of Information Science
Tohoku University