||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.