Elementary mathematics refers to courses in categories of numbers, inequalities, algebraic equations, calculus-like sequences, functions, integrals, and differential equations. If the student manages to accumulate a solid foundation in this type of mathematics, then he can study advanced mathematics without any problem. This is why countries like the United States pay more attention to elementary mathematics.
First courses in elementary mathematics
At the very beginning of the mathematics course, we study operations on numbers, types of numbers, even and odd numbers, fractions, and application to units of measurement. At the same time, there is a course in geometry in the plane, triangles, rectangles, and squares,… Thus the pupils learned surfaces and volume. All this material is needed to study Algebra 1 about inequalities and algebraic equations, quadratic equations. This is the mild school level.
At the beginning of the high school mathematics program, students discover advanced tools on real numbers, trigonometric functions, the behavior of functions, graphs of functions, and the integral of a continuous function over bounded intervals.
Math courses in the first year of college
At the University the first important elementary mathematics course is the topology of the set of real numbers. We learn more about this set, such as the density of rational numbers, and characterization of the compact sets in $\mathbb{R}$. Also, subsequences and the Bolzano-Weierstrass theorem are the most important part.
