Research of Mathematics

Research of Mathematics
We know that in mathematics there is formal mathematics, applied mathematics, and also school mathematics. Now, I will define about each of that.

Formal Mathematics
As we know, mathematics is a system which is deductive and it consist of definitions, axioms, and theorem. In formal mathematics, we must learn calculus, geometry, algebra, number theory, etc.



Applied Mathematics
Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains. Historically, applied mathematics consisted principally of applied analysis, most notably differential equations, approximation theory, and applied probability. These areas of mathematics were intimately tied to the development of Newtonian physics, and in fact the distinction between mathematicians and physicists was not sharply drawn before the mid-19th century. Today, the term applied mathematics is used in a broader sense. It includes the classical areas above, as well as other areas that have become increasingly important in applications. Even fields such as number theory that are part of pure mathematics are now important in applications, though they are not generally considered to be part of the field of applied mathematics per se. Sometimes the term applicable mathematics is used to distinguish between the traditional field of applied mathematics and the many more areas of mathematics that are applicable to real-world problems.



School Mathematics
School mathematics is a mathematics that is learn at school. there, we just focus on the mathematics phenomenon.

Mathematics is used to communicate information about a wide range of different subjects. Here are three broad categories:
• Mathematics describes the real world: many areas of mathematics originated with attempts to describe and solve real world phenomena - from measuring farms (geometry) to falling apples (calculus) to gambling (probability). Mathematics is widely used in modern physics and engineering, and has been hugely successful in helping us to understand more about the universe around us from its largest scales (physical cosmology) to its smallest (quantum mechanics). Indeed, the very success of mathematics in this respect has been a source of puzzlement for some philosophers.
• Mathematics describes abstract structures: on the other hand, there are areas of pure mathematics which deal with abstract structures, which have no known physical counterparts at all. However, it is difficult to give any categorical examples here, as even the most abstract structures can be co-opted as models in some branch of physics.
• Mathematics describes mathematics: mathematics can be used reflexively to describe itself. this is an area of mathematics called meta-mathematics.

References
http://en.wikipedia.org/wiki/Applied_mathematics
http://en.wikipedia.org/wiki/Mathematics_as_a_language