The definition of Mathematics

In the first time when we learn about mathematics, sometimes we want to know about what really mathematics is? What are the functions of mathematics in our life, and etc. We were learning mathematics in every stage of school that is in elementary school, in junior high school, are in senior high school. But, are you know that there are some differences from mathematics in that schools and mathematics in university? Yes, because according Mr. Marsigit there are two types of mathematics. The first is school mathematics and the second is pure mathematics or applied mathematics that we usually get this one in university.
Some or may be almost people in university think that mathematics is very abstract and it means not need to use the actual object. But, the object of it is the abstract idea in your mind. Mathematics as the branch of science actually has a formal and material object. This is thinking thing or abstract ideas in your mind.
The next problem that we found in study mathematics is how to learn it. There are two ways to get the abstract object in mathematics:

1. Abstraction
The means of abstraction here is different from abstract, because abstract means something out of physical object. But, the only one thing that will be the essence of abstractions is value. For example, we know that we can get too much assumptions number 5, but we just need and talk about the value of this number in mathematics, not about the other assumptions. Not about the colors, the taste, the materials, and etc.

2. Idealization
What is an idealization? Idealization is some assumptions or some actual imaginations to think about mathematics. For example, we know that in this world there is no really cute angle, because every goods in this world are consist of molecules that has a very small measure. And in molecule there are some atoms. And in each atom, there are some electrons that have the circle orbits surrounding the centre of atom. So we can conclude that although we can see that the needle is an example of cute angle, but that is actually wrong because the smallest thing in the top of needle is an electron orbit or electron. So we just can see the really cote angle is in our mind.

We are going to talk about what is the definition of mathematics. Mathematics is structure of systems that built with deductively methods. It consists of the definitions, some axioms, theorems, lemmas, formulas, and the role of pattern. And the characteristic of mathematics is logically compound and always be consistent when obey the roles.

According Prof. Kayestesi, mathematics consists of two things, which are:
1. Conjecture
Conjecture is to think or to predict something in our mind.
2. Convince
Convince is to communicate the result of some search to other people. We can communicate it by a lot of ways. For example, by the test, by write it in some journals, or by write it in blog.


The next definition of mathematics is from Prof. Katagiri from
Japan, he said that:

Mathematics is mathematical thinking. Mathematics is not come from books, not from encyclopedia, not from computer, but just from our mind.
There are three components of mathematics thinking:

- Mathematics Attitude
Mathematics Attitude is shows by always has a question. Always positive thinking always be consistent and critical, and always be careful.
- Mathematics Methods
Methods in Mathematics are how to learn Mathematics. There are So many ways to learn it, for example:

Deductions Method
It means explaining something from general to specific items, for example, if we meet someone and know him or her, we a the first sight is just know about the general characteristics, but if we always meet him or her, we can know him until the details characteristics.

Inductions Method
Inductions method means we look something from specific items to general items. For example, we study mathematics in the first time from learn 1+1=2, 2+1=3, 3+1=4, and etc. And after that we learn about something larger from it. That is an example from inductions method.

Syllogism Method
It is the method that taking a conclusion according some
premises or some statements. To be the example is:
Lyra is student.
Every student has an id card.
The conclusion: Lyra has an id card.


Logical Method
It is about mathematics sentence and mathematics prepositions. Mathematics sentence is the sentence that from that we can take a conclusion it is true or not.

And the other methods are:

If then Statement
If and If Then Statement
Direct Proof
Indirect Proof
Incomplete Induction

- Mathematics Content
Mathematics content is the object of mathematics too because in it
there are so many roles and the fixed assumption that used to the source.