THE RESEARCH OF MATHEMATICS

BACKGROUND

Mathematics is the general characteristics. It’s become the another science always has the connectivity with mathematics. Another science can’t be apart from mathematics. Such a mathematics in our life too. Our life is the same with the science. It can’t be apart from mathematics. In the real example, when we go to the traditional market, we can demand and bargain what we will buy in there. Surely, mathematics always in there, between seller and customer.

Mathematics use in the world as the important tools in many subject, including a science, medical, and social knowledge as economic and psychology.

In a formal side, mathematics is to analyzed the abstract structure, that defined axiomatic with a logical symbols. Mathematics also used as a tools for studying many kinds of complex physics phenomenon, especially the nature phenomenon that observed. With mathematics, the structure, transformation, space, and the phenomenon characteristics can be approach and can be write in the systematic formulation and with many kinds of appointments and symbols. The result that describe about the physics phenomenon called mathematics models.

A mathematics models in optimization and control usually explain the system as the combination from the variables and also from the collection of equations that defined of relation of that variables. The variable value can be like a real number, or can be like a number arrays and strings.

Variables actually served in many characteristics system. Mathematics models actually is a collections of functions that has the relation between the different variable.

Models theory started with the assumption of mathematics object, searching, and analyzing the operations, relations, or axioms in every object or in the collections of object.

Mathematics as the logical science that study the ability of the right thinking. Logical is a branches of philosophy. Logical can be applied in a day’s life. Logical used for proofing. Logical can’t be avoid in a life process to find a honesty.


RESEARCH OF MATHEMATICS

Mr. Marsigit said that research of mathematics are the aim to examine and develop mathematics. And in my opinion, research mathematics is more explain the details of mathematics, from the theorems, axioms, then the proof of all the theorems. All of them trained us to always open our mind to be a scientist that has the mathematical thinking. Beside that, research of mathematics also means all the activity that have relation with mathematics in our life. It means that all of the applications of the theorems until the characteristics of mathematics can applied in our life, especially in habitual activity. Because mathematics has the general character, so it also can be applied in another subjects, for example in the chemistry, physics, etc. Its all means that our life and all of the science can’t be apart from mathematics.

“Mathematics is a deductive system. Consist of definition, axioms, and theorems in which there is no contradiction inside”, said Mr. Marsigit.

Mathematics has the philosophy. Philosophy of mathematics is a branches of philosophy that its learn about the basics and the results of mathematics. The purpose of philosophy mathematics is to give characteristics and mathematical methods and to know more about the position of mathematics in our life.

The characteristics of mathematics, is an abstract objects. An abstract object also called the mental object, its in our mind. The basic object consist of fact, concept, definition, operations, and principal. From the basic object, it can be constructed the structure of mathematics. The fact in abstract object in the conventions form and its in the many kinds of symbols. The definition are the appreciation that bounded a concept.

The system of mathematics is the important structure, especially in algebra and generally in mathematics. Group is one of the example of system mathematics.
For example: (G,x) is a mathematical system, so (G,x) called group if complete:
1. Associatif characteristic, for every a, b, c in G so ax(bxc) = (axb)xc
2. Has the neutral unsure , write e as the unsure, where for all a in G conduct exa = axe = a
3. Every member of G has neutraler, every a in G has b in G, so axb = bxa = e

Action research in a traditional aspects means a frame research to solving the problems, where there are have the collaboration of scientist and client to reached the purpose (U. Sulaksana, 2004).

Action research also defined as the action of planning, realization, and evaluation to be better as the purpose, and its doing with the systematic (Gunawan, 2007).

Action research also means a process that has an action ciclus, based the reflection, feedback, evidence, and the evaluation of action before and the situation now. The aim of action research is to give the role of problem solving in problematically situation like now (S. Madya, 2006).


DISCUSSION

A. Formal Mathematics

The complex mathematical object consist of many fact, many concept, that related with operation like axioms, theorems, characteristics, etc.

Axioms is undefined term, a basic explanation but it doesn’t important to proof it. Its to avoid the confusing on proofing. The axioms can establish a system of axioms, and it can to get the lemma and theorems.

The example of formal mathematics is in the number theory. The definition of number theory is a basic theory to learn the algorithm cryptography. And an integer is a kind of number that learn in number theory. Integer means a number that doesn’t has a fractional decimal, for example: 8, 21, -21, 0 etc.


B. Applied Mathematics

Applied mathematics is a branches of mathematics that enclose the application of mathematical knowledge in another aspect, and made a new discover of mathematics.

An applied mathematics was combined with the traditions that agree with mathematics, but its out of mathematics. For example: statistics, operation research, and computer.

Applied mathematics has a relation with the usage of abstract mathematical tools to solving the concrete problems in a science, business, and another aspects. For example statistics. Its use the opportunity theory as the equipment and explain, analyze, and calculation of phenomenon in which the opportunity has the important role, because all of the test, survey, and learn of control needs statistics.

One of the applied mathematics is the application of number theory, that it used in barcode methods. Barcode is a simple code that used to save the specific data, like production code, an expired date, and also an identity number. A rows code consist of a bar and space with the different bold that presented alpha-numeric characteristic.


C. School Mathematics

Mathematics is a science that has alot of usage for us in our live. It use in many kinds of aspects and used by many kinds of subjects. There are a lot of brances of mathematics that apllied in another science. So, mathematics is a universal science. And because of that, we can study mathematics everytime and anywhere.


REFERRENCES

Sulaksana, U. 2004. ”Managemen Perubahan”. Cetakan I. Yogyakarta: Pustaka Pelajar Offset.
Madya, S. 2006. “Teori dan Praktik Penelitian Tindakan (Action Research)”. Bandung: Alfabeta.
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