As mathematicians, we should understand about scientific work, mathematical thinking and their relationship. Scientific work is an activity done to find something new and different. We also can define that scientific work is products which are produced by scientific researchers. The example of scientific work are scientific journal, scientific paper, research etc. the specific example of scientific work in mathematics is mathematic research. It also has many characteristics.
First, scientific work is impersonal. It is not related to our mood and feeling. If we do scientific work, we should be professional. Although our feeling is not good enough, but we can’t show that in our work. Second, scientific work has standard. SW can be local, national or international work. SW also has writing criteria. And it depends on what kind of the writing. Third, SW must be objective work. And the last, SW has a regulation that SW is free from plagiarism.
What is mathematics research like? It is like the lectures do research related to mathematics. Or maybe we, as mathematics students do research. Mathematical research is very important because with a lot of research, we can find new formulas, methods, renovations and new concepts in Mathematics. To be a good researcher, we must have good mathematical thinking.
Mathematical thinking is a thinking needed to build our curiosity and ability in mathematics. Mathematics is consistent thinking. It means based on the earlier agreement like the definitions, concepts and procedures. Mathematics consists of pattern and relationship, problem solving, communication and investigation. As we know, mathematics can be divided into Pure Mathematics and Applied Mathematics. Now, we are near with pure mathematics. Pure mathematics is more formal mathematics because it has more axiomatic math. Pure mathematics has a ground of a system. Many mathematicians also have different opinions about mathematics. One expert said mathematics is deductive. The order is from concept, axiom, theorem, proof, then we can find the procedure to prove the theorem. The other expert also said mathematics is a system because mathematics has assumption.
The most important in mathematics is we must have object. Where does it come from? Yeah, it comes from our ideas. It comes from our mind. Because mathematics’ object is abstract. Sometimes, we have difficulties to find the object. So, how do we get mathematics’ object?
The mathematics’ objects are made from the possibility existence and the existence. There are two ways to find mathematics’ objects from concrete objects.
- Idealization
We assume the object is perfect because we need absolutely plane in math. Just assume that the line is straight, the line is absolutely flat. There is nothing which is perfectly formed.
- Abstraction
We just learn many characteristics which are should learned. If we find an object, we can explain million characteristics of that object. We can have a lot of perceptions abut that thing. But in mathematics, we just talk about the shape and the size, the value of that thing. Because those all which we learn in mathematics.
The characteristic of mathematical thinking is logic. It comes from our daily life. We can differ the smaller and the bigger ones. There are many things which show mathematical thinking is logic. The first is mathematical thinking based on order. Then, relationship is very important. Every element in mathematics has a relationship with the others although the relationship is disjoint. The third is MT related to Arithmetic operation. MT use operator like addition, subtraction etc. MT also contains If…Then… statement. For example if N is odd number and M is even number, then N times M is even number. Then, how to get conclusion of statement is one of proof that MT is logic. We can use minor premise and mayor premise. MT use thesis, antithesis and hypothesis to conclude a statement.
Mathematical thinking and Scientific work are very important for mathematics world. With those, we can find newest mathematics information. We can do scientific work if we have an idea. And this idea comes from our mathematical thinking. On the other side, scientific work can be the ways to publish and introduce mathematical thinking. So, both of them are complete each other.
If we want to be success mathematicians, we should make a development in our world. One way is increase our mathematical thinking. We can have new ideas then realize the ideas on scientific work.
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