The meaning of mathematics

The object of mathematics is abstract object. There are 2 ways to get the abstract object.

1. Abstraction

Abstract and abstraction is different. Example abstract: the price of thing, the value of thing, the material of thing, etc. what happen in mathematics? In mathematics, abstraction means the value of something.

2. Idealization

Nothing is perfect . We always assume that something is perfect, but perfect is God’s. We assume that something is sharp, but truly there is nothing which is sharp perfectly. We assume that line is straight. But truly there isn’t a perfect straight line. Mathematics is an art.

What is the object of mathematics?

The object of mathematics is structure, system, formula, pattern, etc. Mathematics is a science which is formed deductively and contains theorems.

The characteristic of mathematics is logic and consistent.

Based a professor from Melbourne University, the characteristic of mathematics is conjecture (thinking, predict) and conviction( to communicate the thinking)

Based from Prof Katagiri from Japans, mathematics consist of 3 aspects:

1. Mathematical attitude

Mathematical attitude is positive thinking, have a question, have a critical when study mathematics.

2. Mathematical method

The mathematical method is :

a. Deduction

Deduction is a method to take a conclusion from general to specific.

b. Induction

Induction is a method to take a conclusion from specific to general.

c. Syllogism

example:

Premise 1 : I am a UNY student

premise 2 : all UNY student have a student card

conclusion : I have a student card.

d. Logic

logic is a knowledge to learn the principle of reflections and take the valid conclusion.

e. Prove

3. Mathematical content

Kinds of the object of mathematics:

a. Formal object: deductive method, inductive method, syllogism method, logic, prove

b. Material object: thinking object, learning based on the ages.

The power of mathematics is critical thinking.

The meaning of mathematics is realistic mathematics:

1. Horizontal mathematics

2. Vertical mathematics

It is my writing about mathematics and its characteristics. I hope I will be useful for the readers. I hope you can see that mathematics is not a simple thing.