The Power of Category and Networking

According Kant’s theory, in our mind there are some category. With the categories which are in our mind, we can get some knowledge. In Immanuel Kant’s theory, category involves four things. They are Quantity, Quality, Relation, and Modality.
Every category consists of three aspects:
1. Quantity
• Universal
 Universal is only one
 It can load all of everything
• Particular
 Form a parts or groups
 Easy to be in groups
• Singular
 Form a parts or groups
 Be autonomous
2. Quality
• Affirmative
 All of things which has positive character
 Explanation of some statements
• Negative
 All of things which has negative or abjuration character
 Explanation of some statements
• Infinite
 All of things which has infinite character
 Restrictive
3. Relation
• Category
 Has function to difference thing with another
• Hypothetic
 Explanation about cause and effect relation
• Community
 Interaction between active and passive
4. Modalities
• Probabilities
 Has problematic character
 In between possible and impossible
• Asetorik
 In between exist and not exist
• Apodictic
 Work based on consistency
With those categories, we can build knowledge that we get it before. With use those category, contains of experiences are managed and then will be product.
We study to understand about category, it means we study to aware that there are things that should be in phenomena, there are things that should be in mind, and there are things that should be in “epoke”.
We study about category, will make us easy to face some knowledge. And we can get knowledge from school or from daily life. The example of category is mathematics education phenomena.
In the teaching and learning of Mathematics, there are idealization and abstraction. What are they?
1. Idealization
Idealization is only in our mind. We assume that the characteristic of Mathematics is absolutely true. So we consider that something is perfect. It is just to consider because there is no anything in this world can be perfect.
2. Abstraction
Abstraction is not same with abstract. Abstraction is only to learn some characteristics from object, not at all. There are differences between abstract and abstraction. We know that abstract is not concrete. We can’t see, touch, and observe, but we can imagine about it. On the other side abstraction is the value which is contained in mathematics.
Mathematics consists of three aspect:
1. Math-attitude
As mathematicians which have good attitude, we must always positive thinking, consistent, diligent, and always have questions about problem.
2. Math-method
How to learn mathematics? We can use one of some methods of mathematics. They are deductive, inductive, syllogism.
o Deductive is based of each lesson about formal logic
o Inductive
o Syllogism can be used to make new conclusion from some premise
3. Content
Mathematics consists of two kinds:
o Horizontal mathematics
Example: daily mathematics. The object of this mathematics is real object.
o Vertical mathematics
It is pure mathematics, which is developing in college.

HOW TO UNCOVER PSYCOLOGICAL PHENOMENA

In Mathematics learning psychology course, at November 10th 2009, the lecturer, Mr. Marsigit tell us that we must give one suggestion or comment about our learning. There are some comments teaching learning process:
1. More responsible
2. In the teaching and learning should be more systematic and clear
3. Syllabus is not clear
4. The Teaching Learning process is not monotone
5. The student should read a lot
6. The student are not ready in the learning process, because the material is not clear

This case is considered as one of communication form between the lecturer and student. So we can know what the better for the learning process. And this case can increase student motivation in following the course.
One communication problem that is discussed in the class is about traumatic. Traumatic is all events that can’t be explained. Philosophically, traumatic is known as accident. In politics, authoritative governance can cause a traumatic. While psychologically, traumatic is known as hermeneutic. In Hermeneutic, there is spiral dynamic. A good communication is a dynamic communication, which is consisting of two kinds, flexible and contextual.
Psychologically, spiral dynamic is known as contextual. While philosophically spiral dynamic is known as flexible, depends on the place and the time. So it is fixing with the real condition.
Authoritarianism can cause traumatic. Everything without any sign or other situations can cause traumatic, too. That case should be notice in the teaching learning process. Don’t become authoritative, because it will cause traumatic for the students.
In this life, we can see outside through three ways:
1. With concepts
2. With perception
3. With sensation
If we look the world only through the sense, it’s not enough, because it is a part of concepts. Experiences that is got from sense is called empirical concept. While the meaning of a priory concept is everything that isn’t look reality, and isn’t look for a data. This concept often is used in pure mathematics. Example: f(x) =x+5, where x is integer. This case can be founded without a data. Sometimes we can use assumption. Assumption is undefined term. It is not need explanation, because it has been assumption for general people. In pure science, we often use definition, axiom, and theorem. All of those are concepts. Generally, life is traumatic, so if you want to still alive, you have to be a courageous person in facing traumatic.

In teaching and learning process there are some cases that we must understand about it.
1. Structure of Teaching
a.Introduction
b.Teaching Learning Process
c.Closing remark
2. The scheme of Interaction
a.Classical
b.Group Discussion
c.Individual
3. The scheme of competencies achievement
a.The nature student
b.The nature subject
4. The Nature of student learn Mathematics, in fact the student:
a.Need motivation
b.Individual
c.Need collaboration
d.Learn in content

We can get mathematical object from the existent and possibility of existent in this world.
How to get mathematical object?
1. Idealization
To consider something is perfect. Just to consider because there is no anything in this world can be perfect.
2. Abstraction
Only to learn some characteristic from object. Look and analysis something from certain side.
Kind of Mathematical Object :
1). Mathematical thinking
Think consistently according first certainty.
2). Mathematical logic
Meaning of mathematical logic :
1. Can differentiate between two object
2. Can to order
Addition, Subtraction, Multiplication, etc are the example of mathematical logic.
Connection between mathematical thinking and Scientific work :
1. The Scientific work must be impersonal
Not concerned with personal.
2. The Scientific work must have a criteria.
Depend on the purpose.
3. The Scientific work must be objective.
The example of Scientific work, they are like proposal, text book, etc.

Quadratic Equation, Trigonometry, Limit and My Exercise in Lesson English

Last Meeting, I get some homework from English lesson. I have to posting about quadratic equation, trigonometry, and statistics. And I will try to explain about those.
1.Quadratic Equation
General formula of quadratic equation is a x square plus b x plus c equals zero, where a, b, and c is real number and a is not equals zero.
The value of x which to fulfill quadratic equation are called the roots of quadratic equation.
There are three ways to finish quadratics equation, they are:
1)with factorization
2)with completing perfect quadratics
3)with a formula
I will to try explaining these one by one
1) With factorization
For example there is a quadratic equation: x square plus ten x plus twenty one. And we will find the factors of that quadratic equation.
x square plus ten x plus twenty one
factors of x square are x and x
factors of twenty one which its sum is ten are seven and three
So, factors of x square plus ten x plus twenty one are x plus seven and x plus three.
2) With completing perfect quadratic
x square plus two a x plus a square is form of perfect quadratic, because x square plus two a x plus a square equals x plus a in bracket square. Whereas x square plus two ax is not perfect quadratics, because x square plus two a x is not equals x plus a in bracket square.
For example we will finish quadratic equation: x square plus six x plus two equals zero.
Answer:
x square plus six x plus two equals zero
x square plus six x equals negative two
x square plus six x plus a half of six in bracket square equals a half of six in bracket square minus two
x plus three in bracket square equals seven
x plus three equals plus minus the square root of seven
x equals the square root of seven, minus three, or
x equals negative the square root of seven, minus three
3) With Formula
The roots of quadratic equation a x square plus b x plus c equals zero, can be finished with formula.
x1 equals negative b plus the square root of open bracket b square minus four a c close bracket, all over two a
x2 equals negative b minus the square root of open bracket b square minus four a c close bracket, all over two a
Formula above usually called with abc formula

I have explained about three ways to finish a quadratic equation. And now, I will give example about quadratic equations.
Example:
Derry has a park which its shape is rectangle. Width of rectangle is three less than of the length. If the area of the park are twenty eight meters square. Find the length and width of the park.
Answer:
Given: x is the length of rectangle (park) in meter
x minus three is the width of rectangle (park) in meter
Twenty eight is the area of rectangle (park) in meter square
Equation
The area equals the length times the width
Twenty eight equals x times x minus three in bracket
Twenty eight equals x square minus three x
x square minus three x minus twenty eight equals zero
x minus seven in bracket times x plus four in bracket equals zero.
x equals seven or
x equals negative four (unacceptable)
So the length of the park equals seven meters and the width of the park equals four meters.

2.The Function of Trigonometry
At the plane coordinate, each point P(x,y) determinant the angle of XOP equals alpha. Between alpha, x, y and OP, there are connection as like this :
Sinus alpha equals y over OP
Cosines alpha equals x over OP
Tangents alpha equals y over x
Cotangents alpha equals x over y
Secants alpha equal OP over x
Co secants alpha equal OP over y
If we look the position of point P(x.y) at the coordinate plane, absis and ordinate can get the value negative, positive, and zero. Combination from the value absis and ordinate of point P, will determinant the value for the function of trigonometry.
Function of Trigonometry
1). Formula of cosines alpha plus beta in bracket
Cosines alpha plus beta in bracket equals cosines alpha times cosines beta in bracket minus sinus alpha times sinus beta in bracket.
Example: Cosines seventy five degrees
Answer:
Cosines seventy five degrees equals cosines forty five degrees plus thirty degrees in bracket.
Equals cosines forty five degrees times cosines thirty degrees in bracket minus sinus forty five degrees times sinus thirty degrees in bracket.
Equals a half the square root of two times a half the root square of three in bracket minus a half the square root of two times a half.
Equals a quarter the square root of six minus a quarter the square root of two
Equals a quarter times open bracket the square root of six minus the square root of two close bracket.
2). Formula of Cosines alpha minus beta in bracket
Cosines alpha minus beta in bracket equals cosines alpha times cosines beta in bracket plus sinus alpha times sinus beta in bracket.
Example: Cosines fifteen degrees
Answer:
Cosines fifteen degrees equals cosines forty five degrees minus thirty degrees in bracket.
Equals cosines forty five degrees times cosines thirty degrees in bracket plus sinus forty five degrees timer sinus thirty degrees in bracket.
Equals a half the root square of two times a half the square root of three in bracket plus a half the square root of two times a half in bracket.
Equals a quarter the square root of six plus a quarter the root square of two.
Equals a quarter open bracket the square root of six plus the root square of two close bracket.
3). Formula of Sinus alpha plus beta in bracket
Sinus alpha plus beta in bracket equals sinus alpha times cosines beta in bracket plus cosines alpha times sinus beta in bracket.
Example: Sinus one hundred and five degrees
Answer:
Sinus one hundred and five degrees equals sinus sixty degrees plus forty five degrees in bracket.
Equals sinus sixty degrees times cosines forty five degrees plus cosines sixty degrees times sinus forty five degrees in bracket.
Equals a half the square root of three times a half the square root of two in bracket plus a half times a half the square root of two in bracket.
Equals a quarter the square root of six plus a quarter the square root of two.
Equals a quarter open bracket the square root of six plus the square of two close bracket.
4). Formula of Sinus alpha minus beta in bracket.
Sinus alpha minus beta in bracket equals sinus alpha times cosines beta minus cosines alpha times sinus beta in bracket.
Example : Sinus fifteen degrees
Answer :
Sinus fifteen degrees equals sinus sixty degrees minus forty five degrees in bracket.
Equals sinus sixty degrees times cosines forty five degrees in bracket minus cosines sixty degrees times sinus forty five degrees in bracket.
Equals a half the square root of three times a half the square root of two in bracket minus a half times a half the square root of two in bracket.
Equals a quarter the square root of six minus a quarter the square root of two.
Equals a quarter open bracket the square root of six minus the square root of two close bracket.
5). Formula of tangents alpha plus beta in bracket
Tangents alpha plus beta in bracket equals tangents alpha plus tangents beta all over one minus open bracket tangents alpha times tangents beta close bracket.
6). Formula of tangents alpha minus beta in bracket
Tangents alpha minus beta in bracket equals tangents alpha minus tangents beta all over one plus open bracket tangents alpha times tangents beta close bracket.

My Exercise in Learning English
1.Explain how to proof that the square root of two is irational number!
Answer:
If the square root of two is rational number, so the square root of two equals a over b.Given a and b are prime integer number
a equals the square rot of two times b
a square equals two times b square
Because a square is two times any integer number, so a square is even, so that a is even too.
If a equals two times c
Two times c in bracket square equals two times b square
Four times c square equals two times b square
B square equals two times c square
So that, if b square is even, so is even too. But this is impossible because a and b bilangan bulat prima. So, can be proved that the square root of two is irrational number.

2.Explain how to show or to indicate that the sum angles of triangle is equal to one hundred and eighty degrees!
Answer:
There is a triangle ABC.
We can prove that the sum angles of triangle is equals to one hundred and eighty degrees by drawing a line through one vertex of triangle (through point B), parallel to the side opposite the vertex (parallel to AC). Note that the measure of straight angle at B equals the sum of the measure of the angles of triangle ABC.
Angle A plus angle B plus angle C equals one hundred and eighty degrees.

3.Explain how you are able to get phi!
Answer:
We can get phi from the circle. In a circle, we find the diameter and perimeter of that circle. And if we cut the circle, we can get the perimeter of the circle.So, we can get phi from the perimeter divided by diameter of the circle.

4.Explain how you are able to find the area of region boundered by the graph of y equals x square and y equals x plus two.
Answer:
First we must find the intersection point of y equals x square and y equals x plus two. We can use substitution method to find them.
X square equals x plus two
X square minus x minus two equals zero
X minus two in bracket times x plus one in bracket equals zero
X equals two or x equals negative one.
If x equals two, so y equals four. And if x equals negative one, so y equals one.
So that intersection point of curve y equals x square and the curve y equals x plus two are (two, four) and (negative one, one).
After we know about the intersection point of them, we must draw the curves.
And we can find the area of the region boundered by the graph of y equals x square and y equals x plus two with integral.
The area of the region is A
A equals definite integral x plus two minus x square dx from x equals negative one to x equals two.
A equals a half x square plus two x minus one third x cube, from x equals negative one to x equals two.
A equals a half times four plus two times two minus one third times eight in bracket minus a half plus two times negative one minus one third times negative one in bracket.
A equals two plus four minus eight third in bracket minus a half minus two plus one third in bracket.
A equals six minus eight thurd minus a half lus two minus one third.
A equals eight minus a half of seven.
A equals a half of nine.

5.Explain how you are able to determine the intersection point between the circle x square plus y square equals twenty and y equals x plus one!
Answer:
To determine the point between the circle x square plus y square equals twenty and y equals x plus one, wecan use substitution method.
X square plus y square equals twenty.
And we know that y equals x plus one, so this equation can be substitutioned in the equation above.
So,
X square plus open bracket x plus one close bracket square equals twenty.
X square plus x square plus two x plus one equals twenty.
Two times x square plus two x plus one minus twenty equals zero.
Two times x square plus two x minus nineteen equals zero.
Quadratic equation above can be finished by abc formula
x1 equals negative b plus the square root of open bracket b square minus four a c close bracket, all over two a
x2 equals negative b minus the square root of open bracket b square minus four a c close bracket, all over two a
So,
x1 equals negative two plus the square root of open bracket two square minus four times two times negative nineteen close bracket, all over two times two.
x1 equals negative two plus the square root of one hundred sixty six, all over four.
x1 equals negative two plus the square root of one hundred sixty six, all over four.
And,
x2 equals negative two minus the square root of open bracket two square minus four times two times negative nineteen close bracket, all over two times two.
x2 equals negative two minus the square root of one hundred sixty six, all over four.

If x1 equals negative two plus the square root of one hundred sixty six, all over four, So y1 equals two plus the square root of one hundred sixty six, all over four.
If x2 equals negative two minus the square root of one hundred sixty six, all over four, So y2 equals two minus the square root of one hundred sixty six, all over four.
So, we can find the intersection point of x square plus y square equals twenty and y equals x plus one.

My Interpretations of the Videos in My English Lesson

In Last meeting, My friends and me watch some videos in English lesson. And from those videos we get something that will be important for us.

Video 1
In video 1, teach for us so that we not only look something from one side, but also we have to look something from another side. Because we will find different something from that another side. Don't afraid to do something, because we can’t know before we do it.

Video 2
In this life, we must have some dreams and wish. We have to believe in ourselves to reach that our dreams. Because self confidence is one of the modals for us to be better in the future. Although our self confidence is good and very important, but it’s not enough. So, we must believe to other people, like parents, teachers, friends etc. Because they can help us to reach our wish and what we want.

Video 3
What you know about Mathematics?
In Mathematics, there are symbols, graphic and then there are many lessons that is trigonometry, geometry, calculus, etc. For me, Mathematics is too difficult if only imagined. So I have to use calculator, graphic, table to ease for us to learn Mathematics lesson.
Video 4
Solving this Differential Equation!
(dy dx equals four x square)
(dy equals four x square dx)
(Integrate definite dy equals integrate four x square dx)
(y equals four third x cube plus constanta)

Video 5
1. (seven equals four a minus one)
(seven plus one equals four a minus one plus one)
(eight equals four a)
(a equals two)

2. (two third x equals eight)
(three second times two third x equals three second times eight)
(x equals twelve)

My Reflection in Learning English

Yesterday, March 12nd 2009, I got daily test in english lesson. And I consider that daily test as a self reflection in learning english. My lecturer, Mr. Marsigit suggest that the reflection can do whenever and not always to be reminded. So, I must always ready to face daily test.
Everyday we must study, study about whatever, not only study the lessons in class, but also will be better if we escalate object's scope that we will study. So we can improve our competent in daily life.
And then how we can get some references or information to be learnt? We can get that source from books, internet, etc. And with those sources, we can write a research. The research of mathematics may be.
How someone could be called competent in english and mathematics? If someone can do how to comunicate mathematics in english. How to write? How to translate? How to express? And so, we must work hard to get a good result.
Reflection can use to introspect our self, whether we have done the best or yet? And result from yesterday's reflection, I have to work hard to study and learning english.

The Meaning of Mathematics

In the second meeting in my english class, I can get some information and knowledge from our discuss. My lecturer, Mr. Marsigit, give me some lessons about the meaning of Mathematics based on How the type of Mathematics, how the object of mathematics, etc. If you learn Mathematics in school mathematics or university mathematics, you can get pure mathematics and applied mathematics.

1) Abstraction
Abstract is not same with abstract. There is differences between abstract and abstraction. We know that abstract is not concrete. We can't see, touch, observe, but we can imagine. On the other side abstraction is the value which is contained in mathematics.
2) Idealization
Idealization only in our mind. I assume that the characteristic of mathematics is absolutely true.
Definition of mathematics is science which is built deductively, consist of definition, axiomatic, theorem, lemma, formula, etc.
From the statement above, we know that the characteristic of mathematics is logic and consistent.

Mathematics consist of two :
1) Conjecture : predict, assume a problem in mathematics
2) Convince : deliver the result that we have predicted to others

Mathematics consist of three aspect :
1) Mathematics attitude
As mathematicians which have good attitude, we must always positive thinking, consistent, diligent and always have questions about problems
2) Mathematics method
How to learn mathematics? We can use one of some method of mathematics. They are deductive, inductive, syllogism.
3) Content
Mathematics consist of two :
1)Horizontal mathematics, example daily mathematics. The object of this mathematics is real object
2)Vertical mathematics :pure mathematics, which is develop in college.