MATHEMATICAL THINKING AND SCIENTIFIC WORK

Mr. Marsigit is my awful English lecturer. He always study all about life and often share his knowledge and his experiences to us, university student.
Last meeting, he told about mathematical thinking and scientific work. There was different thing about my lecturer when he taught our class. He brought a set of thick paper. He showed that paper and we saw that the title of paper was “ Math for Junior High School VII”. He said that this paper was one of result of scientific work. There were people studied in Gajah Mada University or in Institute Technical Bandung to do research about the University. Scientific work was formal writing that be arrange scientifically. For the example research that be done by Gajah Mada or ITB’students. Then, what was scientific? Scientific had many characters, they were,
•Impersonal
•Have criteria
•Objective.
Next, about kinds of scientific work format. The format of it were ;
•Report
•Explanation
•Paper.
Scientific paper consisted of four parts. There were:
1.Introduction
2.Discussion
3.Conclusion
4.And reference.
The important thing when we wrote scientific paper that don’t make any plagiarism and we must suitable with ethical code.
It was all about scientific work.

Before we discussed about Mathematical Thinking, we must knew about math. Nature math was relationship. Math had an object. The object was my idea. We could take object from anything around. How to get an idea in math? There were some method to get idea.
1.Idealism
Idealism was we assumed that all object or things were perfect.
2.Abstraction
Abstraction was we took any things that be need only.
There was terminology that had relationship with Mathematical Thinking. ” Meta Math” was thought all about math. Mathematical Thinking was thought mathematically. Mathematical Thinking had three criteria,
•Consistent; suitable with agreement
•And logic.
I think it is enough about Mathematical Thinking and Scientific Work. I’m so sorry if I have some mistakes.

My Mathematics

It is about my mathematics writing. In this time I will share about sphere, parallelogram, and integral.

SPHERE
A sphere is a set of all points that are given distance from a point called center. Sphere has diameter, radius, and tangent. Sphere is one of three dimensional shape.
Diameter of sphere is a chord of the sphere that dividing the area of sphere in two similar parts. The radius of sphere is line from the center to on the sphere. The length of radius is half of the diameter. Tangent of a sphere is a line that has intersection point exactly one point at the sphere.
Application the sphere in our life is a ball. The form of ball is similar with sphere.

A sphere has surface area and volume.
The surface formula of sphere is four time phi time radius square. It can be wrote,
S (surface ) equal 4phi time r square.
The volume formula of sphere is four-third phi time radius cube.
V (volume ) equal 4/3 phi time r cube.

Problem solving,
Find the surface area and volume of the sphere since the diameter fourteen centimeters, the radius is seven centimeters.
Solution ,
Volume ( V) equal four-third phi time radius cube.
V equal four-third time seven cube time twenty two-seventh
V equal one thousand four hundreds thirty seven point three three.


PARALLELOGRAM
Parallelogram is quadrilateral with two pairs of parallel sides. For example parallelogram ABCD. It has two pairs of parallel sides, they are AB parallel with CD and AD parallel with BC. Parallelogram ABCD also have two pairs of congruent angles. The opposite angels of parallelogram are congruent ( < A with < C and < C with < D ). The consecutive angles of parallelogram are supplementary 180 degree.
Parallelogram have two diagonals. The diagonals of parallelogram bisect each other. A diagonal of parallelogram separate it into two congruent triangles.

Problem,
In quadrilateral ABCD, with diagonal BD, AB parallel with CD, AB congruent CD. Show that ABCD is parallelogram!
Solution ,
One way to show that ABCD is a parallelogram is to show AD congruent CB. It can do by showing ABC triangle congruent CDB triangle.
-ABD angle congruent CDB angle. If two parallel lines are cut by transversal, then each pair of alternate interior angle is congruent.
-BC congruent CB
-AB congruent CD
-ABD triangle congruent CDB triangle.
-AD congruent CB
For the conclusion, ABCD is a parallelogram.




DIFFERENTIAL
The differential f function ( f’ ) is other function f’ that the value in any number c, is
F’ ( c ) equal limit h approach 0 of f ( c plus h ) minus f ( c ) over h,

The rule to look for differential,

A theorem,( the rule of constant function )
If f(x) equal k, with k is constant
Then to any x f(x) equal 0. Is Dx (k) equal zero.

B theorem, ( the rule of identity function )
If f(x) equal x, then f’(x) equal one.
Is Dx (x) equal one.

C theorem, ( the rule of power )
If f(x) equal x to be n, with n is positive integers, so f’(x) equal n time x to be n minus 1.
Dx ( x to be n ) equal n time x tobe n minus one.

D theorem ( the rule of constant multiply )
If k is constant n function can be differential, so
(kf’) (x) equal k time f(x) is
Dx [ k tme f(x)] equal k time Dx f(x).

E theorem (the sum / dispute rule)
If f and g are functions that can be differentiated, so
( f plus or minus g )’ (x) equal f’(x) plus or minus g’(x)
Is Dx [f(x) plus or minus g(x)]’ (x) equal Dx f(x) plus or minus Dx g(x).

Application,
Andi run in street. His position S suitable with S equal two t square plus twelve t plus eight, ( S in meters, t in second ).
When two second, he run with velocity twenty meters/hours.
Proof,
V ( velocity ) equal Ds ( two t square plus twelve t plus eight )
V equal Dt (two time t square) plus Dt ( twelve t) plus Dx eight
V equal four time t plus twelve.
To get his velocity at four second, we substitute t equal in equation above.
We get V equal twenty meters/hours.

It is all about sphere, parallelogram, and diferential. My posting not complete,my knowledge about it still low, so I need advice from readers. Thankyou..

Reflection in Video

This is second reflection for the class of Mathematics education 2008. There are some videos containing different means. We watch video together only from Mr. Marsigit’s laptop. It’s cause by the lacking of facilities in our university. So, we get any difficulties to understand the stories in video.

But, I will try to retell the video in my posting.

The first video is “Dead Poets Society”. That video tells about William Shakphere. From that video we can study about views. If we view thing we must not only from one view, but also in much views. We must try to find our choice and improve that choice.

Second video, there is a boy speech in front of adults. He advice the adult people to still have confidence in every condition.
We must believe with our skill and we should believe “other people” to improve our skill.

The most interesting video to all is the third video. This video give different thing about mathematics to University student. There are two men sing a song. The song tell all about mathematics. There are exponent, grade, multiple, matrix, etc. This video try to show that mathematics can be made as interesting thing.

Next video contain about math truly. The title of video is “ Solve an Integral Equations” ( solving differential equations).

It is about the way to find y= f(x) if dy over dx = .4x square
• Multiple both of the segment with dx.
dy multiple by ( dy over dx ) = 4x square multiple by dx
So, we get
dx ( dy / dx ) = ( 4x ) square. dx.

• Integrate the both of segment,
integral of dy = ( 4x ) square. dx
y = (4x/3) cubed + c

• try to get variable

The next video is Solving Algebraic Equations. There are some prolem:
1. x – 5 = 3
the ways to solving are,
• add both of the segment with 5.
x – 5 + 5 = 3 + 5
x = 8
2. 7 = 4a – 1
• add both of the segment with 1 to eliminate -1.
So, 7 + 1 = 4a + 1 – 1
We find, 8 = 4a.
• multiple both of the segment with one-fourth
4a multiple by one-fourth equal 8 multiple by one-fourth
4a. (1/4) = 8( 1/4 )
a= 2

3. ( 2/3 ) x = 8
• multiple both of the segment with 3/2 to find x.
(3/2) . ( 2/3 )x = 8 . ( 3/2 )
so,
x = 12

4. 5 – 2x = 3x + 1
• add both of the segment with 2x
5 – 2x + 2x = 3x + 2x + 1
• so, 5= x + 1
• add both of the segment with -1
5 – 1 = x + 1 – 1
• we get it x = 4

5. 3 – 5(2m – 5 ) = -2
• It is equivalent with 3- 10 m + 25 = -
- 10 m = -30
• Devide both of the segment with 10.
• Multiple both of the segment with (-1)
• We get, x = 5
It is all about video 5.

Next video is Solving Logarithm Equations.
There are equation
1. log base x A equal B. it is similar with x power B equal A.
log base x A equal B equivalent with x power B equal A.
devided the left segment with C,
so C ( log base x A ) =BC,….(1)
and the right segment to be with C.
so,( X to be B) to be C = A to be C
we get, log base x A to be C = BC,…(2)
back to equation (1)
C ( log base x A) = BC equivalent with log base x A to be C = BC ,..(2)
The result,
equation (1) similar with equation (2).

2. log base x A + log base x B equal log base x (A multiple by B)
Analog, log base x A = l so, x to be l = A
log base x B= m so, x to be m = B
log base x (A multiple by B) = n,
so
x to be n = A multiple by B.
= (x to be l) multiple by (x to be n)
= x to be ( l + m)
n = l + m
so,
log base x A + log base x B equal log base x (A multiple by B)


3.log base x A - log base x B equal log base x (A devided by B)
Analog, log base x A = l so, x to be l = A
log base x B= m so, x to be m = B
log base x (A devided by B) = n, so
x to be n = A devided by B.
= (x to be l) devided by (x to be n)
= x to be ( l - m)
n = l - m
so,
log base x A - log base x B equal log base x (A devided by B)