ridwan's blog: 2009

Jumat, 18 Desember 2009 di 22.47 | 0 komentar

Mathematical Research
This is Description about the opinion how to do Mathematical Research. There are several ways or steps to do the Mathematical Research. All of the steps must be done continuously because each step based on the others. We have to do all of the steps without reduce one of them.
The steps of Mathematical Research are:
I. In deep Study References
II. Identify and Formulate The Problem
III. Develop Method of Research
IV. Process of Research
V. Finding
VI. Publish
VII. Journal

Before starting to do research of mathematics, we must also do the preparation. This preparation determine the mathematician what he is reasonable or not to do the research. The preparations are:

1. We need references to do Mathematical research
We can do many ways to get references, in the modern era like now, there are many tools and infrastructures supporting our works. The ways we can do such as:
• Browsing Internet
The Internet provides opportunities galore, and can be used for a variety of things. Some of the things that you can do via the Internet are:
E-mail: E-mail is an online correspondence system. With e-mail you can send and receive instant electronic messages, which works like writing letters. Your messages are delivered instantly to people anywhere in the world, unlike traditional mail that takes a lot of time. Access Information: The Internet is a virtual treasure trove of information. Any kind of information on any topic under the sun is available on the Internet. The ‘search engines’ on the Internet can help you to find data on any subject that you need.
So we can get anything we needed in internet that can support our preparation to start Mathematical Research.
• Reading the Books
Books are portable. You can take them almost anywhere. As such, you can learn almost anywhere too. Books for professionals contain arguments for or against the actions within. A book on cooking argues that Chili powder goes well with beef and goes poorly with ice-cream. A book on building a business argues that testing an idea for profitability before setting up is a smart strategy and argues against just barreling forward with the idea without testing. Books take you places and you learn from books too. Books can help you understand things.
• Reading the magazines, scientist paper, etc.

2. Knowing The Nature of Mathematics
There are a lot of definitions about the nature of mathematics, all of definitions have the same idea about mathematics. The natural mathematics is a science or system which is constructed by deductive method composing definition, axiom, and theorem in such a way that there is no contradiction inside.
So we can say that mathematics is the science and mathematics is the system. As the science, mathematics is knowledge that very large in mind and it can be applied in our life. There are many contents in mathematics that become our task to find out them.
As the system, mathematics is constructed by definition, axiom and theorem.
Definition is a formal passage describing the meaning of a term (a word or phrase). The term to be defined is the definiendum (plural definienda). A term may have many subtly different senses or meanings. For each such sense, a definiens (plural definientia) is a cluster of words that defines that specific sense of the term.
Axiom is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths. In mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Unlike theorems, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow (otherwise they would be classified as theorems).
Theorem is statement which has been proved on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms. The derivation of a theorem is often interpreted as a proof of the truth of the resulting expression, but different deductive systems can yield other interpretations, depending on the meanings of the derivation rules. The proofs of theorems have two components, called the hypotheses and the conclusions.
The examples of mathematics system are:
• Group Theory
• Ring Theory
• Numbers Theory
• Eucledian Geometry
• Non-Eucledian geometry
• Numbers system

3. Knowing The Purpose to do Mathematical Research
Before doing everything we must know the aim inside. It is the same if we want to do research of mathematics. The Aim of Mathematical Research is examine and establish the new system of mathematics. We can find many aspects in mathematics that examined the new system. The aspects are definition, axiom, theorem, pattern, rule, procedure, low etc.

4. Finding the supporting factors to do Mathematical Research
The factors that support the research of mathematics such as:
• Knowledge of Mathematics
• Knowledge of History of Mathematics
• Knowledge of philosophy of Mathematics
• Knowledge of world famous mathematician
• Experiences of developing Mathematics
• Asking

The Example, we learn about history and philosophy of mathematics, we can learn about Godel Theorem and Hilbert theory.
Godel theorem issued to reject or pushed away the Hilbert theory. In his Theory, Hilbert come to make one and only one system of mathematics, he certain that the system of mathematics can be composed by one system. Then, this theory is rejected by Godel with the theorem called Godel theorem.
Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory
The substance of godel theorem are:
- Complete system of mathematics is not consistent
- Consistent system of mathematics is not complete
The conclution of godel theorem is impossible that there is only one system of mathematics. The proof is theorem of incompleteness. Gödel's incompleteness theorems are two theorems of mathematical logic that state inherent limitations of all but the most trivial axiomatic systems for mathematics. They state that any consistent system of axioms whose theorems can be listed by a computer program is incapable of proving certain truths about arithmetic. This means that any consistent computable formal theory which can prove some arithmetic truths cannot prove all arithmetic truths. The theorems were proven by Kurt Gödel in 1931, and are important in the philosophy of mathematics. The result is widely interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all of mathematics is impossible, thus giving a negative answer to Hilbert's second problem.

The last, we can not said a truth Mathematician if we never do the research of mathematics. If we want to start research, we have to do the preparation above and also do each steps of mathematical research.

Diposting oleh ridwan putunaja

My Appreciation about World Class University Program in UNY

Rabu, 25 November 2009 di 04.35 | 0 komentar

World Class University, a sentence that buzzed and echoed in college, recently began touted in yogyakarta state university. World Class University is a measure used to rank universities in the world using the survey, known as The Times Higher Education Supplement (THES).
Based on the literature on world class university, we think that world class university evaluation should consider:
1. international characteristics that may affect quality
2. instructional quality
3. research quality
4. student quality

Research quality is the indicator that shows how well the publication of research results of a university. If a university is a center of excellence of the multidisciplinary science of the university will be recognized by the whole world because it has contributed to the advancement of science. This indicator can also be seen from peneltian quality, productivity (number of papers published), which gained recognition and even awards like the Nobel or fields medals. Teaching quality is how well does the teaching methods, including teaching facilities. Graduate employability is an indicator that shows how well university graduates can work in various fields and how much their salaries. International outlook is an indicator that shows whether a particular university can contribute not only to his country but also for other countries as seen from the proportion of foreign students, foreign staff, student exchange, and the power of international relations with other universities around the world.

I think i very enthusiastic with the university program to become our university to be international class, This is the need for us all, to become an international class of university, we can know our capabilities when compared to other universities in the over of world.
By employing WCU program, our university can further develop better than now. with 4 components of WCU program in above we will get more motivated to improve all of our capabilities in this university.

WCU become UNY benchmark for the world Whether we have been able to compete with other universities in the world. I strongly support the existence of this program. hopefully this program can run smoothly.

Strategic steps have been made by marsigit as chairman of the WCU program and those from the Rectorate to realize the program, such as by held collaboration with universities and other institutions abroad, such as in Japan, Germany, Australia and China .

I think this is an excellent step for the future UNY. student exchange programs, administration staff , staff experts, experts laboatorium, etc. UNY university can make a calculated world.
the end absolutely agree and support Yogyakarta state university to be a World Class University.

Diposting oleh ridwan putunaja

My Concern about English For Mathematics

Rabu, 04 November 2009 di 06.53 | 0 komentar

I. Properties of Logarithm
When x and b are restricted to positive real numbers, logb(x) is a unique real number. The magnitude of the base b must be neither 0 nor 1; the base used is typically 10, e, or 2. Logarithms are defined for real numbers and for complex numbers.
The major property of logarithms is that they map multiplication to addition. This ability stems from the following
A related property is reduction of exponentiation to multiplication. Using the identity:
In words, to raise a number to a power p, find the logarithm of the number and multiply it by p. The exponentiated value is then the inverse logarithm of this product; that is, number to power = bproduct
Besides reducing multiplication operations to addition, and exponentiation to multiplication, logarithms reduce division to subtraction, and roots to division.
Logarithms make lengthy numerical operations easier to perform by converting multiplications to additions. The manual computation process is made easy by using tables of logarithms, or a slide rule. The property of common logarithms pertinent to the use of log tables is that any decimal sequence of the same digits, but different decimal-point positions, will have identical mantissas and differ only in their characteristics.

II. Common Factor and Grouping
In mathematics, factorization (also factorisation in British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained .The aim of factoring is usually to reduce something to "basic building blocks," such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots. The opposite of factorization is expansion. This is the process of multiplying together factors to recreate the original, "expanded" polynomial. Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA. A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ. Another example is the factorization of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a surjective function with an injective function. This situation is generalized by factorization systems.

III.Trigonometry Function
• The sine function (sin), defined as the ratio of the side opposite the angle to the hypotenuse.

• The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.

• The tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.

IV. Function Terminology
a function is a relation between a given set of elements called the domain and a set of elements called the codomain. The function associates each element in the domain with exactly one element in the codomain. The elements so related can be any kind of thing (words, objects, qualities) but are typically mathematical quantities, such as real numbers. An example of a function with domain {A,B,C} and codomain {1,2,3} associates A with 1, B with 2, and C with 3. An example of a function with the real numbers as both its domain and codomain is the function f(x) = 2x, which associates every real number with the real number twice as big. In this case, we can write f(5) = 10.
There are many ways to represent or visualize functions: a function may be described by a formula, by a plot or graph, by an algorithm that computes it, by arrows between objects, or by a description of its properties. Sometimes, a function is described through its relationship to other functions (for example, inverse functions). In applied disciplines, functions are frequently specified by tables of values or by formulae. In a setting where outputs of functions are numbers, functions may be added and multiplied, yielding new functions. Collections of functions with certain properties, such as continuous functions and differentiable functions, usually closed under certain operations, are called function spaces and are studied as objects in their own right, in such disciplines as real analysis and complex analysis. An important operation on functions, which distinguishes them from numbers, is composition of functions. The composite function is obtained by using the output of one function as the input of another. This operation provides the theory of functions with its most powerful structure. In pure mathematics, functions are defined using set theory, and there are theorems that show the existence of uncountably many different functions, most of which cannot be expressed with a formula or algorithm

V. Parallelogram

• Opposite sides of a parallelogram are equal in length.
• Opposite angles of a parallelogram are equal in measure.
• The area, A, of a parallelogram is A = bh, where b is the base of the parallelogram and h is its height.
• Opposite sides of a parallelogram will never intersect.
• The area of a parallelogram is twice the area of a triangle created by one of its diagonals.
• The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.
• The diagonals of a parallelogram bisect each other.
• Any non-degenerate affine transformation takes a parallelogram to another parallelogram.
There is an infinite number of affine transformations which take any given parallelogram to a square

To prove that the diagonals of a parallelogram bisect each other, we will use congruent triangles:

angle ABE congruent angle CDE (alternate interior angles are equal in measure)
angle BAE congruent angle DCE (alternate interior angles are equal in measure).

(since these are angles that a transversal makes with parallel lines AB and DC ).

Also, side AB is equal in length to side DC, since opposite sides of a parallelogram are equal in length.

Therefore triangles ABE and CDE are congruent (ASA postulate, two corresponding angles and the included side).

Therefore,

AE = CE
BE = DE.

Since the diagonals AC and BD divide each other into segments of equal length, the diagonals bisect each other.

In addition, the diagonals AC and BD are each bisected by point E. Therefore, point E is the midpoint of each diagonal.

Diposting oleh ridwan putunaja

My Efforts in Catching up English Vocabulary for Mathematics

Selasa, 02 Juni 2009 di 07.54 | 0 komentar

(My Small Dictionary for Mathematic )
1. Acute = Sudut Lancip
2. Addition = Penjumlahan
3. Angle = Sudut
4. Approximate = pendekatan
5. Average = Rata-rata
6. Base = Alas
7. Bisect line = garis bagi
8. Concept = Pengertian
9. Cylinder = tabung
10. Circle = lingkaran
11. Comparison = perbandingan
12. Curve = Garis lengkung / kurva
13. Cross = Bersilangan
14. Conclusion = Kesimpulan
15. Common = factor
16. Cube = kubus / pangkat tiga
17. Coordinate = koordinat
18. Congruent = Sama dan Sebangun
19. Decimal = decimal
20. Definition = Pengertian
21. Denominator = penyebut
22. Diameter = garis tengah
23. Difference = selisih
24. Division = pembagian
25. Empty = kosong / himpunan kosong
26. Equilateral = sama sisi
27. Estimation = Penaksiran
28. Even = genap
29. Exponential = pemangkatan
30. Fraction = pecahan
31. Imaginary = garis khayal
32. Integers = Bilangan Bulat
33. Intersection = Berpotongan
34. Mapping = Pemetaan
35. Measure = Ukuran
36. Median = Garis Berat
37. Numeral = bilangan
38. Numerator = Pembilang
39. Obtuse = sudut Tumpul
40. Odd = Ganjil
41. Ordering = Mengurutkan
42. Pattern = Pola
43. Parallel = Sejajar
44. Perpendicular = Tegak Lurus
45. Power = Pangkat
46. Plane = bangun datar
47. Prime = Bilangan prima
48. Prism = Prisma
49. Proof = Bukti
50. Proportions = Perbandingan
51. Protactor = Busur Derajat
52. Ranks = baris
53. Rectangle = Persegi Panjang
54. Reduce = pengurangan
55. Rhombus = Belah Ketupat
56. Relation = Hubungan
57. Right Angle = sudut Siku- siku
58. Right prism = prisma tegak
59. Root = Akar
60. Round = pembulatan
61. Subset = himpunan bagian
62. Sets = himpunan
63. Series = Deret
64. Secant = garis potong
65. Scalene = sebarang
66. Shadow = arsiran
67. Straight = Lurus
68. Solution = penyelesaian
69. Supplementary = pelurus
70. Superimpose = berimpit
71. Substraction = pengurangan
72. Tangent = Garis singgung
73. Top = puncak
74. Term = Suku
75. Union = Gabungan
76. Vertex = titik sudut
77. Zero = nol

Diposting oleh ridwan putunaja

English Task

Selasa, 14 April 2009 di 10.50 | 0 komentar

1. How to get phi numeral
To get phi, we can use a circle. Suppose we choose a circle with unit diameters .The length of the circumference of a circle lies between the perimeter of any inscribed polygon and that of any circumscribed polygon. We easily obtain bounds for phi. From the perimeters of given regular inscribed and circumscribed polygons, we may obtain the perimeters of the regular inscribed and circumscribed polygons having twice of number of sides. Starting with six-sided polygons, we can compute the perimeters polygons of 12, 24, 48, and 96 sides and we can get ever closer bounds for phi. This formula shows that phi is between two hundred twenty three per twenty one and twenty two per seven or in two decimal places is 3.14.
2. How to get abc formula
The abc formula is got for search the solution of the quadratic equations. If we have the quadratic equation ax square plus bx plus c equal 0, the abc formula get by:
a). make 1 the coefficient of x by dividing the equation with a,
b). passing constant in left side by quite the sides with c per a.
c). using the completing square to make the left side be a complete square. We can add square of half of x coefficient.
3. how to compute the area bounds of y equals x square and y equals x plus 2.
We must find bounds of curves with get the point of the curves. After that, we can use integral operation i.e. the top curve minus the under curve with bounds of x.
So, we find that the area is four half.
4. Cone’s volume
If we have a cone with a half of base diameter is r and the high is t, we can compute the volume is the area of base crossed by the high. Because the base of cone is a circle, so the volume is Phi cross a half of diameter cross t.
5. Proof that the summary of the angles of triangle is 180 degrees.
First, we make any kind of triangle, then make the length line of point anywhere. For example, C is same line with AC then passed AC, make the parallel line with AB.
Angle ACB + angle ABC +Angle CAB equals 180 degrees.
So, it proofed that the summary of the angles of triangle is 180 degrees.
6. Explain how to fixed probability the number more than six from 2 cubes throws once.
By using the chance, the sum which more than six from two cubes throws once is twenty one. So the probability number more than six is twenty one per thirty six.
7. Explain the way to get the equation throws (10,0) and x square plus y square equals nine.
Use tangent equation which throws (a,b) i.e. x index 1 cross x plus y index 1 cross y equals quadrate of half diameter.
So the equation can find by entering the founding elements.
8. Explain how to proof the Pythagoras
For example, a, b, c explain the right side and the sideway of right triangle. At two square which each with a plus b as a side. The first square divided be six part, that is two square and four of right triangles which congruent with the definite triangle. The second triangle divided be five part, that square at sideways and four right triangles congruent with definite triangle. So we found that the third number is triple Pythagoras. To find one of the numbers is square of sideways is equal to square of the right side plus the others.
9. Search the sum of first 200 odds.

Using the arithmetic series. First part is 1 and the difference is 2 and there is a hundred numbers. The sum of first two hundreds of odd is equals half of hundred cross twice first part plus hundredth minus 1 cross 2. The result is one hundred thousand.
10. Explain how to draw the cube if the side is found.
For example, the cube ABCD EFGH, the base is ABCD and each the right sides is AC, BF, CG, and HG.
The steps are:
Draw line of AB to horizontal purpose
In A, draw the deviation angle
Projection sideways ABCD is parallelogram, so the base can be finished
The middle are vertical lines, so EFGH can be drawed
We can draw the cube ABCD EFGH

Diposting oleh ridwan putunaja

di 10.48 | 0 komentar

I don’t have a title to my written now because I don’t have a specific topic. I just only write about whatever I feel and whatever I get in English class with Mr. Marsigit.

First, I want to deliver my points of view about the English class in fourth week. In that meeting, as usual Mr. Marsigit looks tidy. As a very busy person, I think its okay if he mengutamakan his performance. “I must meet many people everyday, so I must look good”. He said with smile.
Mr. Marsigit always looks funny in every meeting. In every meeting, he also never felt bored to give us high motivation and spirit to get our aims. He never stops tell us about his experiences to be motivation for us.

Tell about the class, the material of study in this meeting is about linear equations and quadratic equations. Mr. Marsigit gave us about the definition of linear and quadratic equations and how to get the solution of it and also how to make it in the graphic. Solve the solution of equations means to substitute the variable by a constant to make the equations be a true statement. We can apply “substitute method“ and “eliminate method“ to solve the solution of the equations. The difference of linear and quadratic equation is linear equation is the equation which the highest power of the variable is “one” but quadratic equation is the equation which the highest power of the variable is “two”. So if the solutions are made in graphic we will get the straight line for linear equation and curve for the other.
The materials was same which we got in junior high school and senior high school and I think its very simple for us, but by using the different learning method it be interest more. We got English in mathematic.

In the last time of that meeting, Mr. Marsigit shown us his book. The title is mathematic for junior high school. The interested of his book is the settings of pages. In every page consist of two languages which Indonesian in the left side and English in the others. The essentials of his book is simple mathematic. Not too hard to study. The formulas, theorems, graphics and the examples for problem studies are very simple. I think his book is very good used to students of junior high school. They can get a lot of knowledge from his book. Not only for mathematic but also the English. They can exercise to use English. But, because of the cost, I think the book only used in the city, the students in the villages can’t buy this book.

Diposting oleh ridwan putunaja

The Nature of Mathematics

Sabtu, 21 Maret 2009 di 07.00 | 0 komentar

The one way to learn mathematics is "abstraction". method is used by taking the important materials of mathematics. for example, we didn't need to describe the real form of cube to get it. we just only have to describe the elements of cube i.e the six sides of cube with the same measure. so, we just only need to describe the pattern without see the thing orderly.

Mathematics can be applied in every sector of our life. everything in around of us can be connected with mathematics. A long time ago, when the ancient people saw the river, they thought about the comparation ways for the canal to flow the rice fields. Then, they used the right formulas to compare the water for the rice. They made the irrigation system. It was very high concept for the ancient people.

The another, they also could build the great buildings by using the sophisticated of the computations. They didn't know if they used mathematics formulas, but they used it well. It is called the nature of mathematics.

Whe nature of mathematics is hoe to see the daily phenomena in our life by using mathematics. We can see everything by mathematics perspectives. We can relate anything with mathematics, the football game can be related with mathematics, we can relate the voice interval of the animal with mathematics,etc.

So the meaning of the nature of the mathematics is everything can be related with mathematics.

Diposting oleh ridwan putunaja

My First Meeting in English Class

Senin, 16 Maret 2009 di 21.41 | 0 komentar

There is no meeting of my English class until three times because of the schedule of our lecturer didn’t match. So the first meeting we held on fourth week, on Tuesday, 10 march 2009. This meeting started at seven o clock in the Ex. Jica room.
The name of our English lecturer is Drs. Marsigit. For the early, I felt strange because our seat is made a half of circle and the lecturer’s seat in the centre. “It is for the good communication between students and the lecturer”. He said.
I think, with that position, the students can focus and concentrate more, there is no noisy in the class.
Mr. Marsigit told us much about his studies experiences. Actually, he was study in London. He always go to foreign country just for a presentation. The experience was made us motivated.
The other thing it becomes the point of our first meeting is talking about the syllabus and also about our task made a blog.
In the evening, we held the second meeting. The materials was same as the morning materials. Mr. Marsigit explained about our English learning. He explained about everything we can get in this subject. “There is five points that will be reached in English subject”. He said. “Communication, Understand, Application, Skills and Experience”, He added.
The interesting moment from the second meeting is when there was a sleeping student, he gave examination to us orderly, it was very shocked. The exam was to translate the mathematic Indonesian words into English. There were fifty questions for us. From all of the students, there is no one who could answer correctly even though an half of it. It means that we must study harder.
The conclusion of the second meeting is everyone is not allowed sleeping in his class.

Diposting oleh ridwan putunaja

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