Mathematical Research

To be able to learn mathematics well and fun, we can present creative ideas about mathematics in meaningful learning and fun. Empowerment of students in learning mathematics through the presentation of creative mathematics, the development of research and learning of school mathematics. To make the study, needed some way to be included in the study of mathematics. The existence of references that can support our research by looking for one on the internet. The Internet is a vast network, we can know what we want to know because the internet includes up to the rest of the world. Many things can be found there. So, information about the study of mathematics can be found there for finish what we're looking for. We also need to be able to explain the definition of mathematics according to our own thoughts. There are many definitions of mathematics, but everyone has different definitions of mathematics in the making. They have a different opinion and according to those same thoughts and their experiences in learning mathematics. Learning and understanding of the concept can be initiated by inductively through experience or intuition real events. Inductive-deductive process can be used to learn math concepts. Activities can be started with some examples or observable facts, make a list of properties that appear (as a symptom), estimates that the new results are expected, which later proved deductively. Thus, how inductive and deductive learning can be used and are equally important role in learning mathematics. Application of mathematical workings of this kind are expected to form a critical attitude, creative, honest and communicative on the students. Also studied mathematics also has a very favorable destination for all people.
Mathematics learning goals are:
1. Train the way of thinking and reasoning in drawing conclusions, for example through investigation activities, exploration, experimentation, shows the similarities, differences, consistency and inconsistency.
2. Activity Involving Developing creative imagination, intuition, and discovery by developing divergent thinking, Originality, curiosity, make predictions and expectations, and to experiment.
3.Develop problem-solving skills.
4. Develop the ability to inform or communicate ideas among others through verbal conversation, graphs, maps, diagrams, in explaining the idea.
Research requires a proof of Mathematics, Mathematics and proof are two inseparable things. But in this case, the proof is the main focus, for example: Proof of Fermat's Last Theorem. In Mathematics many problems unsolved / proven. We stayed choose one-one and we try to prove otherwise in accordance with the theorem. We took an existing concept and to the extension, then expand and can also develop. For example, modern algebra originally there were only structure Group and grew to appear catagory, universal algebra, etc. By using existing concepts, we can apply it to the field / science. In general, the research projects in this category try to formulate real problems. We can examine an object or a mathematical concept for caracter addition we can explore a mathematical structure that already exists for the search for a new connection objects in it and prove (theorem) that in the end we find new properties of the structure it. Actually this is part of the Characterization Here we examine whether quality of a mathematical object exists or not. As an example we can examine the existence of odd perfect numbers, because until now not known whether odd perfect numbers exist or not.

world class univercity

World Class University (WCU) is one program that was created in Yogyakarta State University. This program is a program to introduce the Yogyakarta State University into the world of international education. Therefore, to make this happen a lot that must be met and corrected himself both from a financial or in terms of human resources. So in this case Mr. Marsigit has a very big expectations for kesuksesaanny. According to him was not easy to achieve World Class Universities program because in addition to funds that are not less well supported by teachers who meet the international standards that can be studied abroad like to learn to Australia and with it will get a certificate internasional.Untuk achieve international class also have several advantages. These advantages include, among others, excellence in research that recognized the international academic community through international publications; excellence in teaching staff (professors) who are highly qualified and best in its field; excellence in academic freedom and intellectual excitement; benefits management and governance, adequate facilities for academic work, such as a complete library, the latest laboratory and adequate funding to support teaching and learning process and research. And no less important, advantage in international cooperation, both in academic programs, research, and so on. Clearly not easy for high-University-college in Indonesia reaches the various benefits.
It also required the establishment of an international standard curriculum and a special space in the classroom teaching. In this case, the program of World Class University (WCU) is very good in order to realize the State University of Yogyakarta in the competition in the world of education, especially in the international world. The formation of human resources is a high level, which should be adequate facilities and financial support that is used to smooth this program. All that just to introduce the Yogyakarta State University in the eyes of the world. With this, the world will see a little later one of the universities in Indonesia are able to give a big contribution in the efforts to improve education in Indonesia, especially in the eyes of the international community. So I am very supportive and very proud of one of the programs that are not only playing the program but the program really great in the field of education, this program is the World Class University.
I hope that if this program ssukses in implementation should be done later in the expansion of this program, including opening the same program without cost or with the wider department. So with the expected and almost all faculty at the State University of Yogyakarta has an international class that is not the only class capable of opening and internationally, but also from the State University of Yogyakarta itself, which will be one of the international universities. But this is for the first time we have to maximize our program to be run first, and with this there will be a stepping stone to further develop the same programs other faculties. So with that we will together develop Jogjakarta State University became one of the university to be known in international education will also introduce Indonesia to the world.

References of mathematic in english

1. FACTOR
In mathematics, factorization 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

2. TRIGONOMETRY
Trigonometry is a branch of mathematics that studies triangles, particularly right triangles. Trigonometry deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships, as well as describing angles in general and the motion of waves such as sound and light waves. Trigonometry is usually taught in secondary schools either as a separate course or as part of a precalculus course. It has applications in both pure mathematics and in applied mathematics, where it is essential in many branches of science and technology. A branch of trigonometry, called spherical trigonometry, studies triangles on spheres, and is important in astronomy and navigation.

3. LOGARITM
Logaritms in mathematics, the exponent or power to which a stated number, called the base is raised to yield a specific number
Example:
In the expression10²=100, the logarithms of 100 to the base 10 is 2.
This written log₁₀ 100=2

4. CUBE
A cube is a block with all right angles and whose height, width and depth are all the same. A cube is one of the simplest mathematical shapes in space. Something that is shaped like a cube is sometimes reffered to as cubic.

5. TRIANGLE
Triangle (geometry), geometric figure consisting of three points, called verticles, connected by three sides. In Euclidean plane geometry the sides are straight line segments. A Euclidean plane triangle has three interior angles.

· An angle A is acute if 0⁰<>0

· The angle is right f A =90⁰

· And it is obtuse if 90⁰ <>0

6. POLYNOMIAL
Polynomial, mathematical expression consisting of the sum (or differences) of any number of terms, each of which contains a constant. Expression (mathematics) in mathematics, any meaning full combination of constant, operator and variable representing. Constant, in mathematics a fixed quantity or one that does not change its value in relation to variables. Variable, mathematical or physical quantity that does not have a fixed numerical value. A quantity that does have a fixed numerical value is known as a constant.

7. DIFFERENTIAL
An ordinary differential equation is an equation involuing an independent variable, a dependent variable (one or both of these two may be missing),and one or more derivaties (at least one derivative must be present). A defferential equation is solved if an equivalent equation is found involving only the independent and dependent variable.

8. LIMIT
In mathematicss, the concept of a "limit" is used to describe the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives and integrals. The concept of the limit of a function is further generalized to the concept of topological net, while the limit of a sequence is closely related to limit and direct limit in category theory. In formulas, limit is usually abbreviated as lim as in lim(a_n) = a or represented by the right arrow (→) as in a_n → a.

9. PROBABILITY
Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

10. CALCULUS
Calculus is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.

11. SPHERE
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in three dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the radius of the sphere. The maximum straight distance through the sphere is known as the diameter of the sphere. It passes through the center and is thus twice the radius. In higher mathematics, a careful distinction is made between the sphere (a two-dimensional spherical surface embedded in three-dimensional Euclidean space) and the ball (the three-dimensional shape consisting of a sphere and its interior).

12. VOLUME
The volume of any solid, liquid, gas, plasma, or vacuum is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space. Volume is commonly presented in units such as cubic meters, cubic centimeters, liters, or milliliters. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. More complicated shapes can be calculated by integral calculus if a formula exists for its boundary. The volume of any shape can be determined by displacement. In differential geometry differential geometry , volume is expressed by means of the volume form, and is an important global Riemannian invariant.

13. INTEGRAL
Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral



is defined informally to be the net signed arae of the region in the xy-plane bounded by the graph of ƒ, the x-axis, and the vertical lines x = a and x = b. The term integral may also refer to the notion of antiderivative, a function F whose derivative is the given function ƒ. In this case it is called an indefinite integral, while the integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between antiderivatives and indefinite integrals. The principles of integration were formulated independently by Isaac andGottfried Leibniz in the late 17th century. Through the fundamental theorem of calculus , which they independently developed, integration is connected with differentiation : if ƒ is a continuous real-valued function defined on a closed interval [a, b], then, once an antiderivative F of ƒ is known, the definite integral of ƒ over that interval is given by



14. PRISM
A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies if the joining faces are rectangular. If the joining edges and faces are not perpendicular to the base faces, it is called an oblique prism. Some texts may apply the term rectangular prism or square prism to both a right rectangular-sided prism and a right square-sided prism. The term uniform prism can be used for a right prism with square sides, since such prisms are in the set of uniform polyhedra. An n-prism, having regular polygon ends and rectangular sides, approaches a cylindrical solid as n approaches infinity. Right prisms with regular bases and equal edge lengths form one of the two infinite series of semiregular polyhedra, the other series being the antiprisms. The dual of a right prism is a bipyramid. A parallelepiped is a prism of which the base is a parallelogram, or equivalently a polyhedron with 6 faces which are all parallelograms. A right rectangular prism is also called a cuboid\, or informally a rectangular box. A right square prism is simply a square box, and may also be called a square cuboid. An equilateral square prism is simply a cube.

My efforts in catching up English vocabulary for mathematics(my small dictionary of mathematic)

A My efforts in catching up English vocabulary for mathematics(my small dictionary of mathematic)
A
Alas : base

Aljabar : algebra
Akar : roots, radic
Anggota : member
Angka : numeral
Arti : meaning
Berarti : mean

Asosiatif : assosiative
Aturan : rule
Asal : origin

B
Balok : rectangular parallelepiped, block
Banding : equivalent
Perbandingan : proportions
Bangun :
Sebangun : similar
Sama dan sebangun : congruent
Batas : limit
Tanpa batas : infinite
Belah ketupat : rhombus
Bentuk baku : scientific notation
Berimpit : superimpose
Bilangan : number
Bilangan asli : natural number
Bilangan bulat : integer
Bilangan cacah : whole number
Bilangan khayal : imaginary number
Bilangan prima : prime number

Bola : sphere
Parabola : hemisphere
Bukti : proof
Bulat : circle
Pembulatan : the rounded, secant
Busur : arc
Tali busur : chord
Busur derajat : protactor

C
Campuran : mixed
Cekung : conveks
Cepat ; fast, quick
Kecepatan : velocity
Percepatan : acceleration

D
Daerah : domain

Dasar : elementary

Dekat : near

Pendekatan : approximate

Derajat : degree

Deret : series, row
Desimal : decimal
Diarsir : shadow
Dimensi : dimension

Distributif : distributive

E
Elips : ellipse

Eksponen : exponent

F
Faktor : factor, element

Pemfaktoran : factorization
FPB : the greatest common divisor
Fungsi : function
Fungsi linear : linear function

G
Ganjil : even
Garis : line
Garis keliling : perimeter
Garis lengkung : curved
Garis lintang : latitude
Garis lurus : straight line
Garis mendatar : horizontal line
Garis miring : diagonal line
Garis singgung : tangent
Garis tegak : vertical line
Garis tengah : diameter
Gelombang : wave
Genap : odd
Geser: transform
Grafik : graph

H
Hakikat : natur

Hasil : product
Hasil bagi : quotient

Hasil kali : product
Himpunan : sets
Himpunan bagian : subsets
Gabungan himpunan : union
Irisan himpunan : intersection

Hiperbola : hyperbola
Hitung : arithmetic
Berhitung : count
Menghitung : compute
Hubungan : relation

I
Interval : interval

Imbang : balance

Irisan : slice, section
Istimewa: special

J
Jari-jari : Radius
Jajar genjang : parallelogram
Jika … maka… : if…that…
Jumlah : sum

K
Kali : time
Mengalikan : multiply
Perkalian : multiplication
Keliling : circumference
Kerucut : cone
Kesimpulan : conclusion

Koefisien : coefficient

Komutatif : komutative

Konstanta : constant

Kosong ; empty, blank
KPK : the least common multiple
Kurang : decrease
Pengurangan : subtracer
Kurva : curve
Kwadran : quadrature

L
Lancip : acute
Latihan : excercise
Lingkaran : circle
Setengah lingkaran : semi circle
Logika : logic
Luas : area, wide

M
Majemuk : komplex
Maksimum : maxsimum
Maksud : purpose
Matrik : matrix
Membagi : divide
Minimum : minimum
Misal ; example

N
Naik : climb
Negative : negative
Nilai : value
Nilai mutlak : absolute value
Nol : zero
Nominal : nominal

O
Obyektif : objective
Operasi : operation

P
Pangkat : power
Panjang : lenght
Pecahan : fraction
Pembilang : numerator
Pembagi : divisor
Penaksiran : estimation
Pengertian : conception
Penyebut : denominator
Penyelesaian : solution
Perbandingan : ratio
Perbedaan : different
Permukaan : surface
Perpotongan : intersection
Perkiraan : estimate
Persegi : square

Persegi panjang : rectangle
Persen : percent
Persilangan : crossing
Peta : map
Pemetaan : maping
Piramida : pyramid
Pola ; pattern
Prisma : rectangular prism
Proporsi : proportion

Proyeksi : projection
Puncak : top, peak
Pusat : center
Positif : positive


R
Rahasia : secret
Rancang : stake
Rangkai : bunch
Rasio : reason
Rasional : rational
Rata-rata : average
Rumus : formula

S
Sama : equal, same
Penyamaan : equation
Segibanyak : polygon
Segienam : hexagon
Segitiga : triangle
segitiga sama kaki : isosceles triangle
segitiga sama sisi : equilateral triangle
segitujuh : heptagon
Sejajar : parallel
Sempurna : perfect
Setengah : half

Statistika : statistics
Sudut : angle
Sudut siku-siku : right angle
Sudut miring : obligque angle
Suku : terms

T
Tabel kebenaran : truth table
Tabung : tube
Tahap : stage
Tahun : year
Tajam ; sharp
Tali : string
Tampak : appear
Tebal : thick
Tegak lurus : perpendicular
Tinggi : altitude
Titik : point
Titik persekutuan : comman point
Titik sudut : vertex
Trapesium : trapezoid
Tumpul : obtuse

U
Ubah : difference
Mengubah ; change
Ukur : measure
Pengukuran : measuration
Ulang : frequent
Mengulang : repeat
Urutan : sequence
Utama : prime

V

Volume : volume

variabel : variable

W
Waktu : time
Wujud : shape

Y
Yaitu : that, is
Yakin : sure
Yakni : that is

1. Jajar genjang : parallelogram

Parallelogram is a flat shape with four straight lines, one pair of opposite sides being parallel and other pair are not paralllel.

2. Statistika : statistics

Statistics is the science of learning how to plan, collect, analyze, interpret, and present data.

3. Perpotongan : intersection

A vertex is a intersection of two line.

4. Rata-rata : average

Suppose the average height of triangle of this shape is k times its height.

5. persegi panjang : rectangle

The longitudinal section of a rectangular prism is shape like rectangle.

6. puncak : peak

Having its opposite peak at the point where the tangent is parallel the base.

7. nilai : value

The value of 72 divided by 8 is 9.

8. Bola : sphere

Earth is a example of sphere.

9. segitiga sama sisi :equilateral triangle

Equilateral triangle is a triangle that the three sides the same length .

10. luas : area

The area of trangle is half of the base multiplied by altitude.

1. Terangkan bagaimana memperoleh bilangan phi.Closely allied to the quadrature problem is the computation of phi, the ratio of the circumference of a circle to its. By successive aplications of process, starting with the regular inscribed and circumscribed six-sided polygon, we can compule the perimeter of the regular inscribed and circumscribed polygon of 12,24,48 and 96 sides, in this way obtainins ever closer bounds for phi. This is esssentialy what Archimedes, fanally obtaining the fact that phi is between 223/71 and 22/7 or that, to two decimal places, it is qiven by 3,14. 

2. Terangkan bagaimana memperoleh bilangan a b c. 
Step by step : 
• Change coefficient x become one 
• Eliminating constanta of at laft internode ( the joint lessened by c/a ) 
• Enhancing the joint with the square of semi from coefficient x 

3. Terangkan bagaimana mencari luas daerah yang dibatasi y = x2 dan y = x + 2. 
For the first searc the intersection point of the both of curve that is in point (negative one, one) and (two, four). Both of the equation have been integral that is curve on the top minus curve which in underof it., so that it's area can be find from integral x plus two minus x square equel a half x square plus two minus x to the power of third with negative limit one until two so that its area can be count that is four comma five units area 
4. Terangkan bagaimana menentukan volume kerucut. 
If known a cone with radius of its base is r and its altitude is t, so that to find the volume of cone equel the area of base multiply the altitude where it’s area of base is a circle, so that the volume of cone is equal to phi multiply radius square multiply altitude. 

5. Terangkan bagaimana membuktikan bahwa dalam dalam sembarang segitiga 
  Proof:
For the first, make a scalare triangle, making lengthening of lines from whatever point. Here, for example point of C collinear with AC. Then, through the point of C, make a line which parallel with AB. 
The corner of DCE is equal to the corner of CAB because it’s facing.
The corner of BCE is equal to the corner of ABC because it’s opposite.
The corner of ACB plus the corner of BCE plus the corner of ECD be located in one line is equal one hundred and eighty degree, so that the corner of ACB plus the corner of ABC plus the corner of CAB is equal to one hundred and eighty degree.
Proven

6. terangkan bagaimana menentukan probabilitas munculnya jumlah angka > 6 dari 2 buah dadu yang dilambungkan sekali. 
By using opportunity, sum up the number more than six from two dice which lobed once there are twenty one, so that the probability of number appearance mare than six is twenty one devided thirty six.

7. Terangkan bagaimana menentukan persamaan garis yang melalui (10,0) dan menyinggung lingkaran x2 + y2 = 9. 
line equation which is through in point(ten, zero) with the radius is three, to determine by x multiply ten plus y multiply zero equal to three square, and then the line equation become ten x plus zero equal to nine, then x equal to zero comma nine.

8. Terangkan bagaimana membuktikan dalil phytagoras. 
for example a b c represent the side straighten and hypotenuse from right triangle, at two square which is each by a plus b as a sliced. The first square sliced become six shares, that is two squere its sides and four right triangle which congruen trilaterally is determined. While squere is secondly slides to become five shares that is square hypotenusa and four right triangle which congruen trilaterally is determined . integer a b c deputize the foot and right triangle hypotenuse. Three the number known as by triple phytagoras. And then to look for one of the number a b c that is hypotenuse square equal to square from bevel side which is one plus square from other bevel side, earn is also conceived by teorema phytagoras.

9. Terangkan bagaimana mencari jumlah bilangan ganjil 200 pertama. 
by using series of arithmetical, the first terms equal one, whit different two and there are one hundred terms, so that sum of add number two hundred first equal a half of one hundred multipled two multiple first of terms plus terms of hundred minus one multipled two , a result equal ten thousand.

10. terangkan bagaimana melukis atau membuat kubus yang diketahui rusuk-rusuknya.
example, will made cube ABCDEFGH, with bsae ABCD and side right are AE, BF, CG, and HG, length of side is five centimeter, angle of deviation is thirty degree, and proporsition of project equal two fifth.
• Drawing line Ab five centimeter with horizontal 
• On point of A, point angle of deviation thirty degree, Ad is line orthogonal, because length of project is two fifth so that length of ADequal two centimeter
• Project aslant of square ABCD us parallelepipedum, so that base can finished
• Centre of side is vertical line, so point of angle EFGH can be drawn, then cube of ABCDEFGH shaped.