HENDRA LISTYA KURNIAWAN
MATEMATIKA SWADAYA 08
08305144014
A.) Reference
Reference is the cornerstone of research because many sources we can use to search for references. With many references we will get a lot of material to make a study. We can seek a reference from various sources, for example we can use books that relate to what we'll use as research material, but that we also can browse the internet to get all the information that will be used as research material.
B.) English for Mathematics Research
In building a new system of mathematics that we need to know the mathematical research into several aspects that must be understood and met. In a mathematical system that must be met include:
1.) Describes the existing definition.
2.) Explaining the axioms that are used.
3.) Explaining the theory or the theorem is the basis of mathematical research.
4.) Explain the rules and procedures in Mathematika Research.
C.) Factors supporting
Many supporting factors which are essential in mathematical research, include:
a.) the mathematical knowledge possessed
b) Experience in developing mathematical
c) Philosophy of mathematics that have
d) Knowledge of the history of mathematics
In this case the most famous is the story of Godel's incompleteness theorem
1. Theorem: Each recursively enumerable language of arithmetic.
Arithmetic formulas much larger class than recursively enumerable classes. In fact, all the language that has proven to be decided or recognized in this book, the arithmetic. The only example of nonarithmetical language encountered so far is the set of true formulas in arithmetic.
2. Theorem: For any reasonable method of provability, the language of arithmetic formula proved enumerable (and so identified).
3. Theorem: true arithmetic formula language is not even recognized.
Godel's incompleteness theorem states that if there is a complete system of mathematics that this system would not be consistent, and vice versa if the system is consistent so that the system would not be complete or cover all the theories.
d.) Step-by-step mathematical research
To build a mathematical research requires a variety of measures, including:
1.) Indepth studies reference
Step to take is to find many references to reinforce the basic theory has been used in the study of mathematics.
2.) Identifying and defining problems
Identify and formulate the problem is a step we have to do when we can find a reference series of very young to process what we get.
3.) Develop mathematical research methods
The next step is to develop existing research methods to menvariasikan so something is not there an update monotonous.
4.) Process of mathematical research
In this case doing the actual research process is to perform data collection, hypothesis formulation, implementation of mathematical research to test hypotheses and perform calculations to conclude that ultimately makes the publication of mathematics research has been conducted.
Senin, 21 Desember 2009
World Class University
HENDRA LISTYA KURNIAWAN
08305144014
MATEMATIKA SWADAYA
World Class University (WCU)
To get something more, someone needs ahard effort. Just as university whom we live for 3 semester requires a change to more. As has been pretty much by the Rector of Yogyakarta State University, in the coming years Yogyakarta State University will be World Class University.
World Class University is a program that is now made in Yogyakarta State University, especially those now being carried on prodeo mathematics education and accounting education. This program is one program to introduce the Yogyakarta State University into the world of international education.
One month ago, Mr. Marsigit and friends went to Japan to Memorandum of Understanding (MOU) head for World Class University. Firstly, Mr. Marsigit and friends traveled to Tokyo Development Center (TDLC) for meeting, workshop, and coordinating as for World Class University. Secondly, Mr. Marsigit, Rector of Yogyakarta State University, and friends continued of travel to Aichi University to Memorandum of Understanding. Point of Memorandum of Understanding are commitment of exchange of student, teacher, and staff of Yogyakarta State University with Aichi University.
So I was very supportive and very proud of the one program that did not just play the program but the program really great in education, a program of this World Class University. Business needs with very hard, from father marsigit also note that only for just search for representatives to learn and obtain a certificate from the international communities need to be rigorous selection and the difficulty to find, but business is still there, which in turn also obtain the desired representative, although was not as much with that have been targeted.
08305144014
MATEMATIKA SWADAYA
World Class University (WCU)
To get something more, someone needs ahard effort. Just as university whom we live for 3 semester requires a change to more. As has been pretty much by the Rector of Yogyakarta State University, in the coming years Yogyakarta State University will be World Class University.
World Class University is a program that is now made in Yogyakarta State University, especially those now being carried on prodeo mathematics education and accounting education. This program is one program to introduce the Yogyakarta State University into the world of international education.
One month ago, Mr. Marsigit and friends went to Japan to Memorandum of Understanding (MOU) head for World Class University. Firstly, Mr. Marsigit and friends traveled to Tokyo Development Center (TDLC) for meeting, workshop, and coordinating as for World Class University. Secondly, Mr. Marsigit, Rector of Yogyakarta State University, and friends continued of travel to Aichi University to Memorandum of Understanding. Point of Memorandum of Understanding are commitment of exchange of student, teacher, and staff of Yogyakarta State University with Aichi University.
So I was very supportive and very proud of the one program that did not just play the program but the program really great in education, a program of this World Class University. Business needs with very hard, from father marsigit also note that only for just search for representatives to learn and obtain a certificate from the international communities need to be rigorous selection and the difficulty to find, but business is still there, which in turn also obtain the desired representative, although was not as much with that have been targeted.
Senin, 02 November 2009
HENDRA LISTYA KURNIAWAN
08305144014
MATEMATIKA SWADANA
MATHEMATIC IS MY LIFE
I.Properties of Logarithms
Just as you have been knew, logb x = y equal by = x. To search of “x”, we can use formula it.
Example 1 :
log10 x = log x
We are assumption 10 equal b, log x equal y. And then, we are substitute of 10 and log x in the formula by = x.
10x = 100
102 = 100
x = 2
So, we are come into possession of x = 2 from log10 x = log x. In the natural logarithms, we can also use formula log ex = ln x.
Example 2 :
log 2 x = 3
Just as example 1, we are assumption with 2 equal b and 3 equal y.
log2 x = 3
23 = x
8 = x
From log2 x = 3 and use formula logb x = y equal by = x, with that x = 8.
Example 3 :
log7 () = x
We are assumption 7 equal b, x equal y.
log7 () = x
7x =
7x = 7-2
x = -2
From example 1 up to 3, we can nature of logarithms, such as :
logb (M.N) = logb M + logb N
logb () = logb M – logb N
logb (xn) = n logb x
Expand !!!
log3 ()
From nature of logarithms, we can calculate :
log3 () = log3 (x2(y+1)) – log3(z3)
= log3 (x2) + log3 (y+1) – log3 (z3)
= 2 log3 x + log3 (y+1) – 3 log3 2
II.Common Factors and Grouping
Onetime, we have been introduced “FPB” by teacher. In English, “FPB” is Common Factors and Grouping (GCF). It’s consist of product and factors. Example :
15 = 3 x 5
15 is product and (3 or 5) are factors.
Finding The Greatest Common Factors (GCF) of Numbers
a)The GCF of a list of integers in the largest common factor of integers in the list.
Example :
Find of the Greatest Common factors from 45 and 60 !
45 = 3.3.5 = 32.5
60 = 2.2.2.3.5 = 23.3.5
To search GCF, we must search same number in the number of the Greatest Common with the smallest power. So, the GCF of 45 and 60 are 3.5 = 15.
b)The Finding the GCF, choose prime factors with the smallest exponents and find their product.
Example :
Find the GCF from 36, 60, 108.
Firstly, we must search factors 36 = 22.32 ; 60 = 22.3.5 ; 108 = 22.33
After we are find factors, just example 1 we are search number with smallest power. With that, we are find 22.3 = 12.
To fast formula, we can use share of joint.
236 60 108
218 30 54
3 9 15 27
3 5 9
III.Trigonometri Function
Ratios of different sides of a triangle with respect to an angle. You only need to know valves of sides to find measure of all parts of atriangle.
Rigonometri function consist of sine, cosine, tangent, cosecant, secant, and cotangent. The six basic trigonometri function defined by :
1.Side of atriangle.
2.Angle being measured.
HYP
OPP
ⱷ
ADJ
Information:
OPP : side opposite theta
ADJ : side adjacent to theta
HYP : hypotenuse
To calculate sine, cosine, tangent, cosecant, secant, and cotangent we can use formula :
sin ⱷ = csc ⱷ =
cos ⱷ = sec ⱷ =
tan ⱷ = cot ⱷ =
Astudent usally use quick formula. To facilitate commit to memory, we can memorize with :
S O H C A H T O A
i p y o d y a p d
n p p s j p n p j
e o o i a o g o a
s t n c t e s c
i e e e e n i n
t n n n t t n
e u t u e t
s s
e e
IV.Factoring Polynomials
Algebraic long division
Example is x-3 a factor of x3-7x-6
equal
- 3
3 -
3 - 9x
2x – 6
2x – 6
0
is no remainder, x -3 is a factor x3-7x-6
= x2+3x+2
x2+3x+2 also a factor of x3-7x-6. If we are write to mathematics.
x3-7x-6 = (x-3) (x2+3x+2) = (x-3) (x+1) (x+2)
roots = 3,-1,-2
3 roots for this 3rd degree equation quadratic (2nd degree) equastion always have at most 2 roots. A 4 th degree equation would have 4 or fewer roots. The degree of a polynomial equation always limits the number of roots.
Long division for a 3rd order polynomial :
1.Find a partial qouetient of x2, by dividing x into x3 to get x2.
2.Multiply x2 by the divisor and sustract the product from the dividend.
3.Repeat the process until you either “clear it out” or reach a remainder.
V.Function Terminology
Definition of function :
1.An algebraic statement that provides a link betweentwo or more variables.
2.Used to find the value of one variable if you know the values of the others.
Example :
y = 2x. If you know x = 5 with that y = 2.5 =10
One variable appears by itself on one side of the equation.
Example : y = 3x + 4, y equal by it self.
A function is a codependent relationship between x’s and y’s without x, you can’t get y.
Definition of function from Master of Mathematics :
1.Any numerical expression relating one number, or set of numbers, to another.
2.Two kind of relations are equations and inequalities. Equation is 1+3 = 4, inequality is 8 > 5.
Spesific numbers are being related to each other.
Equations and inequalities the kind that can be used to determine just one value for one of the variables y=3x+4. When you substitute a value for y. An equation with one variable is a function of whatever variables appear on the other side.
Function of x, f(x)=y, f of x
y = 3x+4function of x
f(x) = 3x+4 (standard form).
Put function that are not in standard form into standardform.
Example :
g(x) = x3-3x+2
x = 5g(5) = x3-3x+2
= 52-3.5+2
= 25-25+2
= 12
VI.Parallelogram
If a quadrilateral is a parallelogram, then opposite sides of parallel.
A B
D C
A quadrilateral consist of 4 side; , , If ABCD is a parallelogram, with that :
\\
\\
If a side is not abreast, with that quadrilateral is not parallelogram.
08305144014
MATEMATIKA SWADANA
MATHEMATIC IS MY LIFE
I.Properties of Logarithms
Just as you have been knew, logb x = y equal by = x. To search of “x”, we can use formula it.
Example 1 :
log10 x = log x
We are assumption 10 equal b, log x equal y. And then, we are substitute of 10 and log x in the formula by = x.
10x = 100
102 = 100
x = 2
So, we are come into possession of x = 2 from log10 x = log x. In the natural logarithms, we can also use formula log ex = ln x.
Example 2 :
log 2 x = 3
Just as example 1, we are assumption with 2 equal b and 3 equal y.
log2 x = 3
23 = x
8 = x
From log2 x = 3 and use formula logb x = y equal by = x, with that x = 8.
Example 3 :
log7 () = x
We are assumption 7 equal b, x equal y.
log7 () = x
7x =
7x = 7-2
x = -2
From example 1 up to 3, we can nature of logarithms, such as :
logb (M.N) = logb M + logb N
logb () = logb M – logb N
logb (xn) = n logb x
Expand !!!
log3 ()
From nature of logarithms, we can calculate :
log3 () = log3 (x2(y+1)) – log3(z3)
= log3 (x2) + log3 (y+1) – log3 (z3)
= 2 log3 x + log3 (y+1) – 3 log3 2
II.Common Factors and Grouping
Onetime, we have been introduced “FPB” by teacher. In English, “FPB” is Common Factors and Grouping (GCF). It’s consist of product and factors. Example :
15 = 3 x 5
15 is product and (3 or 5) are factors.
Finding The Greatest Common Factors (GCF) of Numbers
a)The GCF of a list of integers in the largest common factor of integers in the list.
Example :
Find of the Greatest Common factors from 45 and 60 !
45 = 3.3.5 = 32.5
60 = 2.2.2.3.5 = 23.3.5
To search GCF, we must search same number in the number of the Greatest Common with the smallest power. So, the GCF of 45 and 60 are 3.5 = 15.
b)The Finding the GCF, choose prime factors with the smallest exponents and find their product.
Example :
Find the GCF from 36, 60, 108.
Firstly, we must search factors 36 = 22.32 ; 60 = 22.3.5 ; 108 = 22.33
After we are find factors, just example 1 we are search number with smallest power. With that, we are find 22.3 = 12.
To fast formula, we can use share of joint.
236 60 108
218 30 54
3 9 15 27
3 5 9
III.Trigonometri Function
Ratios of different sides of a triangle with respect to an angle. You only need to know valves of sides to find measure of all parts of atriangle.
Rigonometri function consist of sine, cosine, tangent, cosecant, secant, and cotangent. The six basic trigonometri function defined by :
1.Side of atriangle.
2.Angle being measured.
HYP
OPP
ⱷ
ADJ
Information:
OPP : side opposite theta
ADJ : side adjacent to theta
HYP : hypotenuse
To calculate sine, cosine, tangent, cosecant, secant, and cotangent we can use formula :
sin ⱷ = csc ⱷ =
cos ⱷ = sec ⱷ =
tan ⱷ = cot ⱷ =
Astudent usally use quick formula. To facilitate commit to memory, we can memorize with :
S O H C A H T O A
i p y o d y a p d
n p p s j p n p j
e o o i a o g o a
s t n c t e s c
i e e e e n i n
t n n n t t n
e u t u e t
s s
e e
IV.Factoring Polynomials
Algebraic long division
Example is x-3 a factor of x3-7x-6
equal
- 3
3 -
3 - 9x
2x – 6
2x – 6
0
is no remainder, x -3 is a factor x3-7x-6
= x2+3x+2
x2+3x+2 also a factor of x3-7x-6. If we are write to mathematics.
x3-7x-6 = (x-3) (x2+3x+2) = (x-3) (x+1) (x+2)
roots = 3,-1,-2
3 roots for this 3rd degree equation quadratic (2nd degree) equastion always have at most 2 roots. A 4 th degree equation would have 4 or fewer roots. The degree of a polynomial equation always limits the number of roots.
Long division for a 3rd order polynomial :
1.Find a partial qouetient of x2, by dividing x into x3 to get x2.
2.Multiply x2 by the divisor and sustract the product from the dividend.
3.Repeat the process until you either “clear it out” or reach a remainder.
V.Function Terminology
Definition of function :
1.An algebraic statement that provides a link betweentwo or more variables.
2.Used to find the value of one variable if you know the values of the others.
Example :
y = 2x. If you know x = 5 with that y = 2.5 =10
One variable appears by itself on one side of the equation.
Example : y = 3x + 4, y equal by it self.
A function is a codependent relationship between x’s and y’s without x, you can’t get y.
Definition of function from Master of Mathematics :
1.Any numerical expression relating one number, or set of numbers, to another.
2.Two kind of relations are equations and inequalities. Equation is 1+3 = 4, inequality is 8 > 5.
Spesific numbers are being related to each other.
Equations and inequalities the kind that can be used to determine just one value for one of the variables y=3x+4. When you substitute a value for y. An equation with one variable is a function of whatever variables appear on the other side.
Function of x, f(x)=y, f of x
y = 3x+4function of x
f(x) = 3x+4 (standard form).
Put function that are not in standard form into standardform.
Example :
g(x) = x3-3x+2
x = 5g(5) = x3-3x+2
= 52-3.5+2
= 25-25+2
= 12
VI.Parallelogram
If a quadrilateral is a parallelogram, then opposite sides of parallel.
A B
D C
A quadrilateral consist of 4 side; , , If ABCD is a parallelogram, with that :
\\
\\
If a side is not abreast, with that quadrilateral is not parallelogram.
Selasa, 26 Mei 2009
VOCABULARY
Integral = integral
To look for wide at a graph fruit can use the integral concept.
Kombinasi = combination
Combination is share gathering which have member of r element from gathering by n element.
Akar = root
To search of roots in square equation beside use factor can also use a,b,c formula.
Kongruen = congruen
Two develop is told congruen if have form and same size measure.
Sudut = angel
Sum up the triangle interior angle is one hundred eighty degree.
Kemiringan = gradient
Gradient can use formula of a/b or with look at equation beforehand.
Konsep = concept
The concept of a geometry is calculate use algebra concept.
Lingkaran = circle
To calculate area of circle, we must know radius in the circle.
Langkah = step
In mathemetics to do, we must know step by step and accurate.
Bilangan prima = prime number
The prime number is a number which can only be divided by one and itself number.
Sisi = side
A cube and a log have six side and twelve flank.
Pembuktian = verification
Subject of Logica, every statement must followed a verification.
Teorema Pythagoras = Pythagorean theorem
A right triangle, to calculate one of side which not yet been known can use Pythagorean theorem.
Turunan = differensial
The process to look for the derivative named by differensial.
Persamaan linier = linear equation
An equation with the rank one named with the linear equation.
Diagram kartesius = diagram of cartesius
A diagram of cartesius have to have the area of covey and area fight against.
Kurva = curve
Depiction a curve of square equation in form of a parabola.
Koordinat = coordinate
To search ordinat of maximum coordinate, we can use formula of deskriminan is divided with 4 cross a.
Tabel kebenaran = tables of truth
Assess the contraposition can be expressed to use the tables of truth.
Variable = variable
A linear equation have two or more variable.
Determinan = determinant
To get invers,before we have to search the determinant.
Persilangan = cross
Cross of the lines is appear one of intersection
Diagonal = diagonal
The trapezoid is consist of cross of two diagonal
Skala = scale
In the map , you will find scale of place
Aritmatika = arithmatics
In the number line , if reduction between the first line and second line,second line and third line and etc are the same,so we get conclused arithmatic lines.
Aksioma = axiom
In the geometry , every axiom have to accompanied with verification
Vektor = vector
The vector is set of mathematics have value and instruct
Aljabar = algebra
In the subject of algebra , we are only distinguish the system of linear equation.
Cabang = branch
Mathematics science have many branch of subject,consist of calculus, geometry, algebra and etc.
Kerucut = cone
To calculate the volume of cone, we can multiplying area with tall and dividing with the number of three
Selasa, 14 April 2009
HENDRA LISTYA KURNIAWAN
MATEMATIKA
08305144014
1. Explaining how to obtain get the phi!
Chronology of Phi :
Firstlty, research of about phi is Archimedes by using circle which have diameter and to count/calculate circle by making polygon. Afterwards we can count/calculate the perimeter from polygon of exist and about circle with the side twelve,twenty four , fourty eight, and ninety six . And finally we get the boundary from nearer value phi, that is among between two hundreds twenty three per seventy one and twenty two per seven or can be writed by three poin fourteen.
2. Explaining how to obtain get the formula a,b,c!
To obtain get the formula a,b,c that is by altering / manipulate the square equation become the perfect square, among other things :
a) Alter the coefficient of x square become one.
b) Eliminate
c) Enhance second is joint of square half from coefficient x.
d) Alter the left internode become the perfect square.
3. Explaining how to look for wide of area limited by y=x2 and y=x+2!
To obtain get a wide of area from two equation, we have to know the second boundary of that equation. To get our boundary have to equalize second of that equation, that is y one is equal to y two. x square is equal to x plus two, hence x of square of min x min two. Afterwards we get its boundarys that x is equal two and x is equal to min one. After we get its boundarys, we are second integral of equation with of way of y one min y two. Becoming, wide of area limited by y is equal to x of square and y is equal to x plus two is two
4. Explaining how to determine the trapeze volume!
To obtain get the our trapeze volume have to know the radius and high of the trapeze. After we obtain get fingers is we can look for wide of pallet from trapeze that is a circle. With the our formula phi dot r square will get the broadness. To determine the our trapeze volume can use the formula of one per three dot pad broad dot high.
5. Explaining how to prove that in any trilateral hence sum up its angle;corners 1800!
Firstly, we make trilateral any through/ passing one of side at parallelogram and that trilateral have to congruen,with that will be formed to by develop build to level off the parallelogram. Fourth amount of angle corner of parallelogram is three hundred six degree, because parallelogram formed represent the merger two triangle which congruen, with that sum up the angle corner from each trilateral is one hundred eighty degree. With that sum up from third angle corner of trilateral is one hundred eighty degree.
6. Explaining how to determine the probabilitas appearance sum up the number of bigger than 6 from two dice lobed once!
We look for the number amount which possible its amount more than six beforehand that is one andsix,two and five,two and six,three and four,three and five,three and six,four and four,four and five,four and six, five and five,five and six,six and six. Obtained by twelve opportunity
, from darting two dice will yield thirty six.With that probabilitas of opportunity which possible is twelve divided thirty six. So, probabilitas appearance sum up the number of bigger than six from two dice thrown is one-third.
7. Determining how to determine the line equation which is [through/ passing] ( 10,0) and touch the circle x2+y2=9!
Firstly, we alter the radian equation become the x of square of plus of y of square minus nine is equal to zero, c=minus nine. Hence direct us can use the formula x multiply the x one plus y multiply the y one plus c is equal to nol. Coordinat ( ten poin zero) we make as x one, y one. its Tangent equation ten x plus of zero times rill y [of] [is] equal to Nine. Becoming, it’s line equation ten x minus nine is equal to zero.
8. Determining how to determine the theorem Pythagoras!
To determine the our theorem Pythagoras have to take example beforehand with draw the right triangle and have two from the right triangle side. After we obtain get, its both sides or its sides comparison, we can look for it with the square oblique side is equal to second square sum up its side.
9. Explaining how to look for the anomalous number amount 200 first!
To obtain get the anomalous number amount two hundreds first if we use the way of traditional very hard. To facilitate, we can use the theorem of line and row. To get we can use the formula Sn of equal to ½ n multiply the a of plus Un.To get Un we can calculate the U1,U2, and so on and determine the difference. Afterwards Un will meet by including a plus ( n minus one) dot b. Un is equal to two n min one. Because anomalous number two hundreds first, hence Un is equal to two hundreds hence its result three hundred ninety nine. Becoming, anomalous number amount two hundreds first is fourty thousand.
10. Explaining how paint/ making cube knew [by] its flanks!
We paint the frontal area beforehand, then make the angle of deviation withdraw. From each our angle corner dot get the area frontal and we make the side orthogonal, big of inclination according to angle corner with draw. Hence by connecting each our dot get a cube.
Kamis, 09 April 2009
EPISODE RASHER OF MR. MARSIGIT
At young old, Mr. Marsigit is a diligent, his friends only pass the Senior High School he can pass the strata 1. After passing strata 1,he is studied in
Nowadays Mr. Marsigit have passed the strata 3 and have pride of place in Yogyakarta State Universitty. As student we shall be grateful to also have the experienced teacher. His Experience shall become our reference to more achievement in so many matter. If our desire why don’t.
Not yet this old, Mr. Marsigit compile a book of mathematics Junior High School by basic English language which its contents very captivating of reader to be diligent learn. Besides us can learn the mathematics perhaps we also can learn the to have Ianguage inggris. One of its contents which he is explain that is hit the linear equation and kuadratic equation. For the equation of our linear enough know the existing variable. And then, the our square equation can look for it with the factor and or with the formula abc. To use the our formula abc have to know the deskriminan from the square equation. There is three kinds of form assess the deskriminan, that is :
1. If D>0 hence proportioned parabola in two dot representing its solution gathering
2. If D=0 hence proportioned parabola in one dot.
3. If D<0 hence parabola is not proportioned.
Selasa, 24 Maret 2009
NATURE OF MATHEMATICS
NATURE OF MATHEMATICS
Mathematics model is phenomenon continue become to contain infinite of elements, for example phenomenon of light is represent the energy form with set of referred as by smallest of photon, model mathematics produced is approach model.
A mathematics model as approach to a phenomenon natural or made in only include, cover as much till perception or only include, cover the finite area from the phenomenon unlimited or only have the character of the diskrit, although the model still be considered to be a very ideal form and very coming near of genuiness physical phenomenon.
In the past, branchs of mathematics learned the phenomenon of physical continue (wave, hot, elasticity of a material, move the dilution, and another) predominating applicable mathematics branchs at various ordinary physical phenomenon such as those which learned in physics and chemical. As a result, this mathematics branchs is classified in group of physics mathematics.
But since expanding computer science, applying of branchs of mathematics learn the phenomenon is non simply diskrit, even till, expanding swiftly. For example, conception the field till is first considered to be a pure branch from algebra represent one of important backbone in coding theory.
That way also, size measure theory ( English: measure theory) and its applying, specially in theory fraktal and its bearing with the theory chaos. Of course all mathematics still can learn the aspect from theory of fraktal and chaos without having to deepen the size measure theory.
For the phenomenon of physical which till, model its mathematics ( for example mathematical formulation and model for the sinyal of, decoder and encoder of code Reed-Muller), It’s made not again the approach model, but have represented the eksak model.
At some mathematics branchs, term ' the mathematics model ' can be narrowed and as a result, definition or congeniality (special) from word ' the mathematics model ' in a mathematics branch can differ from the same word meaning in other mathematics branch.
Source : *Model Theory
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