Tuesday, April 14, 2009

Part I
Words in mathematics
1. Bilangan rasional = a rational numbers
2. Garis paralel = parallel lines
3. Garis tegak lurus = perpendicular lines
4. Kombinasi = combination
5. Permutasi = permutation
6. Teori bilangan = number theory
7. Bilangan prima = prime number
8. Bilangan bulat = Integers
9. Bilangan genap = Even
10. Sebangun= Similar to one another
11. Statistiks = statistic
12. Pecahan = fraction
13. tidak sama dengan = an inequation
14. diferensial sebagian = partial differential
15. Perhitungan Integral = Integral Calculation
16. Bilangan cacah = Whole
17. Limas = Pyramid
18. Prism = prisma
19. Persamaan eksponen = Exponent equations
20. Integral tentu = Definit integral
21. Limit tak hingga = Limit a function of infinity
22. Nilai-nilai kebenaran = Truth value
23. Radian = radian
24. Persamaan linier 2 peubah = Linier equations in two variable
25. Akar pangkat 3= Cube root
26. Nilai mutlak = Absolute value
27. Segi tiga = Triangle
28. Aritmatika = Arithmetics
29. Persegi empat = Square
30. Persegi panjang = Rectangle
Part II
Definition and example
1. A rational numbers
Is any number that can be raiten in the from a over b. Where a and b are integers and b cannot equal 0.
Rational number can be represented by fracktions or decimal.
Example: 3 over 8 equal 0.375
2. Parallel lines
Two lines are parallel if and only if they are in the same plane and do not intersect.
Example: AB parallel CD
3. Perpendicular lines
Are lines that intersect to form a right angle.
Example: AB prependicular with CD
4. Combination
The combination is combining several objects from a group regardless of the order. In combination, the order is not observed.
{1,2,3} adalah sama dengan {2,3,1} dan {3,1,2}.
Example: A child is only allowed to take two of three envelope envelope envelope provided, namely A, B envelope and the envelope C. Decide how many combinations there are to take two of three envelope envelope provided?

Solution: There are 3 combinations namely; A-B, C and A-B-C
One application is the combination is used to find the probability of occurrence.

5. Permutation
Combine some permutation is the object of attention with a group order. In the permutation, the order observed.
(1,2,3) is not equal to (2,3,1) and (3,1,2)

Example: There is a box contains 3 balls of each red, green and blue. If a child is assigned to take 2 balls at random and the observed sequence, there is a permutation happening?

Solution: There are 6 permutation namely; MH, MB, HM, HB, BM, BH.
One application is the permutation is used to find the probability of occurrence.
6. The basic theory
Traditionally, the theory is a branch of pure mathematics to learn that nature integer and contains a variety of problems can be easily understood even by non-mathematician.

In the basic theory, integer without using techniques learned from other areas of mathematics. Questions about the nature can be divided, Euklidean algorithm to calculate the largest alliance of factors, integer factorization in prime numbers, research on the perfect and kongruensi learned here.
7. Prime number
Prime numbers is number that the original greater than one, and the devided factor is the number one and itself.
Example: one, three, five, seven, etc.
8. Integers
Integer consists of a number (0, 1, 2, ...) and negative (-1, -2, -3, ...; -0 is equal to 0 and no longer included separately). Integer can be written without a fractional or decimal component.
Example: (-3,-2,-1,0,1,2,3,…)
9. Even
Numbers are numbers that even out the number 2 divided by.
Example: (2,4,6,…)
10. Similar to one another
Meaning: two geometrical objects are called similar if they both have the same shape.
Example: If triangle ABC is similar to triangle DEF in such a way that the angle at vertex A is equal to the angle at vertex D, the angle at B is equal to the angle at E, and the angle at C is equal to the angle at F. Then, once this is known, it is possible to deduce proportionalities between corresponding sides of the two triangles, such as the following:

{AB \over BC} = {DE \over EF},

{AB \over AC} = {DE \over DF},

{AC \over BC} = {DF \over EF},

{AB \over DE} = {BC \over EF} = {AC \over DF}.

11. Statistics is the science of learning how to plan, collect, analyze, interpret, and present data. In short, statistics is the science related to the data. From the collection of data, statistics can be used to construe or describe your data; this is called descriptive statistics.

Example: Most of the basic concept of probability theory, statistics mengasumsikan. Some term statistics such as: population, sample, sample unit, and probability.
12. Fraction consists of numerator and denominator. Transaction in fact is a fraction how to simplify the numerator and the denominator with the same number, so that is very eerie to see a more imut-imut for ditatap.
Example: if the comparison between 50/100 and ½ the more interesting to see how a number ½. 50/100 seen as a "gigantic figure" who seems to be more complex than ½, the second number is actually still have the same value.
13. An inequation
Meaning: a statement that two objects or expressions are not the same, or do not represent the same value. This relation is writtwn with a crossed-out equal sign, like x ≠ y
Example: 2 minus 3 not equals zero, because 2 minus 3 equals negative 1, and negative 1 inequation zero.
14. Partial differential equation
Partial differential equation (PDP) is the equality in which there are tribes partial differential, which is defined in mathematics as an associate relationship of a function that is not known, which is a function of some variable-free, with the derivative through the variables that referred to.
PDP is used to perform and complete the formulation of the problems involve functions that are not known, which is formed by several variables, such as spreading the sound and heat, electrostatics, electrodynamics, fluida flow, elasticity. Sometimes some problems fisis have a very different mathematical formulations that are similar to one another
15. In mathematics, theorems binomial formula is important to give the rank of the expansion of Answer.
Example: for n equals 2 to 5
X plus y inbracket squared equals x squared 2 times x times y plus y squared
X plus y in bracket cubed equals x cubed plus 3 times x times y in bracket squared plus y cubed
16. Whole
The whole is set integer that is not negative, ie (0, 1, 2, 3 ...}. In other words, the original set of numbers plus 0.
Example: (0,1,2,3,…)
17. Pyramid
A building where the outer surfaces are triangular and converge at a point. The base of pyramids are usually quadrilateral or trilateral (but may be of any polygon shape), meaning that a pyramid usually has four or five faces.
Example: Pyramid volume formula is 1 / 3 wide base X high
18. Prism
a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same. A prism is a subclass of the prismatoids.

Example: Prism volume formula that is wide base Xhigh
19. Exponent equations
Meaning: an equation in which a polynomial is set equal to another polynomial.
Example: x squared plus x minus 6 equals x minus 2 in bracket times x plus 3 in bracket is exponent equations
20. Definite integral
The limit of a sum of areas of rectangles, called a Riemann sum.
Example : 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

\int_a^b f(x)\,dx = F(b) - F(a)\, .

21. Limit a function of infinity

If the extended real line R is considered, i.e. R (- ~,+ ~), then it is possible to define limits of function at infinity
22. Truth value
Meaning : a value indicating the extent to which a proposition is true
Example : The truth value of a proposition is shown using 0s and 1s.

True = 1
False = 0
23. Radian
A Radian is: the angle made by taking the radius and wrapping it along the edge of the circle.
A plane is a flat surface with no thickness. Our world has three dimensions, but there are only two dimensions on a plane.
Examples: ength and height, or x and y.
24. Linier equations in two variable
Meaning: an algebratic equation in which each term is either a constant or the product of constant.
Example: liner equation in thte two variable x and y is y = mx + c, where m and c designer constants ( the variable y is multiplied by the constant 1, which as usual is not explicilly written)
25. cube root
a cube root of a number, denoted or x1/3, is a number a such that a3 = x. All real numbers have exactly one real cube root and a pair of complex conjugate roots, and all nonzero complex numbers have three distinct complex cube roots.
Example: the real cube root of 8 is 2, because 23 = 8.
26. absolute value
absolute value (or modulus) of a real number is its numerical value without regard to its sign.
Example, 3 is the absolute value of both 3 and −3.

The absolute value of a number a is denoted by | a |.
27. Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC.
28. arithmetics
is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. In common usage, the word refers to a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numbers
29. square
A four-sided polygon with all sides the same length and all angles = 90 degrees
30. rectangle
a rectangle is a closed planar quadrilateral having four right angles.
The shape is like a square, but the sides are not necessarily all equal in length.

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