THE RESEARCH OF MATHEMATICS

BACKGROUND

Mathematics is the general characteristics. It’s become the another science always has the connectivity with mathematics. Another science can’t be apart from mathematics. Such a mathematics in our life too. Our life is the same with the science. It can’t be apart from mathematics. In the real example, when we go to the traditional market, we can demand and bargain what we will buy in there. Surely, mathematics always in there, between seller and customer.

Mathematics use in the world as the important tools in many subject, including a science, medical, and social knowledge as economic and psychology.

In a formal side, mathematics is to analyzed the abstract structure, that defined axiomatic with a logical symbols. Mathematics also used as a tools for studying many kinds of complex physics phenomenon, especially the nature phenomenon that observed. With mathematics, the structure, transformation, space, and the phenomenon characteristics can be approach and can be write in the systematic formulation and with many kinds of appointments and symbols. The result that describe about the physics phenomenon called mathematics models.

A mathematics models in optimization and control usually explain the system as the combination from the variables and also from the collection of equations that defined of relation of that variables. The variable value can be like a real number, or can be like a number arrays and strings.

Variables actually served in many characteristics system. Mathematics models actually is a collections of functions that has the relation between the different variable.

Models theory started with the assumption of mathematics object, searching, and analyzing the operations, relations, or axioms in every object or in the collections of object.

Mathematics as the logical science that study the ability of the right thinking. Logical is a branches of philosophy. Logical can be applied in a day’s life. Logical used for proofing. Logical can’t be avoid in a life process to find a honesty.


RESEARCH OF MATHEMATICS

Mr. Marsigit said that research of mathematics are the aim to examine and develop mathematics. And in my opinion, research mathematics is more explain the details of mathematics, from the theorems, axioms, then the proof of all the theorems. All of them trained us to always open our mind to be a scientist that has the mathematical thinking. Beside that, research of mathematics also means all the activity that have relation with mathematics in our life. It means that all of the applications of the theorems until the characteristics of mathematics can applied in our life, especially in habitual activity. Because mathematics has the general character, so it also can be applied in another subjects, for example in the chemistry, physics, etc. Its all means that our life and all of the science can’t be apart from mathematics.

“Mathematics is a deductive system. Consist of definition, axioms, and theorems in which there is no contradiction inside”, said Mr. Marsigit.

Mathematics has the philosophy. Philosophy of mathematics is a branches of philosophy that its learn about the basics and the results of mathematics. The purpose of philosophy mathematics is to give characteristics and mathematical methods and to know more about the position of mathematics in our life.

The characteristics of mathematics, is an abstract objects. An abstract object also called the mental object, its in our mind. The basic object consist of fact, concept, definition, operations, and principal. From the basic object, it can be constructed the structure of mathematics. The fact in abstract object in the conventions form and its in the many kinds of symbols. The definition are the appreciation that bounded a concept.

The system of mathematics is the important structure, especially in algebra and generally in mathematics. Group is one of the example of system mathematics.
For example: (G,x) is a mathematical system, so (G,x) called group if complete:
1. Associatif characteristic, for every a, b, c in G so ax(bxc) = (axb)xc
2. Has the neutral unsure , write e as the unsure, where for all a in G conduct exa = axe = a
3. Every member of G has neutraler, every a in G has b in G, so axb = bxa = e

Action research in a traditional aspects means a frame research to solving the problems, where there are have the collaboration of scientist and client to reached the purpose (U. Sulaksana, 2004).

Action research also defined as the action of planning, realization, and evaluation to be better as the purpose, and its doing with the systematic (Gunawan, 2007).

Action research also means a process that has an action ciclus, based the reflection, feedback, evidence, and the evaluation of action before and the situation now. The aim of action research is to give the role of problem solving in problematically situation like now (S. Madya, 2006).


DISCUSSION

A. Formal Mathematics

The complex mathematical object consist of many fact, many concept, that related with operation like axioms, theorems, characteristics, etc.

Axioms is undefined term, a basic explanation but it doesn’t important to proof it. Its to avoid the confusing on proofing. The axioms can establish a system of axioms, and it can to get the lemma and theorems.

The example of formal mathematics is in the number theory. The definition of number theory is a basic theory to learn the algorithm cryptography. And an integer is a kind of number that learn in number theory. Integer means a number that doesn’t has a fractional decimal, for example: 8, 21, -21, 0 etc.


B. Applied Mathematics

Applied mathematics is a branches of mathematics that enclose the application of mathematical knowledge in another aspect, and made a new discover of mathematics.

An applied mathematics was combined with the traditions that agree with mathematics, but its out of mathematics. For example: statistics, operation research, and computer.

Applied mathematics has a relation with the usage of abstract mathematical tools to solving the concrete problems in a science, business, and another aspects. For example statistics. Its use the opportunity theory as the equipment and explain, analyze, and calculation of phenomenon in which the opportunity has the important role, because all of the test, survey, and learn of control needs statistics.

One of the applied mathematics is the application of number theory, that it used in barcode methods. Barcode is a simple code that used to save the specific data, like production code, an expired date, and also an identity number. A rows code consist of a bar and space with the different bold that presented alpha-numeric characteristic.


C. School Mathematics

Mathematics is a science that has alot of usage for us in our live. It use in many kinds of aspects and used by many kinds of subjects. There are a lot of brances of mathematics that apllied in another science. So, mathematics is a universal science. And because of that, we can study mathematics everytime and anywhere.


REFERRENCES

Sulaksana, U. 2004. ”Managemen Perubahan”. Cetakan I. Yogyakarta: Pustaka Pelajar Offset.
Madya, S. 2006. “Teori dan Praktik Penelitian Tindakan (Action Research)”. Bandung: Alfabeta.
http://id.wikipedia.org
http://wordpress.com

Questions from ANDINI SETIARI (08305141017):

1. Given 2 baskets, Basket A contents of 20 duck's eggs, 5 among them are rotten. And 10 hen's eggs which 3 among them are rotten. Another basket, named basket B contents of 10 duck's eggs that 2 among them are rotten. if both of eggs that taked from basket A and basket B are rotten and still fresh, determined the opportunity that the fresh egg is a duck's egg from basket B!
2. Determined the integration of sec x tan quadrat of x dx
3. Determined the integration of cosec 2x dx minus integration of 2x cos 2x offer sin quadrat x dx minus integration of cosec quadrat 2x dx
4. What's the meaning of saddle point or "titik pelana" in a three dimensional function?
5. Determined the integration of 2x quadrat minus 3x minus 36 offer with 2x minus 1 multiplied with x quadrat plus 9 dx

Finished by WIDHATUL MILLA (08305141012)
Answer:

1. Describe that basket A contents with 20 duck's eggs, 5 among them are rotten. Basket B contents of 10 duck's eggs, 2 among them are rotten.
Because the equation is about the duck's eggs so I will ignore the hen's eggs. And I will use Bayes's Theory for solving this problem.
The opportunity between basket A and B is a half (1/2)
For example: B1 = opportunity for fresh eggs from basket A
B2 = opportunity for fresh eggs from basket B
P (B1) = 15/20 = 3/4
P (A) : opportunity for taken the egg randomly
P (A) = P (B1) P (A I B1) + P (B2) P (A I B2)
= 1/2 . 3/4 + 1/2 . 4/5
= 3/8 + 2/5 = (15+1)/40 = 31/40
So the opportunity for fresh eggs from basket B is (1/2)/(31/40) = 31/80

2. The integration of sec x tan quadrat of x dx is the same with the integration of 1 offer cos quadrat of x multiplied with sin x offer cos x dx, so the equation become integration of sin x offer cos cube of x dx
The way to get the solution. First we must assume that u is cos x and du = -sin x
so, dx = du offer (-sin x)
after that the equation become:
integration of sin x offer cos cube of x
equals to the integration of sin x offer u cube multiplied with du offer (-sin x)
equals to the integration of du offer u cube
equals to u power (-3) du
equals to one offer 2u quadrat plus constant . . . . . this is as the solution (1)

In the first time we assume that u is cos x. Now, substitute u as cos x in the solution (1). And the solution become:
the integration of sin x offer cos cube x is equals to 1 offer 2 cos quadrat of x plus constant
is equals to a half of sec quadrat of x plus constant
So, integration of sec x tan quadrat x dx is equals to a half of sec quadrat of x plus constant


4. Saddle is a point of function or surface a stationary point but not an extremum. An example of a one dimensional function with a saddle point is
f(x) = x cube which has
f’(x) = 3x quadrat
f’’(x) = 6x
f’’’(x) = 6
This function has a saddle point at x0 = 0 by the extremume since f’’(x0) = 0 and f’’(x0) = 0 and f'''(x0) = 6 ≠ 0.
Surface can also have saddle point is which has the sacond derivatif test can sometimes be used to identify. Examples of surface with saddle point include the handkerchief surface and monkey saddle

Book Review

PROBLEM

Two weeks ago, my group read "Mathematics For Junior High School Students" wich writen by Mr. Marsigit especially for billingual class. I think all the questions is very suitable for the junior high school students. This questions very match with they level as a junior high school students. This book give a lot of exercises. And in every subchapters, always has the example of exercise and the solve of it. Whereas in the end of every subchapters, given exercise in essay form, not in multiplechoice form.
We are very agree with your method because your method can be more usefull for every student to enlarge their creativity to solve that questions. Besides that, giving exercises in every subchapters can help the students to be more understand about the material. That exercises also visualized not only in cartoon picture, but it also visualized in a real life picture.
We know if the purpose of that is to make the students interested to solve that exercises. Beside that, the visualizations from that questions help the students to be more understand about what are really the questions want? and what are really the meaning of that questions. That book also completed with examinations questions. But, why in the end of this book not completed with the correct answers? No problem if this book not completed with the way to solve that questions, but what a perfect book it is if the end of this book completed with the correct answers.

1. ahli matematika: mathematician -> an expert or or specialist in mathematics.
for example: Phytagoras, Euler, etc. they are an expertiest in mathematics.

2. mata kuliah statistik: statistic subjects -> one of the subjects in mathematics wich studied about a numerical datum, a numerical value, such as standard deviation or mean, that characterizes the sample or population from wich it was derived.
based from the informations in http://www.thefreedictionary.com, statistic as a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters
from http://www.geocities.com, statistic is defined as following the science that looks into the generic phenomena, formally complex and framed in a variable universe by means of the employment of reduction models of introduction and validation analysis of the results in representative terms. we can verify that the calculation of the mean is a strictly mathematical operation, and in a strict sense, the fault in the example is the interpretation of an arithmetic result.
in the other side, from http://mathnstuff.com explain that a statistic is a one number description of a set of data, or number used as measurements or counts. Mathematicians use the statistic to describe data much as you might use one word to describe a situation or thing or person. it's not a perfect summary, but it's all that might be needed.

3. aplikasi komputer dalam pembelajaran matematika: the applications of computer in mathematics learning.
based from http://www.anrushmath.wordpress.com, computer have a lot of advantages for our life. for instance in education, the applications of computer not only used for administration, but also used as one of the alternative choice for the effective learning. because used computer can built a motivation and also can make student exited to study. used computer for learning make the student easier to understand the subject matter.

4. teorema dasar: elementary theorem
based from the http://thefreedictionary.com, the definitions of theorem is a statement proved on the basis of previously accepted or established statements such as axioms. in formal mathematical logic, the concept of a theorem may be taken to mean a formula that can be derived according to the derivation rules of a fixed formal system. the statements of theory as expressed in a formal language are called its elementary theorem and are said to be true.
for example: the calculus theorem

5. bilangan desimal: the decimal number
based from http://encyclopedia2.thefreedictionary.com, decimal is a fraction that has a denominator of a power of ten, the power depending on or deciding the decimal place. it's indicated by a decimal point to the of numerator, the denominator being omitted. zeros are inserted between the point and the numerator, if necessary, to obtain the correct decimal place. the numbering system used by humans, which is based on 10 digits. In contrast computer use binary numbers because it's easier to design electronic system that can maintain two states rather than 10. decimal notation is the writing of numbers in the base ten.
from the http://www.mathleague.com, the example of the decimal number is 3,762. as with whole numbers, a digit in a decimal number has a value which depends on the place of the digit. the places to the left of the decimal point are ones, tens, hundredths, and so on, just as with whole numbers. in the number 3,762, the 3 is in the ones place, the 7 is in the tenths place, the 6 is in the hundredths place, and the 2 is in the thousandth place

6. bilangan tidak real: unreal number, imaginary number
based from the definition from the http://www.yourdictionary.com, imaginary/unreal number is designating or of the square root of a negative quantity, or of a complex number that is not a real. unreal number is a complex number in the form a+bi where b is not zero, when a is zero, its a pure imaginary number.
from http://www.mathsisfun.com, unreal number is a number that when squared gives a negative result. The unit imaginary numbers (the same as "1" for Real Numbers) is √(-1) (the square root of minus one), and its symbol is i, or j.

7. tidak terhingga/tidak terdefinisi: unlimited
http://www.dictionary.net, unlimited is having no bounds. a problem which is capable of an infinite number of solutions.
http://www.wiredal.wordpress.com, unlimited is having no restrictions or controls, having or seeming to have no boundaries; infinite, without qualification or exception; absolute.
the notation for unlimited is " ~ "

8. himpunan kosong: null set
is a collection which it doesn't have member. null set was once a common synonym for empty set, but this usage should be avoided because "null set" is now a technical term in measure theory (http://en.wikipedia.org). the notation for the null set are { }
take from http://www.onlinemathlearning.com, the definition of the null set or the empty is there are some sets that do not contain any element at all. for example: the set of months with 32 days. We call a set with no elements the null or empty set. It is represented by the symbol { } . the other example: {1, 3, 5, 7, 9, ...} ∩ {2, 4, 6, 8, 10, ...} = { }

9. prisma segiempat: rectangular prism or square prism
based from http://www.mathforum.org, the rectangular prism can be thought of as the shape you'd get if you put a rectangle flat on the table in front of you and then lift it straight up and imagine that it leaves a shape behind it as it goes.

10. luas kubus: surface area of cuboid
based from http://www.mathforum.org, the surface area of an objects means how much paper it would take to cover it (or how much paint, if you follow the directions and don't put it on too thick or too thin). cubes are three dimensional, it involves the height, width, and thickness. but if we talking about the surface area, we have to be careful, because although the objects you're measuring has three dimensions, you're just measuring its surface, which like a piece of paper is two-dimensional.
the formula for surface area of cubes is: A= 2wd + 2dh + 2hw. (w=width, d=depth, h=height)
The square cuboid, square box or right square prism (also ambiguously called square prism) is a special case of the cuboid in which at least two faces are squares. The cube is a special case of the square prism in which all faces are squares.

11. pembuktian: proof
based from http://www.thefreedictionary.com, proof is the validation of a proposition by application of specified rules, as of induction or deduction, to assumptions, axioms, and sequentially derived conclusions. in maths, proof is logic a sequence of steps or statements that establishes the truth of a proposition

12. limas segitiga: triangular pyramids
based from http://www.easycalculation.com, the definition of pyramid is a polyhedron with one face as base, a polygon and all the other faces triangles meeting at a common polygon vertex as the apex. so the meaning of triangular pyramid is a geometric solid with a base that is a triangle and all other faces are triangles with a common

13. laboratorium komputer: computer laboratory
a laboratory wich has a computer media in it

14. perhitungan tunggal: single calculation

15. bilangan pecahan: fragment numeral
a fragment numeral is a number which the amount of this less than or more than a whole numeral. for examples: ¼, ¾, ½

16. rumus: formula
based from http://www.thefreedictionary.com, formula is a statements, especially an equations, of a fact, rule, principle, or other logical relation
example: the formula of phytagoras is A²=B²+C²

17. perangkat peragaan: the demonstration equipment
the demonstration equipment is an equipment which used to demonstrate about something.

18. proposal: proposal
based from http://www.ardictionary.com, the definition of proposal that which is proposed, or propounded for consideration or acceptance. proposal is something proposed (such as a plan or assumption)

19. balok: rectangular prism
from http://www.mathsisfun.com, rectangular prism is a solid (3-dimensional) object which has six faces that are rectangles. It is a prism because it has the same cross-section along a length.
its explained in number 9 before.
the rectangular prism based from http://www.mathforum.org, the rectangular prism can be thought of as the shape you'd get if you put a rectangle flat on the table in front of you and then lift it straight up and imagine that it leaves a shape behind it as it goes.

20. kalkulator: calculator or calculating machine
based from http://www.thefreedictionary.com, the meaning of calculator is device for performing numerical computations, it may be mechanical, electromechanical, or electronic. calculator is a machine for performing arithmetic operations and certain mathematical functions automatically

21. sempoa: abacus
frOM http://www.yourdictionary.com, abacus is a frame with beads or balls that can be slid on wires or in slots, for doing or teaching arithmetic

22. trapesium: trapezoid
based from http://www.mathopenref.com, trapezoid is a quadrilateral that has one pair of parallel sides, and where the vertices have known coordinates

aN aduLts LeaRner

Discussion with Mr. Marsigit in my class, 24th february 2009.

Mr. Marsigit said: we are an adults learners. take your own responsibility.
Now what really meaning of the mathematics?
Mathematics is apart in our life. Definition of mathematics is coming from the high motivation/high spirit. especially for mathematics need a good understanding too. It must build consistenly in study mathematics.

The meaning of mAthematics taking from google is the study of masuremants, properties, and relationships of quantities and sets, using numbers and simbols.

there are many ways to express the idea of mathematics:
1. looking at dictionary
2. looking at web
3. looking at blog
if you want to study mathematics,you must know about mathematics thinking, like:
1. mathematics attitude
2. mathematics method
3. mathematics contain
Mr. Marsigit said: "Train by yourself, so you get a skills"

dOn't tHink to bE a MathEmatiCian, if yOu thiNk mAtheMatics iS beyOnce of yOu!!

english one for mathematics

take from Mr. Marsigit's explanation one week ago, 17th februari 2009, I can get a lot of information about manythings. One of them is about . . . hOw tO bE a cOmpetEn peOple.
to be a competen people, we need some steps.

1. your motivation. your motivation in this steps are spirit. one we must to know and remember that the highest motivation in our life are praying.
2. make sure your behaviour/attitude. start now we must choose behaviour/attitude wich can support or can give many purpose in our life.
3. knowledge. we must have a lot of knowledge if we want to be a competen people. such if we want to be a scientiest, we must have enough knowledge about How tO cOmmuNicatE matHematiCs iN enGliSh for example.
4. skills
5. experience

important for us to know, that the lowest levels of knowledge are -> skills for ourself. then the higher from the lowest levels of knowledge are -> skills for the others. then -> professional networking. and the last, the highest achievements are -> international networking. as adults people, we must have responsibility, independent learner, an colaborate. responsibility are 80% important than the others.