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| Selasa, 29 Desember 2009 |
| The research of mathematics |
1) Formal mathematics/Axiomatic mathematics/pure mathematics
Mathematics is a deductive system consist of definition, axioms, and theorem in which there is no contradiction inside. It is very easy to establish mathematics system.
Background
The stability of criteria of finding a solution of problems
The important
To formulate the aim of research of mathematics
To develop method of number teory
For example : analyze, syntetic, deductive, phenomenologi, hermonitica.
To collect data or literature
Discussion
Mathematics is a deductive system consist of definition, axioms, and theorem in which there is no contradiction inside. It is very easy to establish mathematics system.
Research in mathematics education has two main purposes, one pure and one applied:
• Pure (Basic Science): To understand the nature of mathematical thinking, teaching, and learning;
• Applied (Engineering): To use such understandings to improve mathematics instruction.
I got a theorem from number teory to proof. I try to proof and the result is above.
Theorem:
If p is a prime number and d|p-1, congruent of x^d-1= 0(mod p) have exactly d solution.
Solution
Proof :
According to Fermat’s theorem, whether P is prime number and (a,p)=1, so a^(p-1)= 1(mod p). It have meaning congruent of x^(p-1)= 0 (mod p) have exactly (p-1) solution:
For example d|(p-1), so
x^(p-1) = (x^d-1)( x^(p-1-d)+ x^(p-1-2d)+...+1)
= (x^d-1)f(x)
According lagrange theorem**, f(x) = 0 (mod p) have (p-1-d) solutions. For example x=a is a solution of x^(p-1-1) = 0 (mod p) which non solution of f(x) = 0 (mod p), so a is solution of x^d-1=0(mod p).
Because of 0 = a^(p-1)-1 =(a^d-1)f(a)(mod p)
Because p prime number and p f(a), so p|(ad-1)
So, x^d-1 = 0 (mod p) have minimally p-1-(p-1-d) = d solution
According to lagrange theorem x^d-1 = 0 (mod p) have maximally d solutions. So, congruent of that have exactly d solutions.
foot note:
**lagrange theorem: if p prime number and f is a polynomial n degrees, congruent of f(x)= 0 (mod p) have maximal n solutions.
References
Sukirman, Drs. 2006. Numbers teory. Adhi publisher: Yogyakarta.
http://www.google.com |
posted by sOFFia aNisa H.A.C (08305141004) @ 02.46  |
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| Senin, 28 Desember 2009 |
| The research of mathematics |
A. Marsigit’s Opinion
The aim of the research of mathematics is to examine and develop mathematics.
The kinds of the nature of mathematics instead of:
1) Formal mathematics/Axiomatic mathematics/Pure mathematics.
2) Applied mathematics.
3) School mathematics/concret mathematics/real mathematics.
1) Formal mathematics/Axiomatic mathematics/pure mathematics
Mathematics is a deductive system consist of definition, axioms, and theorem in which there is no contradiction inside. It is very easy to establish mathematics system.
Example:
Definition : x1,x2,x3,... Є R
Axiom
xi + xi+1 Є R
xi . xi+1 Є R
theorem
xi + xi+2 Є R
proof:
xi + xi+1 Є R
xi + xi+2 Є R
theorem:
xi + xi+2 Є R
formal mathematics is tell about numbers theory, group theory, ring teory, field teory, Euclidean geometry, non Euclidean geometry.
2) Applied mathematics
Applied mathematics using appropriate method to make a model airfield.
3) School mathematics/concrete mathematics
Mathematics phenomenon have two kinds, such as abstraction and idealization. Abstraction instead of form and shape. Idealization instead of straight(about perfectly). According to Ebbute Straker (1995), there are four parts of school mathematics: pattern/relationship, problem solving, investigation, communication.
To identify problems, we must know about mathematics knowledge, mathematics system, mathematics characteristic. When we make the research of mathematics, we need supporting factors, such as:
- The history of mathematics
- The works of mathematics
- The philosophy of mathematics
- Indepth study of mathematics
Background
The stability of criteria of finding....
the rational
The important
To formulate the aim of research
To develop method
For example : analyze, syntetic, deductive, phenomenologi, hermonitica.
To collect data or literature
Discussion
Solution
References |
| posted by sOFFia aNisa H.A.C (08305141004) @ 21.03 |
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| Jumat, 27 November 2009 |
| My Assignment about problems of mathematics |
1. draw a contour curve z=k for values of k which given.
z= 1/2 (x^2+y^2 ) , k = 0,2,4,6,8.
2. showed that surface x^2+4y+z^2=0 and x^2+y^2+z^2-6z+7=0 each other touching in point (0, -1, 2), showing that they have same area in point (0, -1, 2)
3. calculate the area under 32 if given a normal distribution with µ = 40 and σ = 6.
4. calculate the value of x which the area under 45% with µ = 40 and σ = 6.
5. given a randow sample which have measure 24 which pulled by a normal population. calculate k if P (-2.069 < T < k)= 0.965.
SOLUTION:
1. 
2. F(x,y,z) x^2+y^2+z^2-6z+7=0
<=> Fx (x,y,z) = 2x --> Fx (0,-1,2) = 0
<=> Fy (x,y,z) = 2y --> Fy (0,-1,2) = -2
<=> Fz (x,y,z) = 2z-6 --> Fz (0,-1,2) = -2
so, the surface area y+z-1=0
F(x,y,z) x^2+4y+z^2=0
<=> Fx (x,y,z) = 2x --> Fx (0,-1,2) = 0
<=> Fy (x,y,z) = 4 --> Fy (0,-1,2) = 4
<=> Fz (x,y,z) = 2z --> Fz (0,-1,2) = 4
so, the surface area y+z-1=0
because the both of surface area is same, so the surface is proven that they have same area.
3. z = (x-µ)/σ = -4/3
P (X < 32) = P (Z < -4/3)
= 0.0918
so, the answer is 0.0918.
4. P(X < x) = 45% = 0,45
z which have value 0.45 is -0.13
z = (x-µ)/σ
(-0.13)(6) = x-40
x = 39.22
so, the value of x is 39.22
5. P (-2.069 < T < k)= 0.965
-2.069 = t(-0.025)
<=> 1 - k - 0.025 = 0.965
<=> k = 0.010
t(k)=t(0.010)= 2.500
so, the value of k is 2.500 |
| posted by sOFFia aNisa H.A.C (08305141004) @ 22.03 |
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| Sabtu, 02 Mei 2009 |
| Book Review "Mathematics for Junior High School year VIII" |
A.Preface
First of all, we be grateful to Allah because we still given ability to review Mathematics for School Junior High School year VIII. We would like to thank to Mr. Marsigit who give us opportunity to review Mathemathics For Junior High School year VIII.
There are some benefit that we get while review Mathematics for Junior High School year VIII such as remember to grammar, know more about the different between curriculum mathemathics now and 6 years ago, etc.
We hope this review book is useful. It is intended to students and teachers of Junior High School as an opinion before buy mathematics book.
To release of this review book has been made possible due to the assistance and contributions of various people who cannot mention one by one. To all who involved in this preparation of this review book, I would like to express my high appreciation and gratitude.
Comments and suggestions to improve the contents of this review book are always welcome.
Yogyakarta, April 2009
Reviewers
B. Content
There are 7 chapters in this book. All of them are used to learn Mathemathics for Junior High School year VIII. The material divided into 2 units, that is:
UNIT I : Algebra
Chapters:
a. Algebra and its Applications.
b. The relation and Functions.
c. The equations of a Straight Line.
d. The System of Linear Equations in two variables.
UNIT II : Geometry and Measurement
Chapters:
a. The Pythagorean Theorem.
b. A Circle.
c. Polyhedral.
I think that the content of this book is complete enough. There is a previous in every chapter that make the readers know what will they learn in that chapter. All of the chapters are arranged by some subtitle. It is complete with the definitions, examples (and its problem solving), and more exercise. To remember the material or some formula there is an “be remember” in some page in every chapter. It’s content some formula or material briefly. So, it can help the reader (especially the students) to remember the materials of every study easily.
Beside the exercise of every subtitle, there is an exercise in the end of every chapter that content of some mathematics problems suitable to the material of every chapter. There are 20 multiple choices problems and 5 essays. At the end of every unit, there is an evaluation. This book also be completed with “final evaluation” at the last part. Student must solve 30 multiple choices problems and 10 essays.
Generally, this book is very good and interest for student year VIII. Its content is suitable to the curriculum of study in Junior High School in Indonesia at this moment (suitable to KTSP). The problem in the exercise and evaluations are realistic problems. We can find the problems in our daily activities. So, it makes the student can imagine and solve the problem easier.
The excellence of this books is because it is a bilingual books. So, there are two languages (Indonesian and English Language) in one book. Every Indonesian page translate to English directly. It is very useful, because with reading this books, students not only can improve their mathematics skill and knowledge but also develop their English. I think this book is suitable to some school to be world class school in Indonesia (school with international school standardization).
Over all, the content of this book is complete enough and simple (not too difficult to understand all of material mathematics on it). The point plus of this book is about it bilingual. So, I recommend this book to all of student year VIII in Indonesia. I hope it can help you to learn mathematics easier.
By : Artika Kristianingrum
C.Problem
In this book, there are seven chapter. There are exercise in each chapter. In this book also existed three evaluations : evaluation 1 available after 5 chapter, evaluation 2 available after last two-chapter and evaluation final available in the end. Evaluation was made to examine how far the students understand the substances which are in this book.
In this book there are the problem examples which are clarified in each chapter. The problem examples which are given consist of substances which are stated. In examples is given many examples problem solving which is enable the students to choose the easiest way. there are problem solving. After given examples, there are exercises for students. The form of exercises is varied and still consist all of the substances. Method of problem solving is stated and sequential.
By : Soffia Anisa H
D.Information
Book mathematics for Junior High School VIII by Marsigit give complete information about its chapter, so that easy to understand. Reasons information of this book easy to understand are:
a.Each chapter explained in detail that is by sub chapter.
b.Presented with bilingual that is in Indonesian and English language, so English people also can study it.
c.Each sub chapter explained theoretically, given example exercise, and exercise. So, after understand explained fill chapter, then can understand example exercise, so can finish exercise. In this book there are seven chapters, each chapter explained in detail became subchapter.
d.Explained fill chapter not out from studied problem.
e.There are chapter explained with picture (more use picture). For example in chapter six is circle, this book more use picture.
To limiting reader to understand information of this book, depended from reader. But, in general this book present information in detail.
By: Dian Tri Handayani
E.Interest
Mathematics for Junior High School year VIII which is written by Mr. Marsigit is different from the other mathematics book commonly. This book is presented in bilingual (Indonesia’s language and English). We can get many advantages by learn this book such as get mathematics knowledge. The students of Junior high school year VIII also can increase vocabullary owing to mathematics.
This book is suitable used to the students or teachers of international school standardization and students which want to continue their studies abroad. On the other hand, this book will inspire them to study better.
Not all people like reading book with black-white color. Some prefer like reading full color book. Mathematics junior high school year VIII as a full book that will stimulate students more interest to study. Talk about the substance, this book explain the substances early. In the end of chapter, there is exercise which consist of 30 multiple choices and 10 essays. The purpose is students can apply what has been him learn. This book has some of ancient marhematician story such Al-Khwarizmi.
By: Enti Dwiningsih
Written by:
Group III
Enti Dwiningsih (chairman)
Artika Kristianingrum (member)
Soffia Anisa H (member)
Dian Tri Handayani (member) |
| posted by sOFFia aNisa H.A.C (08305141004) @ 01.35 |
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| Senin, 16 Maret 2009 |
| For ayu and ALL |
Ayu..this is my answer..
1. Bujur sangkar = Rectangle
- rectangle(noun) : A parallelogram with four right angles.
Square
- square(noun) : - (geometry) a plane rectangle with four equal sides and four right angles;
- a four-sided regular polygon.
example : "you can compute the area of a square if you know the length of its sides"
- The product of two equal terms.
example : "gravity is inversely proportional to the square of the distance"
- An open area at the meeting of two or more streets.
- Any artifact having a shape similar to a plane geometric figure with four equalsides and four right angles.
example : "a checkerboard has 64 squares"
- square (adjective) : - Having four equal sides and four right angles or forming a right angle.
example : "a square peg in a round hole"; "a square corner"
- square(verb) : - Make square.
example : "Square the circle"
- square (adverb) : - In a square shape.
example : "folded the sheet of paper square"
2. Ruas garis = line segment
3. Garis tinggi = perpendicular
- perpendicular (noun) : - A straight line at right angles to another line.
- perpendicular (adjective) : - Intersecting at or forming right angles.
contour line(math)
- contour line (noun) : - A line drawn on a map connecting points of equal height.
4. Garis sumbu = axial line
5. Bidang = area, sector, field
6. Belah ketupat = Rhombus
- A parallelogram with four equal sides.
- an oblique-angled equilateral parallelogram.
7. Limas = Pyramid
- dipper or cup made of young palm leaves.
- A polyhedron having a polygonal base and triangular sides with a common vertex.
- a form with a base of three or four sides that tapers to a top point.
8. Kerucut = cone
- cone (noun) : A shape whose base is a circle and whose sides taper up to a point.
- a shape with a circular base that tapers to a point at the top.
9. Akar = Square Root
- A number that, when multiplied by itself some number of times, equals a given number,
- The set of values that give a true statement when substituted into an equation.
10. Garis bagi = bisector line
11. Deret = row, line, series. (math) progression,
deret hitung= arithmetical progression,
deret ukur= geometrical pogression
12. Sudut keliling dalam = circumference angle of a circle
13. Sejajar = Parallel line
- Being everywhere equidistant and not intersecting.
- relating to the simultaneous performance of multiple operations
14. Berpotongan = to shape; to have a model; being cut out; having a cut, reduction, intersection.
15. Berhimpit = to be close together; jammed together, press
16. Jari-jari = spokes; radius
17. Tegak lurus = perpendicular; vertical; upright; a right angle.
18. Mengadakan = to arrange; make; create; establish; launch; pursue; invent; to bring into
being
19. Tidak terbatas = unrestricted; unconfined; unlimited; unfinite;
20. Mungkinkah = maybe; possible; possibly; perhaps; perchance; potentially; might; may
21. Bagi (:) = to divide; distribute
22. Kuadrat = square, quadratic
23. Luas = considerable
24. Sumbu simetri = symmetry axis
25. Kurung buka = parenthesis, brackets
26. Kurung tutup = parenthesis, brackets
27. Dalam kurung = parenthesis, brackets |
| posted by sOFFia aNisa H.A.C (08305141004) @ 08.35 |
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| Senin, 02 Maret 2009 |
| Introduction to engLisH one |
EngLish oNe...
EngLish one is one of my programs which I choosed. On 17th February 2009, that is the first time I met Mr. Marsigit, MA, my lecturer.
Mr. Marsigit taught my class, reguler class of pure mathematics, to make a blog. He told us how to make a blog. we must make an email and the email account should have in @gmail.com.Mr.Marsigit said,"in my reseption, you're all adults."adult have responsibility, independen learner, comperate, colaborate with others. If you wants to be a good people, your knowledge must be usefull for others. you also must have skill to communicate mathematics in English.
There are 3 steps to develop my components. The first step is high spirit. The highest motivation is praying to God. Next step is support (behaviour, atitude).the last step is knowledge communication. knowledge communication is about how to talk, to write, to discuss, to translate, to reflect, to comment and to understand. Definition of English is understanding about verb, phrase of verb, compund, etc.
Inside in English I:
- How to comunicate mathematics in English.
- Skill to comunicate mathematics in English.
- Finally your skill to write is very good. |
| posted by sOFFia aNisa H.A.C (08305141004) @ 07.12 |
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