In Marsigit Oponion, purpose The aim of the research of mathematics is to examine and develop mathematics
Mathematics is basic of all applied science. In Marsigit Oponion, the nature of mathematics :
Formal mathematics/ axiomatic mathematics/ pure mathematics
Formal mathematics builds on formal logic. It reduces mathematical relationships to questions of set membership. The only undefined primitive object in formal mathematics is the empty set that contains nothing at all.
Formal mathematics :
• Number theory
Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study.
Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated.
The terms "arithmetic" or "the higher arithmetic" as nouns are also used to refer to number theory. These are somewhat older terms, which are no longer as popular as they once were. However the word "arithmetic" is popularly used as an adjective rather than the more cumbersome phrase "number-theoretic", and also "arithmetic of" rather than "number theory of". e.g. (arithmetic geometry, arithmetic functions, arithmetic of elliptic curves).
• Groove theory
• Ring theory
In mathematics, ring theory is the study of rings, algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings (group rings, division rings, universal enveloping algebras), as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.
• Field theory
Field theory is a branch of mathematics which studies the properties of fields. A field is a mathematical entity for which addition, subtraction, multiplication and division are well-defined.
Field theory is a branch of mathematics which studies the properties of fields. A field is a mathematical entity for which addition, subtraction, multiplication and division are well-defined. In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers.
• Euclidean geometry
• Non Euclidean geometry
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system; usually though the effort towards complete formalisation brings diminishing returns in certainty, and a lack of readability for humans. Therefore discussion of axiomatic systems is normally only semi-formal. A formal theory typically means an axiomatic system, for example formulated within model theory. A formal proof is a complete rendition of a mathematical proof within a formal system.
pure mathematics is mathematics motivated entirely for reasons other than application. It is distinguished by its rigour, abstraction, and beauty. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics,and at variance with the trend towards meeting the needs of navigation, astronomy, physics, engineering, and so on.
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with the mathematical techniques typically used in the application of mathematical knowledge to other domains.
School mathematics/ concret mathematics/ real mathematics
School mathematics :
• Intention
• Awareness
• Abstraction
• Idealization
Concrete Mathematics: A Foundation for Computer Science, by Ronald Graham, Donald Knuth, and Oren Patashnik, is a perennial textbook in university computer science departments. It provides the mathematical background for computer science, especially the analysis of algorithms. While some of the topics in Concrete Mathematics are similar to those covered by traditional Discrete Mathematics textbooks, the authors have a unique approach to the subject matter: They explain in the preface that concrete mathematics "is a blend of CONtinuous and disCRETE mathematics," and calculus is frequently used in the explanations and exercises. The term is also used to denote the opposite of abstract mathematics.
The book is based on a course originally taught in 1970 by Knuth at Stanford University. It expands on the material in the "Mathematical Preliminaries" section of Knuth's The Art of Computer Programming. Consequently, some readers use it as an introduction to that famous series of books.
Concrete Mathematics distinguishes itself through its informal, humorous style. The authors reject what they see as the dry style of most mathematics textbooks, and the margins contain "mathematical graffiti," comments submitted by the text's first editors: Knuth and Patashnik's students at Stanford.
According to Ebbute Straker (1995), school mathematics is about :
• Pattern/ relationship
• Problem solving
• Investigation
• Communication
To identify mathematics problem we need mathematics knowledge, mathematics system, and mathematics characteristic. The three aspects above can we get easily if we have a will, attitude, knowledge, skill, and experience.
Mathematics is a deductive system consist of definition, axioms, and theorem in which there is no contradiction in side.
Reference :
http://en.wikipedia.org/wiki/Applied_mathematics
http://en.wikipedia.org/wiki/concrete_mathematics
http://en.wikipedia.org/wiki/field_mathematics
Selasa, 29 Desember 2009
Kamis, 03 Desember 2009
assigment 5
1. Solve
2. If
find
......
3. find the normal vector
field-a =
4. if a rocket is fired vertically upward from the earth's surface with initial velocity 192 ft / sec, when the rocket reaches its maximum height from the ground and what the maximum height? how long does it take to reach the ground again and how much speed when hitting the ground?
Answer:
1.
3.
4. From that text, we get :
v = 192 – 32t
s = 192t – 16t^2
when v = 0
192 – 32t = 0
32t = 192
t = 6
So, the maximum height or altitude happen when t = 6
s = 192 (6) – 16(6) = 576 feet
That rocket reaches ground whe s = 0
192t - 16t^2 = 0
192t = 16t^2
t = 12
So, it needs 6 seconds to reaches ground again, t = 12
v = 192 – 32(12) = -192 feet/second
So, the last velocity equals initial velocity.
5. Suppose x is distance of improving load
Suppose y is a horizontal distance
From A , where that rope tiech with the truck , on vertical ine which through fulley
2. If
find
......
3. find the normal vector
field-a =
4. if a rocket is fired vertically upward from the earth's surface with initial velocity 192 ft / sec, when the rocket reaches its maximum height from the ground and what the maximum height? how long does it take to reach the ground again and how much speed when hitting the ground?
Answer:
1.
2. 
3.
4. From that text, we get :
v = 192 – 32t
s = 192t – 16t^2
when v = 0
192 – 32t = 0
32t = 192
t = 6
So, the maximum height or altitude happen when t = 6
s = 192 (6) – 16(6) = 576 feet
That rocket reaches ground whe s = 0
192t - 16t^2 = 0
192t = 16t^2
t = 12
So, it needs 6 seconds to reaches ground again, t = 12
v = 192 – 32(12) = -192 feet/second
So, the last velocity equals initial velocity.
5. Suppose x is distance of improving load
Suppose y is a horizontal distance
From A , where that rope tiech with the truck , on vertical ine which through fulley
Assigment 5
1. if a rocket is fired vertically upward from the earth's surface with initial velocity 192 ft / sec, when the rocket reaches its maximum height from the ground and what the maximum height? how long does it take to reach the ground again and how much speed when hitting the ground?
2. a weight W attached to a rope 50 feet long and through the point P, 20 feet above the ground. The other end of the rope attached to a truck at point A, 2 feet above ground level, if the truck was moving away at a speed of 9 ft / sec, how fast it loads up when he was 6 feet from the ground?
2. a weight W attached to a rope 50 feet long and through the point P, 20 feet above the ground. The other end of the rope attached to a truck at point A, 2 feet above ground level, if the truck was moving away at a speed of 9 ft / sec, how fast it loads up when he was 6 feet from the ground?
Senin, 04 Mei 2009
Information
There are so many information that we can get by read and learn this book. Beside can increasing our knowledge of math (lesson), it also can increasing our knowledge of some concept of math in our real life. Some of the informtion are:
Ø In chapter I : When a part of sunshine is blocked by a certain object their will a shadow of the body compare our shadow and the tower shadow besides. By comparing our shadow and tower shadow we can measure the height of the shadow. We can use the concept of similarity to mesure.
Ø In chapter II : If the building has a circle form with the similar diameter on every floor, then the sides of the buildings should be inform of curve. If the tortuous sides of the building are to be layered by glasses, so that the area of needed glasses could be get by using the concept of three dimensional curved surfaces shape.
Ø In chapter III : Rain is one of the natural phenomena on the earth. The highest average of rain density canbe found in Cherrapunji, Bangladesh. The height of that region is 1.290 m above the sea level and average rain density is 1.270 cm so that it is called the wettest points on the earth. While the lowest average of rain density can be found in Atacama desert, Chili. It has 0,01 cm average of rain density so that it is called the driest point on the earth. Hence, the p robability of the rain in Atacama desert is very low ; moreover the area several place in Atacama desert that has never been rained 400 th for predicting the rain density we can use the concept of statistic and probability.
Ø In chapter IV : If someone jumps from a high with original velocity is zero, then it is called free fall movement. The relation between the velocity and height of the man from the ground is formulated by V = where V is the velocity, g is the gravitation at the place, and h is the height from the ground. The form is one of the example of roots that we can learn in chapter IV.
Ø In chapter V : When a ball fallen from a certain height on the flat ground, the ball will bounce back but with the lower height from its initial height. If the camparison between the ball height at this moment and the ball height before ots constant, so we can calculate the height of the ball from the time it was fallen until its stopped using the geometric series.
Ø In chapter I : When a part of sunshine is blocked by a certain object their will a shadow of the body compare our shadow and the tower shadow besides. By comparing our shadow and tower shadow we can measure the height of the shadow. We can use the concept of similarity to mesure.
Ø In chapter II : If the building has a circle form with the similar diameter on every floor, then the sides of the buildings should be inform of curve. If the tortuous sides of the building are to be layered by glasses, so that the area of needed glasses could be get by using the concept of three dimensional curved surfaces shape.
Ø In chapter III : Rain is one of the natural phenomena on the earth. The highest average of rain density canbe found in Cherrapunji, Bangladesh. The height of that region is 1.290 m above the sea level and average rain density is 1.270 cm so that it is called the wettest points on the earth. While the lowest average of rain density can be found in Atacama desert, Chili. It has 0,01 cm average of rain density so that it is called the driest point on the earth. Hence, the p robability of the rain in Atacama desert is very low ; moreover the area several place in Atacama desert that has never been rained 400 th for predicting the rain density we can use the concept of statistic and probability.
Ø In chapter IV : If someone jumps from a high with original velocity is zero, then it is called free fall movement. The relation between the velocity and height of the man from the ground is formulated by V = where V is the velocity, g is the gravitation at the place, and h is the height from the ground. The form is one of the example of roots that we can learn in chapter IV.
Ø In chapter V : When a ball fallen from a certain height on the flat ground, the ball will bounce back but with the lower height from its initial height. If the camparison between the ball height at this moment and the ball height before ots constant, so we can calculate the height of the ball from the time it was fallen until its stopped using the geometric series.
Interest
There are some points of interest of this book, such as:
*) This book is equipted with notes; it contains of additional topic being discuss. In this book, the notes is highlighted.
*) Beside notes, this book is equipted with be remember; it contains any information about a topic that have been studied before. It aims to assist the student in finding the relation between the topic they are studying and the topic they have already learned. In this book, be remember is highlighted too.
This book also equipted wth National Examination at the end of the last chapter of book. It is an evaluation for the student to check their mastery in 1st, 2nd, and 3rd grade they have learned. It contain of whole lessons of so multiple choice. It help the student in preparing theirself for natonal examination, especially for student 9th.
Scheme of Book
Like an usual book lesson for the student 9th, this book is written in a structure or scheme. The scheme of book:
Ø The Beginning of Chapter
The beginning of each chapter is described any aspect of the curiculum. Besides, there is also state the competence standard which must be achieved by the students.
Ø Number of Chapter and Its Title
Are the latest curiculum-based chapter and title.
Ø Basic Competence
Are some targets that must be archieved by students after studying the topic.
Ø Introduction Picture and Its note :
Are a picture and its note in the from of statement or question related to the topic discussion to attract the students curiousity and interest to the topic.
Ø What will you learn it this chapter
It contains the topic that will be learned in that chapter.
Ø Sub-Chapter Explanation
Is the more detailed explanation supported with pictures and tables.
Ø Example :
Its presented after the explanation of a topic to assist the students in recognizing the problem related to the topic.
Ø Exercise :
Its presented after the example to assist the students in applying the topic they have just learned
Ø Note :
It contains of additional topic being discussed.
Ø Be remember
It contains any information about a topic that have been studied before. It aims to assist the student in finding the relation between the topic they are studying and the topic they have already learned.
Ø Chapter Exercise :
Its an evaluation phase to check the students mastery of the topics they have already learned. It contains of 20 multiple choice items and 5 problem solving items.
Ø Chapter Evaluation :
Its an evaluation for the students to check their mastery of several topics have been discussed in the previous chapters. It contains of 30 multiple choice items and 10 problem solving items.
Ø National Examination
It is an evaluation for the student to check their mastery in 1st, 2nd, and 3rd grade they have learned. It contain of whole lessons of so multiple choice.
Ø Final Evaluation
It this an evaluation for the student to check their mastery of whole lessons they have learned. It contains of 25 multiple choice item and 10 problem solving items.
Ø The Beginning of Chapter
The beginning of each chapter is described any aspect of the curiculum. Besides, there is also state the competence standard which must be achieved by the students.
Ø Number of Chapter and Its Title
Are the latest curiculum-based chapter and title.
Ø Basic Competence
Are some targets that must be archieved by students after studying the topic.
Ø Introduction Picture and Its note :
Are a picture and its note in the from of statement or question related to the topic discussion to attract the students curiousity and interest to the topic.
Ø What will you learn it this chapter
It contains the topic that will be learned in that chapter.
Ø Sub-Chapter Explanation
Is the more detailed explanation supported with pictures and tables.
Ø Example :
Its presented after the explanation of a topic to assist the students in recognizing the problem related to the topic.
Ø Exercise :
Its presented after the example to assist the students in applying the topic they have just learned
Ø Note :
It contains of additional topic being discussed.
Ø Be remember
It contains any information about a topic that have been studied before. It aims to assist the student in finding the relation between the topic they are studying and the topic they have already learned.
Ø Chapter Exercise :
Its an evaluation phase to check the students mastery of the topics they have already learned. It contains of 20 multiple choice items and 5 problem solving items.
Ø Chapter Evaluation :
Its an evaluation for the students to check their mastery of several topics have been discussed in the previous chapters. It contains of 30 multiple choice items and 10 problem solving items.
Ø National Examination
It is an evaluation for the student to check their mastery in 1st, 2nd, and 3rd grade they have learned. It contain of whole lessons of so multiple choice.
Ø Final Evaluation
It this an evaluation for the student to check their mastery of whole lessons they have learned. It contains of 25 multiple choice item and 10 problem solving items.
Sabtu, 07 Maret 2009
Tugas English OnE
Oleh : Heni Ayu Pertiwi , 08305141022
Following is definition, follow the example of congeniality or clarifications of the other about terms of made by gist Rochmania Septikasari, which i write in language of inggris as result of from opening dictionary , opening enskliopedia, studying language book of english, opening Mr. Marsigit blog, download internet, as well as following lecturing of Mr. Marsigit in class.
Joint line represent the part of line owning length superior and is usually named with jetty dot and back
part him. ( Dari Wikipedia bahasaIndonesia, Ensiklopedi Bebas)
6. Equation following ( Persamaan Berikut Ini )
7. At the farthest (setinggi-tingginya)
8. In any case (setidak-tidaknya)
9. Less than (kurang dari)
10.Multiplication between equation (perkalian antar persamaan)
11.Vertical (Tegak Lurus)
12.Slash (Garis Miring)
13.Wide of surface (Luas Permukaan)
14.Heavy Line (Garis Berat)
15.Each other is proportioned (Saling Berpotongan)
16.Special conditions (Persyaratan Khusus)
17.Interaction (Saling Berhubungan)
- Equation of square (Persamaan Kuadrat) is an equation of polinomial have order to two. Public form of equation of square is letters of (a, b, c) conceived of by coefficient, square coefficient of (a) is coefficient from x2, linear coefficient of (b) is coefficient from x and (c) is constant coefficient or reffered as also free tribe . Form ax2+bx+c.( Dari Wikipedia bahasaIndonesia, Ensiklopedi Bebas)
- Integer(Bilangan Bulat) consist of count number (0,1,2,3,...) and negative (-1,-2,-3,...; -0 is equal to 0 and don't be included again separately). Integer can be written down without component denary or fraction.( Dari Wikipedia bahasaIndonesia, Ensiklopedi Bebas)
- Original Number (Bilangan Asli). Original number is positive integer which non zero, that is gathering element {1,2,3,...} original number represent one of the simplest mathematics consept which can study and understood by human being.( Dari Wikipedia bahasaIndonesia, Ensiklopedi Bebas)
- Indefinite Number ( Bilangan Tak Tentu ) .
- All, some, Entire, Halfs
- All Comunique will be collected.( Dari Wikipedia bahasaIndonesia, Ensiklopedi Bebas)
Joint line represent the part of line owning length superior and is usually named with jetty dot and back
part him. ( Dari Wikipedia bahasaIndonesia, Ensiklopedi Bebas)
6. Equation following ( Persamaan Berikut Ini )
7. At the farthest (setinggi-tingginya)
8. In any case (setidak-tidaknya)
9. Less than (kurang dari)
10.Multiplication between equation (perkalian antar persamaan)
11.Vertical (Tegak Lurus)
12.Slash (Garis Miring)
13.Wide of surface (Luas Permukaan)
14.Heavy Line (Garis Berat)
15.Each other is proportioned (Saling Berpotongan)
16.Special conditions (Persyaratan Khusus)
17.Interaction (Saling Berhubungan)
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