THE RESEARCH OF MATHEMATICS

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

assigment 5

1. Solve






2. Iffind

......


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?

5. 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?

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?