Saturday, April 11, 2009

Math's History

Elementary mathematics was part of the education system in most ancient civilisations, including Ancient Greece, the Roman empire, Vedic society and ancient Egypt. In most cases, a formal education was only available to male children with a sufficiently high status, wealth or caste.

In Plato's division of the liberal arts into the trivium and the quadrivium, the quadrivium included the mathematical fields of arithmetic and geometry. This structure was continued in the structure of classical education that was developed in medieval Europe. Teaching of geometry was almost universally based on Euclid's Elements. Apprentices to trades such as masons, merchants and money-lenders could expect to learn such practical mathematics as was relevant to their profession.

The first mathematics textbooks to be written in English and French were published by Robert Recorde, beginning with The Grounde of Artes in 1540.

In the Renaissance the academic status of mathematics declined, because it was strongly associated with trade and commerce. Although it continued to be taught in European universities, it was seen as subservient to the study of Natural, Metaphysical and Moral Philosophy.

This trend was somewhat reversed in the seventeenth century, with the University of Aberdeen creating a Mathematics Chair in 1613, followed by the Chair in Geometry set up in University of Oxford in 1619 and the Lucasian Chair of Mathematics, established by the University of Cambridge in 1662. However, it was uncommon for mathematics to be taught outside of the universities. Isaac Newton, for example, received no formal mathematics teaching until he joined Trinity College, Cambridge in 1661.

In the eighteenth and nineteenth centuries the industrial revolution led to an enormous increase in urban populations. Basic numeracy skills, such as the ability to tell the time, count money and carry out simple arithmetic, became essential in this new urban lifestyle. Within the new public education systems, mathematics became a central part of the curriculum from an early age.

By the twentieth century mathematics was part of the core curriculum in all developed countries.

During the twentieth century mathematics education was established as an independent field of research. Here are some of the main events in this development:
  1. In 1893 a Chair in mathematics education was created at the University of Göttingen, under the   administration of Felix Klein.
  2. The International Commission on Mathematical Instruction (ICMI) was founded in 1908, and Felix.
  3. Klein became the first president of the organization.
  4. A new interest in mathematics education emerged in the 1960s, and the commission was revitalized.
  5. In 1968, the Shell Centre for Mathematical Education was established in Nottingham
    The first International Congress on Mathematical Education (ICME) was held in Lyon in 1969.The second congress was in Exeter in 1972, and after that it has been held every four years.

In the 20th century, the cultural impact of the "electric age" (McLuhan) was also taken up by educational theory and the teaching of mathematics. While previous approach focused on "working with specialized 'problems' in arithmetic", the emerging structural approach to knowledge had "small children meditating about number theory and 'sets'."

History of Math

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere. Mathematicians formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.

There is debate over whether mathematical objects exist objectively by nature of their logical purity, or whether they are manmade and detached from reality. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Knowledge and use of basic mathematics have always been an inherent and integral part of individual and group life. Refinements of the basic ideas are visible in mathematical texts originating in the ancient Egyptian, Mesopotamian, Indian, Chinese, Greek and Islamic worlds. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. The development continued in fitful bursts until the Renaissance period of the 16th century, when mathematical innovations interacted with new scientific discoveries, leading to an acceleration in research that continues to the present day.

Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences such as economics and psychology. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.

Friday, April 10, 2009

INVESTMENT rank

→ designation of multiple forms of short repeated with the same multiplier factors. Each product can be repeatedly written or presented in a brief notation by using the exponential notation, or have an important position.

Example:
• The form of repeated multiplication axaxaxa, written in short notation with numbers or have an important position as the exponential notation a4, "a4" read a four-grade.
• The form of repeated multiplication of 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6, is written in short notation with numbers or have an important position as the exponential notation 69, "69" read six ninth-grade.

Nature rank on the floor unanimously positive.
If a and b real numbers and n, p, q and the original, then apply:
1. Distributif rank nature of the multiplication.

Example:

(2 x 3) 3 = 23 x 33
= 8 x 27
= 216
2. Distributif rank nature of the division.

Example:

(4: 2) 2 = 42: 22
= 16: 4
= 4
3. Between the nature of multiplication rank with the same number.

Example:

103 x 104 = 103 + 4

= 107

4. Nature of the division between the have an important position with the same number.

Example:

74: 72 = 74 - 2

= 72
= 49
5. Nature of the promotion have an important position.


Example:
(22) 3 = 22 x 3
= 26
= 64