The word “mathematics” comes from the Greek, which means learning, study, science, and additionally came to have the narrower and more technical meaning “mathematical study”, even in Classical times. Its adjective is math?matikós, related to learning, or studious, which likewise further came to mean mathematical. In particular, (math?matik? tékhn?), in Latin ars mathematica, meant the mathematical art.
The apparent plural form in English, like the French plural form les mathématiques (and the less commonly used singular derivative la mathématique), goes back to the Latin neuter plural mathematica (Cicero), based on the Greek plural ta math?matiká, used by Aristotle, and meaning roughly “all things mathematical”. In English, however, the noun mathematics takes singular verb forms. It is often shortened to math in English-speaking North America and maths elsewhere.
Definition of Mathematics
Most contemporary references define mathematics by summarizing its main topics:
These definitions all include relations and other abstractions, and so these definitions are broader than the Aristotelian definition of mathematics as “the science of quantity.”
Mathematics is the study of quantity, structure, space, relation, change, and various topics of pattern, form and entity. Mathematicians seek out patterns and other quantitative dimensions, whether dealing with numbers, spaces, natural science, computers, imaginary abstractions, or other entities. Mathematicians formulate new conjectures and establish 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.
Fields of Mathematics
The major disciplines within mathematics first arose out of the need to do calculations in commerce, to understand the relationships between numbers, to measure land, and to predict astronomical events. These four needs can be roughly related to the broad subdivision of mathematics into the study of quantity, structure, space, and change (i.e. arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.
These lists include topics typically taught in secondary education or in the first year of university.
• basic discrete mathematics topics
• calculus topics
• geometry topics
• topics in logic
• trigonometry topics
o basic trigonometry topics
• trigonometric identities
For Example in mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.
The most familiar trigonometric functions are the sine, cosine and tangent. The sine function takes an angle and tells the length of the y-component (rise) of that triangle. The cosine function takes an angle and tells the length of x-component (run) of a triangle. The tangent function takes an angle and tells the slope (y-component divided by the x-component). More precise definitions are detailed below.
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Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.
In modern usage, there are six basic trigonometric functions, which are tabulated here along with equations relating them to one another. Especially in the case of the last four, these relations are often taken as the definitions of those functions, but one can define them equally well geometrically or by other means and then derive these relations.
Tes Bidang Studi Dasar (TBSD) SNMPTN 2009 examination consists of Basic Mathematics, Bahasa Indonesia, and English. Basic mathematics is a type of test is more difficult to be seen by most participants SNMPTN. And indeed in the test group of this study Elementary, Mathematics level of complexity is in the top of the other primary field of study.
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Field Test Studies Basic Mathematics Test, followed by the IPA, IPS, and the IPC on the first day of the SNMPTN Wednesday 1 July 2009.
Basic Mathematics exam aims to measure the ability of prospective students basic math, as well as function as a means of evaluating potential candidates and the academic achievement of students.
Basic Mathematics (SBM and the Science and Engineering)
The test measures the ability of prospective students basic math, works as a means of evaluating the potential for academic achievement and potential students.
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