 calculus are applied to curves, surfaces, and other geometric entities. The approach in classical differential geometry involves the use of coordinate geometry (see analytic geometry; Cartesian coordinates),
..... Click the link for more information. , in which the methods of analysis are brought to bear on geometric problems. These fields are now in a vigorous state of development.
The term applied mathematics loosely designates a wide range of studies with significant current use in the empirical sciences. It includes numerical methods and computercomputer,
device capable of performing a series of arithmetic or logical operations. A computer is distinguished from a calculating machine, such as an electronic calculator, by being able to store a computer program (so that it can repeat its operations and make logical
..... Click the link for more information. science, which seeks concrete solutions, sometimes approximate, to explicit mathematical problems (e.g., differential equations, large systems of linear equations). It has a major use in technology for modeling and simulation. For example, the huge wind tunnelswind tunnel,
apparatus for studying the interaction between a solid body and an airstream. A wind tunnel simulates the conditions of an aircraft in flight by causing a high-speed stream of air to flow past a model of the aircraft (or part of an aircraft) being tested.
..... Click the link for more information. , formerly used to test expensive prototypes of airplanes, have all but disappeared. The entire design and testing process is now largely carried out by computer simulation, using mathematically tailored software. It also includes mathematical physics, which now strongly interacts with all of the central areas of mathematics. In addition, probabilityprobability,
in mathematics, assignment of a number as a measure of the "chance" that a given event will occur. There are certain important restrictions on such a probability measure.
..... Click the link for more information. theory and mathematical statisticsstatistics,
science of collecting and classifying a group of facts according to their relative number and determining certain values that represent characteristics of the group.
..... Click the link for more information. are often considered parts of applied mathematics. The distinction between pure and applied mathematics is now becoming less significant.
Development of Mathematics
The earliest records of mathematics show it arising in response to practical needs in agriculture, business, and industry. In Egypt and Mesopotamia, where evidence dates from the 2d and 3d millennia B.C., it was used for surveying and mensuration; estimates of the value of π (pipi,
in mathematics, the ratio of the circumference of a circle to its diameter. The symbol for pi is π. The ratio is the same for all circles and is approximately 3.1416.
..... Click the link for more information. ) are found in both locations. There is some evidence of similar developments in India and China during this same period, but few records have survived. This early mathematics is generally empirical, arrived at by trial and error as the best available means for obtaining results, with no proofs given. However, it is now known that the Babylonians were aware of the necessity of proofs prior to the Greeks, who had been presumed the originators of this important step.
A profound change occurred in the nature and approach to mathematics with the contributions of the Greeks. The earlier (Hellenic) period is represented by ThalesThales
, c.636–c.546 B.C., pre-Socratic Greek philosopher of Miletus and reputed founder of the Milesian school of philosophy. He is the first recorded Western philosopher. Thales taught that everything in nature is composed of one basic stuff, which he thought to be water.
..... Click the link for more information. (6th cent. B.C.), PythagorasPythagoras
, c.582–c.507 B.C., pre-Socratic Greek philosopher, founder of the Pythagorean school. He migrated from his native Samos to Crotona and established a secret religious soci