Mathematics is the science of numbers and their combinations, operations, generalizations, and abstractions. As a science of order and structure, math evolved from counting, measuring, and describing the shapes of objects around us. Mathematics is used in the study of all sciences, such that it is considered an underlying language of science. Among the principal branches of mathematics are algebra, arithmetic, geometry, game theory, number theory, numerical analysis, probability, set theory, statistics, topology, and trigonometry.
There are two broad areas of opportunity in mathematics: theoretical and applied. Theoretical mathematics deals with pure and abstract mathematical concepts rather than the practical application of such concepts to everyday problems. Applied mathematics involves the development and application of mathematical knowledge to practical and research problems.
Physics is a comprehensive natural science dealing with the interaction of matter and energy. Heavily reliant on mathematics, physics studies the behaviors of matter and is organized into a series of related laws. Physicists compare the results of their experiments with existing theories using mathematical techniques.
Basic physics can be studied from two points of view: experimental and theoretical. Experimental physics uses experiments to gather information. Theoretical physics constructs theories to explain experimental results. Physicists develop new theories and technologies based on their research, which in turn deepens our understanding of how things work and contribute to innovative, practical applications.
Galileo is often called the first modern physicist. His most famous experiment, in which he dropped a 10-pound weight and a one-pound weight from the Leaning Tower of Pisa, proved that all weights fall at the same speed. Through mathematical calculations, he proved that the moon reflects the light of the Sun.
In addition to contributing to the development of nuclear energy, applied mathematics played an important role in the 20th century development of the automobile, television, space exploration, and personal computers. It has been instrumental in advancing research and experimental efforts in sociology, psychology, and education, among other fields. The development of new space vehicles and mobile computing devices are but two examples that characterize the dynamic nature and increasing importance of mathematics now in the 21st century.
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