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(1)Quantity: The study of quantity starts with the numbers, first the familiar natural numbers and integers. The deeper properties of integers are studied in number theory, from which arise such popular results as Fermat’s last theorem. The twin prime conjecture and Goldbach’s conjecture are two unsolved problems in the number theory. Another area of study is size, which leads to the cardinal numbers, and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.
(2)Structure: Mathematical objects such as, set of numbers and functions exhibits the internal structure as a consequence of operations and relations that are defined on set. Mathematics then studies properties of those sets that can expressed in the terms of structures. The phenomenon that the originally unrelated areas of geometry and algebra have very strong interactions in modern mathematics. Combinatorics study ways of enumerating the number of objects that fit a given structure.
(3)Space: The study of space originates from geometry- in particularly Euclidean geometry and trigonometry. Geometry deals with the relationship between the sides and the angles of the triangles. They both combine the space and encompass the Pythagoras theorem. The modern study of space generalizes these ideas to include higher-dimensional geometry, non- Euclidean geometry (which play a central role in general relativity) and topology.
(4)Change: Understanding and describing the change in the natural science, calculus a powerful tool was developed to investigate the change. Functions arise as a central concept describing a changing quality. Functional analysing focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied as differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behaviour.
Evolution Of Mathematics
The evolution of mathematics might be seen as an ever increasing series of abstractions or alternatively an expansion of subject matter. The first abstraction was shared by calculating the numbers of the animals. Mathematics was recognized by the humans when they collect the things and count them in numbers. There are many evidences that in ancient time’s humans collect and count the days, months as well as all physical things. The Babylonians were the first to use mathematics as to calculate the taxation and other financial calculations. Between 600-300 BC the ancient Greeks began a systematic study of mathematics in its own right with Greek mathematics. The mathematics has been greatly extended and there are fruitful interactions between the mathematics and science. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs.PURE
(1)Quantity: The study of quantity starts with the numbers, first the familiar natural numbers and integers. The deeper properties of integers are studied in number theory, from which arise such popular results as Fermat’s last theorem. The twin prime conjecture and Goldbach’s conjecture are two unsolved problems in the number theory. Another area of study is size, which leads to the cardinal numbers, and then to another conception of infinity: the aleph numbers, which allow meaningful comparison of the size of infinitely large sets.
(2)Structure: Mathematical objects such as, set of numbers and functions exhibits the internal structure as a consequence of operations and relations that are defined on set. Mathematics then studies properties of those sets that can expressed in the terms of structures. The phenomenon that the originally unrelated areas of geometry and algebra have very strong interactions in modern mathematics. Combinatorics study ways of enumerating the number of objects that fit a given structure.
(3)Space: The study of space originates from geometry- in particularly Euclidean geometry and trigonometry. Geometry deals with the relationship between the sides and the angles of the triangles. They both combine the space and encompass the Pythagoras theorem. The modern study of space generalizes these ideas to include higher-dimensional geometry, non- Euclidean geometry (which play a central role in general relativity) and topology.
(4)Change: Understanding and describing the change in the natural science, calculus a powerful tool was developed to investigate the change. Functions arise as a central concept describing a changing quality. Functional analysing focuses attention on (typically infinite-dimensional) spaces of functions. One of many applications of functional analysis is quantum mechanics. Many problems lead naturally to relationships between a quantity and its rate of change, and these are studied as differential equations. Many phenomena in nature can be described by dynamical systems; chaos theory makes precise the ways in which many of these systems exhibit unpredictable yet still deterministic behaviour.
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