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__Definitions of Mathematics__

__Definitions of Mathematics__##
__1. Introduction to Definitions of Mathematics__

__1. Introduction to Definitions of Mathematics__

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Definitions of Mathematics |

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__2. Definitions of Mathematics__

The simplest meaning of mathematics is reflected in 'computation by enumeration'. Mathematics has been called the science of length-magnitudes and numbers in the education dictionary. Thus, both Hindi and English words mean counting, measuring and computation. In fact, the emergence of mathematics is the inclusion of human curiosity. In the first stage of his mental development, questions must have arisen in human mind by looking at his environment and sky, hearing words, touch, etc. What, how many? Then there are the possible questions that arise at the second level of development, how much? Seeing a change, the question must have arisen from astonishment. This led to the development of spiritual subjects such as philosophy, logic, philosophy of religion, knowledge, etc. As far as the first level question is concerned, even the lower level beings experience it. 'Measurement' is experienced in mental examination. Animals and birds also have its basic natural strength. Due to this, birds come for migrating hundreds and thousands of kilometers away due to the change of seasons. But at this stage, humans have the specific intellectual power for high-level calculation, which while being natural, is also affected by the environment. At this stage in humans, skills are developed in complex to complex processes of experiences, exercises, training. At the ultimate spiritual level, religious, philosophical beliefs and higher mathematical processes are derived.

__2. Definitions of Mathematics__##
Definitions of Mathematics |

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**3. Science of Magnitude and Numbers**

**3. Science of Magnitude and Numbers**###
__4. Mathematics as the science of quantity and space -__

Like science, mathematics is also a systematic and systematic form of Empirical Experiences. In this also, there is a study of the interrelations of numerical facts related to the interval. In the analysis, election and regulation of these facts there is a natural use of Logical Reasoning which is used in problem-solving in a new situation. Mathematics has become a major tool of physical research due to its processing nature.

__4. Mathematics as the science of quantity and space -__According to Barthlaut - "Mathematics is an indispensable instrument for all physical researches."

By thinking about this form of mathematics, it becomes clear that the means of expression for science subjects is mathematics. Establishment of work-causal relationship is based on mathematical logic to understand the phenomena occurring in the interval. That is why Kant went on to say - "Natural science is only science as long as it is mathematical (A natural science is a science only in so for as it is mathematical)." The ideas of comte also correspond to the views of Kant. According to Kamte - "Science education that does not begin with mathematics is necessarily fundamentally flawed (A scientific education which does not commence with mathematics is, of necessity, defective at its foundation)."

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__5. An important means of generalization__

Mathematics is the main tool for perception and generalization of objects based on specific experiences. This is a natural process of induction reasoning. That is why Henri Poincare says - "Mathematics is the giving of the same name to different things". According to the Harvord committee of 45 - "Mathematics can be defined as the science of abstract form. An essential requirement of the essence of structure in a physical system sense is the appreciation of coating in art and connotation in music." Is not less than. It is nothing less than astrology in economics as generalized by objects and events. Mathematics is specific objects and events. The study of the sequence displayed in the generalized format by abstract is - General Education in a Free Society (Mathematics may be defined as the science of abstracted from ...... the discernment of structure is essential no less to the appreciation of a painting or a symphony than to understand the behavior of a physical system, no less in economics than in astronomy. Mathematics studies order obstructed from the particular objects and phenomena which exhibit it, and in a generalized form - General Education in a Free Society). "__5. An important means of generalization__

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__6. Applied Science for the Expression of Sciences__

Mathematics and mathematical methods are the only means for acquiring and presenting knowledge in Physical and Biological Sciences. The major role of mathematics for this is reflected in Roger Bacon's statement - "Mathematics is the gateway and key to the sciences. Since a man who is not ignorant of mathematics cannot get the knowledge of the sciences and the objects of the world, the whole knowledge of mathematics is neglected. Is worse for. Worse than that, such ignorant humans neither know this ignorance nor can they cure it. (Mathematics is the gate and key of the sciences ...... Neglect of mathematics work injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world. And what is worse , men who are thus ignorant are unable to perceive their ignorance and so do not seek a remedy. ")

__6. Applied Science for the Expression of Sciences__Sullivan (JWN Suliwan - Atlantic monthly, March, 1933) showed the importance of mathematics in physics in this way - "As far as physics is concerned, it has been proved that the nature of the principles that are discussed in this, we should Need knowledge of their mathematical structure rather than knowledge of it (it has become evident that, so far as the science of physics is concerned, we do not require to know the nature of the entities, we discuss, but only their mathematical structure) "JW Mellor) in Chemistry made his statement -" Physical and practical Valid Chemicals Uttrapekshit developments is almost impossible without the executive conscious mass of higher mathematics (It is Almost impossible to follow the latter developments of physical or general chemistry without working knowledge of higher mathematics). " It is underlined. The imperative of mathematics in biology is proved by Comte's statement that - "In mathematics we find the primordial source of conscience and see mathematics as the destination of biologists where they conduct research. (In mathematics we find the primitive source of rationality and to mathematics must be the biologists resort to means to carry on their researches). "Physical sciences include physics and chemistry in addition to astronomy. . It is well known that currently astrology itself is a major branch of mathematics. It has arithmetic, geometry, trichrometry, algebra. Thus mathematics is the power to provide expression and existence to physical and biology.

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__7. Mathematics as the method of progress of various subjects -__

The statement of Mathematics Introduction to Economics - Mcgraw Hill Book Co. Inc. 1936) by Evans (G. L. Evans) is an adequate explanation for this definition. It is clear that every scripture of study is satisfied in calling itself science or believing it. Political science, economics, military science, geography, history etc. It is said that scientific method has become the main method of study, which is based on mathematics itself. These subjects are clearly identified by natural and applied sciences. Theoretical sciences have been called from the point of view. Mathematics is a major force in the development of these subjects and in moving them towards completion. Evans, as we call it to be distinguished from the natural and applied sciences, is a process that comes late in the developmental order of the subject. Authentically it has been observed that some fields of knowledge are hardly ready for this, as its free will is an uniqueness in constructing definitions and concepts. It does not just identify the facts, but when we get this feeling for the concept and definition, then we join the chain of deductive reasoning. We are drawn to a characteristic method of construction and analysis. We call this method the mathematical method. It is not a question of whether mathematics is desirable in this subject or not. In fact, the adoption of a mathematical method is an essential condition for moving forward in the path of progress.

__7. Mathematics as the method of progress of various subjects -__(The systematization which occurs in a theoretical science, as we properly call it in order to distinguish it from a natural or an applied science, is a process which is apt to came late in the development of a subject. Everyday some fields of knowledge are hardly ready from it, for it is tyfied by a free spirit of making hypotheses and definitions rather than a mere recognition of facts. But when we find this feeling for hypotheses and definition and, in addition become involved in chains of deductive reasoning, we are driven to a characteristic method of construction and analysis which may be call the mathematical method. It is not a question whether mathematics is desirable or not in such subject. We are in fact forced to adopt the mathematical method as a condition of further progress). "

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__8. Mathematics as the means to draw conclusion and judgment.__

It is clear that mathematics is a process of collection, classification and analysis of numerical facts. This entire action is performed to achieve a certain objective. Its purpose is basically to test the concept. After analysis, there are inference, retesting, Interpretation, conclusion and decision. Thus, mathematics is a means of concluding and deciding in its ultimate destiny. According to Benjamin Peirce 1809–1880, "Mathematics is the science that reaches the required conclusion."

__8. Mathematics as the means to draw conclusion and judgment.__###
__9. Mathematics as the perception of generalization__

In the case of absolute, the subject remains in a state of confusion. There is such a complete state of generalization of mathematics in which a person finds himself unable to explain in normal language what subject he is talking about or what is being said is true. This is the ultimate state of feeling.According to Russell, "Mathematics is a subject in which it can never be said about which subject is being talked about or what is being said is true.

__9. Mathematics as the perception of generalization__
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