Solved Board Paper For ICSE Class 12 Mathematics

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Mathematics is the science of the structure, order and relationship that has evolved from elementary counting, measurement and description of objects' forms. Mathematics has been an essential supplement to physical science and technology since the 17th century and has taken on a similar role in the quantitative aspects of life sciences in later times. In many societies, mathematics has grown far beyond the fundamentals, under the impetus of realistic activities, such as trade and agriculture. All mathematical systems (e.g. Euclidean geometry) are combinations of axiom sets and theorems which can be logically derived from axioms. Surveys of the logical and philosophical basis of mathematics lead to questions about the integrity and consistency of the axioms of a system in question. See geometry, the basis for a full treatment of this dimension. The article presents a history of mathematics from ancient times to today. As a result of the exponential growth of science, since the 15th century AD, it has been mostly mathematical, and historically new mathematical developments were largely concentrated in Europe and North America between the 15th and the end of the 20th centuries. For these purposes, after 1500, most of this essay has been dedicated to European innovations. Nonetheless, this does not mean that other advances were unimportant. Yes, to understand mathematical history in Europe, at least in ancient Mesopotamia and Egypt, ancient Greece and Islamic civilization from the ninth to the fifteenth centuries, it is necessary to know their history. In the first part of this article, how such cultures influenced each other and the significant direct contributions that Greece and Islam made to later developments are discussed. India has been making a significant contribution to the development of contemporary mathematics by Indian achievements in Islamic mathematics during its formative years. A different article, South Asian math, focuses on the early history of mathematics and the emergence of the modern decimal value-number system in the Indian subcontinent. The East Asian mathematics article deals with the most independent mathematical development in China, Japan, Korea and Vietnam. The character of the sources for studying the history of mathematics is significant.

The history of Mesopotamian and Egyptian mathematics is based on the original works by the author. Although these documents are limited in the case of Egypt, they are all kinds and leave little doubt that in general Egyptian mathematics was fundamental and very practical. On the other hand, there are many clay tablets for Mesopotamian mathematics which reveal mathematical accomplishments of a much higher order than those of the Egyptians. The tablets suggest that Mesopotamians have substantial mathematical knowledge, although they do not offer proof that this knowledge has been structured into a deductive method. Future research may provide more details on the early development of mathematics in Mesopotamia or on its impact on Greek mathematics, but that image of Mesopotamian mathematics seems likely to remain. No Greek mathematical documents were preserved from the preceding period of Alexander the Great except for fragmentary paraphrases, and even for the following era, it is well to remember that the oldest copies of Euclid's Elements have been published in Byzantine manuscripts from the 10th century CE.