SSC Mathematics Suggestion Question 2021-6. Mathematicians seek patterns and formulate new conjectures. Mathematicians solve the truth or falsity of conjectures by mathematical proof. The research needed to solve mathematical problems can take years, or even centuries of investigation supported. Since the pioneering work of Giuseppe Peano (1858-1932), David Hilbert (1862-1943), and others on the axiomatic systems by the end of the 19th century, it became customary to show that mathematical research establishing the truth by rigorous deduction from axioms of appropriately chosen and definitions. When these structures are good mathematical models of real phenomena, mathematical reasoning can give an overview or predictions on nature.

## SSC Mathematics Suggestion Question 2021-6

Model Question No. 6

Summary: Based on an enriched by the long-term teaching experience of the authors, this volume covers the major themes of mathematics in engineering and technical specialties. The book addresses the elements of linear algebra and analytic geometry, differential calculus of a function of one variable, and elements of higher algebra. On each theme, the authors first present short theoretical overviews and then go on to give problems to be solved. The authors provide the solutions to some typical, relatively difficult problems and guidelines for solving them.

The authors consider the development of the self-dependent thinking ability of students in the construction of problems and indicate which problems are relatively difficult. The book is geared so that some of the problems presented can be solved in class, and others are meant to be solved independently. An extensive, explanatory solution of at least one typical problem is included, with emphasis on applications, formulas, and rules.

Mathematics has no generally accepted definition. Aristotle defined mathematics as “the science of quantity”, and this definition prevailed until the 18th century. Galileo Galilei (1564–1642) said, “The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to comprehend a single word.

Without these, one is wandering about in a dark labyrinth.” Carl Friedrich Gauss (1777–1855) referred to mathematics as “the Queen of the Sciences”. David Hilbert said of mathematics: “We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise.” Albert Einstein (1879–1955) stated that “as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics.

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