Titlebook: Mathematics and Its History; A Concise Edition John Stillwell Textbook 2020 Springer Nature Switzerland AG 2020 History of mathematics.Calc

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Complex Numbers and Curves,This chapter revisits polynomial equations and algebraic curves, observing how these topics are simplified by introducing complex numbers. That’s right: the so-called “complex” numbers actually make things simpler.

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Complex Numbers and Functions,The insight into algebraic curves afforded by complex coordinates—that a complex curve is topologically a surface—has important implications for functions defined as integrals of algebraic functions, such as the logarithm, exponential, and elliptic functions.

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Non-Euclidean Geometries,One   of the new frontiers in geometry opened up by calculus was the study of .. The concept of curvature is particularly interesting for surfaces, because it can be defined .. The intrinsic curvature, or . curvature as it is known, is unaltered by bending the surface, so it can be defined without reference to the surrounding space.

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Sets, Logic, and Computation,In the 19th century, perennial concerns about the role of infinity in mathematics were finally addressed by the development of . and .. Set theory was proposed as a mathematical theory of infinity and formal logic was proposed as a mathematical theory of proof (partly to avoid the paradoxes that seem to arise when reasoning about infinity).

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Undergraduate Texts in Mathematicshttp://image.papertrans.cn/m/image/626835.jpg