Titlebook: Mathematics Form and Function; Saunders Mac Lane Book 1986 Springer-Verlag New York Inc. 1986 Algebra.Derivative.Eigenvalue.Function.Manif

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Overview: 978-1-4612-9340-8978-1-4612-4872-9

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Real Numbers,This chapter will explore the origins and development of the system of real numbers. These numbers form the most central structure in all of Mathematics. Like other structures it arises from more primitive human activities—in this case, from the measurement and comparison of magnitudes of various kinds.

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Geometry,idean geometry. Subsequently, .-dimensional geometry will appear with linear algebra in Chapter VII, manifolds and spaces with curvature in Chapter VIII, and topology, in its connections with complex analysis, in Chapter X. These and other aspects of geometry pervade Mathematics.

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Concepts of Calculus,how does one calculate its length or the direction of its tangent line at some point? More generally, how does one calculate the rate at which this or that variable quantity is changing with time? The striking discovery (by Newton and Leibniz) that there were systematic methods to calculate . these