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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厭煩

Functions, Transformations, and Groups,wed the assembly of part of that wide variety of examples from which arises the general and abstract notion of function. Though some may hold that “abstract notions are difficult to understand” we hold with G. Kreisel that these notions “in fact, are usually introduced to make concrete situations intelligible” (. . (1969) # 1224).

acolyte

Linear Algebra,e the algebra of vectors is an effective way of handling geometrical ideas in dimensions higher than 3. Analysis soon produces infinite-dimensional spaces such as . (§VI.11). This chapter will summarize the properties of such linear vector spaces over an arbitrary field, not necessarily . or ..

變態(tài)

Forms of Space,heaves, manifolds, and the like. It will appear that the role of intuitive ideas is very important in the analysis of such geometric structures—and that it often is a long time before evident geometric intuitions are brought to a clear formal expression. These expressions provide many different forms for the elusive idea of “space”.

Alveoli

Sets, Logic, and Categories,the basic connectives of logic (or, not, there exists) and the needed primitive terms of each subject (thus “point” and “l(fā)ine” for incidence geometry). Finally, most of the proofs of Mathematical theorems can be stated with absolute rigor as a sequence of inferences, each an instance of a finite number of basic schemes of inference.

可卡

Introduction, answered against the background of a careful assembly of the relevant evidence. In brief, a philosophy of Mathematics is not convincing unless it is founded on an examination of Mathematics itself. Wittgenstein (and other philosophers) have failed in this regard.

vector

SPURN

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.

輕彈

The Mathematical Network,thematics? How does it illuminate the philosophical questions as to Mathematical truth and beauty and does it help to make judgements about the direction of Mathematical research? In particular, what is the foundation of Mathematics?

GLOOM

https://doi.org/10.1007/978-1-4612-4872-9Algebra; Derivative; Eigenvalue; Function; Manifold; Mathematics; Topology; Variable; calculus; equation; geom