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Author: Joseph Ray Publisher: ISBN: 9781462266654 Category : Languages : en Pages : 242
Book Description
Hardcover reprint of the original 1848 edition - beautifully bound in brown cloth covers featuring titles stamped in gold, 8vo - 6x9". No adjustments have been made to the original text, giving readers the full antiquarian experience. For quality purposes, all text and images are printed as black and white. This item is printed on demand. Book Information: Ray, Joseph. Ray's Algebra, Part First: On The Analytic And Inductive Methods Of Instruction: With Numerous Practical Exercises Designed For Common Schools And Academics. Indiana: Repressed Publishing LLC, 2012. Original Publishing: Ray, Joseph. Ray's Algebra, Part First: On The Analytic And Inductive Methods Of Instruction: With Numerous Practical Exercises Designed For Common Schools And Academics, . Cincinnati: Wilson, Hinkle & Co.: Philadelphia: Claxton, Remson & Haffelfinger: : New York: Clark & Maynard, 1848. Subject: Algebra
Author: Ray Mines Publisher: Springer Science & Business Media ISBN: 1441986405 Category : Mathematics Languages : en Pages : 355
Book Description
The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit; much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures.
Author: Ray Joseph Publisher: Mott Media ISBN: 9780880620505 Category : Education Languages : en Pages :
Book Description
Republished version of the Ray's Arithmetic from the late 1870's and early 1880's. Includes the following books: (some in hardback and some in paperback) Primary Arithmetic, Intellectual Arithmetic, Practical Arithmetic, Key to the Primary/Intellectual/Practical, Test Examples in Arithmetic, Higher Arithmetic, Key to Higher Arithmetic, Parent Teacher Guide (by Ruth Beechick).