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A Course in Constructive Algebra (Paperback, 1988 ed.)
Loot Price: R3,098
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A Course in Constructive Algebra (Paperback, 1988 ed.)
Series: Universitext
Expected to ship within 10 - 15 working days
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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."
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