Constructive mathematics
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Constructive analysis
Delivered by Fengyang Wang on Wednesday November 1, 2017
Constructive mathematics, as the name would suggest, is centered on the philosophy that mathematical proofs should be able to be turned into algorithms. We will contextualize constructive approaches to analysis, roughly following Bridges and Vîţă. This talk has no formal prerequisites beyond an elementary understanding of the real numbers and the usual concept of completeness. In particular, no logical background is assumed; intuitionistic logic will be overviewed in the talk. We will finish with a discussion of the ramifications of completeness of the real numbers.
A summary of this talk is available here.
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Constructive Mathematics
Constructive mathematics, or mathematics without the law of the excluded middle, is becoming more popular thanks to connections with computer science, category theory, and topology. Its logical foundations may be initially difficult to grasp for those used to a classical system.
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computability computer science constructive mathematics logic philosophy topology type theory