On the Riemann mapping theorem and Riemann's original proof-argument
نویسندگان
چکیده
منابع مشابه
The Riemann Mapping Theorem
We will develop some of the basic concepts of complex function theory and prove a number of useful results concerning holomorphic functions. We will focus on derivatives, zeros, and sequences of holomorphic functions. This will lead to a brief discussion of the significance of biholomorphic mappings and allow us to prove the Riemann mapping theorem.
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The classical Riemann mapping theorem asserts that any topological quadrilateral in the complex plane can be mapped conformally onto a rectangle. The finite Riemann mapping theorem asserts that any topological quadrilateral tiled by finitely many 2-cells can be mapped with minimal combinatorial distortion onto a rectangle tiled by squares. We prove the finite Riemann mapping theorem, discuss it...
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The story of Gentzen’s original consistency proof for first-order number theory (Gentzen 1974), as told by Paul Bernays (Gentzen 1974), (Bernays 1970), (Gödel 2003, Letter 69, pp. 76-79), is now familiar: Gentzen sent it off to Mathematische Annalen in August of 1935 and then withdrew it in December after receiving criticism and, in particular, the criticism that the proof used the Fan Theorem,...
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ژورنال
عنوان ژورنال: Journal for History of Mathematics
سال: 2017
ISSN: 1226-931X
DOI: 10.14477/jhm.2017.30.1.001