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Essays in Constructive Mathematics
ISBN-13:
9783030985585
Veröffentl:
2022
Seiten:
322
Autor:
Harold M. Edwards
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This collection of essays aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it. All definitions and proofs are based on finite algorithms, which pave illuminating paths to nontrivial results, primarily in algebra, number theory, and the theory of algebraic curves. The second edition adds a new set of essays that reflect and expand upon the first.
Part I.- 1. A Fundamental Theorem.- 2. Topics in Algebra.- 3. Some Quadratic Problems.- 4. The Genus of an Algebraic Curve.- 5. Miscellany. Part II.- 6. Constructive Algebra.- 7. The Algorithmic Foundation of Galois's Theory.- 8. A Constructive Definition of Points on an Algebraic Curve.- 9. Abel's Theorem.
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