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001450060 0247_ $$a10.1007/978-3-030-98558-5$$2doi
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001450060 08204 $$a511.3$$223/eng/20221007
001450060 1001_ $$aEdwards, Harold M.,$$eauthor.$$4aut$$4http://id.loc.gov/vocabulary/relators/aut
001450060 24510 $$aEssays in constructive mathematics /$$cHarold M. Edwards.
001450060 250__ $$aSecond edition.
001450060 264_1 $$aCham, Switzerland :$$bSpringer,$$c2022.
001450060 300__ $$a1 online resource (xiv, 322 pages) :$$billustrations (some color)
001450060 336__ $$atext$$btxt$$2rdacontent
001450060 337__ $$acomputer$$bc$$2rdamedia
001450060 338__ $$aonline resource$$bcr$$2rdacarrier
001450060 504__ $$aIncldues bibliographical references and index.
001450060 5050_ $$aPart I -- 1. A Fundamental Theorem -- 2. Topics in Algebra -- 3. Some Quadratic Problems -- 4. The Genus of an Algebraic Curve -- 5. Miscellany. Part II -- 6. Constructive Algebra -- 7. The Algorithmic Foundation of Galois's Theory -- 8. A Constructive Definition of Points on an Algebraic Curve -- 9. Abel's Theorem.
001450060 506__ $$aAccess limited to authorized users.
001450060 520__ $$aThis collection of essays aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it. All definitions and proofs are based on finite algorithms, which pave illuminating paths to nontrivial results, primarily in algebra, number theory, and the theory of algebraic curves. The second edition adds a new set of essays that reflect and expand upon the first. The topics covered derive from classic works of nineteenth-century mathematics, among them Galois's theory of algebraic equations, Gauss's theory of binary quadratic forms, and Abel's theorems about integrals of rational differentials on algebraic curves. Other topics include Newton's diagram, the fundamental theorem of algebra, factorization of polynomials over constructive fields, and the spectral theorem for symmetric matrices, all treated using constructive methods in the spirit of Kronecker. In this second edition, the essays of the first edition are augmented with new essays that give deeper and more complete accounts of Galois's theory, points on an algebraic curve, and Abel's theorem. Readers will experience the full power of Galois's approach to solvability by radicals, learn how to construct points on an algebraic curve using Newton's diagram, and appreciate the amazing ideas introduced by Abel in his 1826 Paris memoir on transcendental functions. Mathematical maturity is required of the reader, and some prior knowledge of Galois theory is helpful. But experience with constructive mathematics is not necessary; readers should simply be willing to set aside abstract notions of infinity and explore deep mathematics via explicit constructions.
001450060 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 7, 2022).
001450060 650_0 $$aConstructive mathematics.
001450060 655_0 $$aElectronic books.
001450060 655_7 $$aLlibres electrònics.$$2thub
001450060 77608 $$iPrint version: $$z3030985571$$z9783030985578$$w(OCoLC)1296405761
001450060 852__ $$bebk
001450060 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-98558-5$$zOnline Access$$91397441.1
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001450060 980__ $$aEBOOK
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001450060 983__ $$aOnline
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