---

＜電子ブック＞
Essays in Constructive Mathematics / by Harold M. Edwards

版	2nd ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XIV, 322 p. 390 illus., 325 illus. in color : online resource
著者標目	*Edwards, Harold M author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:History LCSH:Mathematical logic LCSH:Algebraic fields LCSH:Polynomials LCSH:Algebraic geometry FREE:General Mathematics and Education FREE:History of Mathematical Sciences FREE:Mathematical Logic and Foundations FREE:Field Theory and Polynomials FREE:Algebraic Geometry
一般注記	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 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. 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 HTTP:URL=https://doi.org/10.1007/978-3-030-98558-5

 類似資料