| 書目名稱 | Essays in Constructive Mathematics | | 編輯 | Harold M. Edwards | | 視頻video | http://file.papertrans.cn/316/315249/315249.mp4 | | 概述 | Introduces new insights into Galois theory, number theory, and algebraic curves from a leading expert.Offers constructive formulations of Galois theory and the theory of algebraic curves.Invites reade | | 圖書封面 |  | | 描述 | .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 newessays 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 t | | 出版日期 | Book 2022Latest edition | | 關(guān)鍵詞 | constructive mathematics; constructive approach to mathematical proof; Kronecker general arithmetic; Ab | | 版次 | 2 | | doi | https://doi.org/10.1007/978-3-030-98558-5 | | isbn_softcover | 978-3-030-98560-8 | | isbn_ebook | 978-3-030-98558-5 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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