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A History of Abstract Algebra : From Algebraic Equations to Modern Algebra / / by Jeremy Gray
| A History of Abstract Algebra : From Algebraic Equations to Modern Algebra / / by Jeremy Gray |
| Autore | Gray Jeremy |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (XXIV, 415 p. 18 illus.) |
| Disciplina | 512.02 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Mathematics
History Algebra Number theory History of Mathematical Sciences Number Theory |
| ISBN | 3-319-94773-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- 1 Simple quadratic forms -- 2 Fermat’s Last Theorem -- 3 Lagrange’s theory of quadratic forms -- 4 Gauss’s Disquisitiones Arithmeticae -- 5 Cyclotomy -- 6 Two of Gauss’s proofs of quadratic reciprocity -- 7 Dirichlet’s Lectures -- 8 Is the quintic unsolvable? -- 9 The unsolvability of the quintic -- 10 Galois’s theory -- 11 After Galois – Introduction -- 12 Revision and first assignment -- 13 Jordan’s Traité -- 14 Jordan and Klein -- 15 What is ‘Galois theory’? -- 16 Algebraic number theory: cyclotomy -- 17 Dedekind’s first theory of ideals -- 18 Dedekind’s later theory of ideals -- 19 Quadratic forms and ideals -- 20 Kronecker’s algebraic number theory -- 21 Revision and second assignment -- 22 Algebra at the end of the 19th century -- 23 The concept of an abstract field -- 24 Ideal theory -- 25 Invariant theory -- 26 Hilbert’s Zahlbericht -- 27 The rise of modern algebra – group theory -- 28 Emmy Noether -- 29 From Weber to van der Waerden -- 30 Revision and final assignment -- A Polynomial equations in the 18th Century -- B Gauss and composition of forms -- C Gauss on quadratic reciprocity -- D From Jordan’s Traité -- E Klein’s Erlanger Programm -- F From Dedekind’s 11th supplement -- G Subgroups of S4 and S5 -- H Curves -- I Resultants -- Bibliography -- Index. |
| Record Nr. | UNINA-9910300129503321 |
Gray Jeremy
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The Real and the Complex: A History of Analysis in the 19th Century / / by Jeremy Gray
| The Real and the Complex: A History of Analysis in the 19th Century / / by Jeremy Gray |
| Autore | Gray Jeremy |
| Edizione | [1st ed. 2015.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 |
| Descrizione fisica | 1 online resource (XVI, 350 p. 71 illus.) |
| Disciplina | 515.9 |
| Collana | Springer Undergraduate Mathematics Series |
| Soggetto topico |
Functions of complex variables
Functions of real variables Mathematics History Functions of a Complex Variable Real Functions History of Mathematical Sciences |
| ISBN | 3-319-23715-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Lagrange and foundations for the calculus -- Joseph Fourier -- Legendre -- Cauchy and continuity -- Cauchy: differentiation and integration -- Cauchy and complex functions to 1830 -- Abel -- Jacobi -- Gauss -- Cauchy and complex function theory, 1830-1857 -- Complex functions and elliptic integrals -- Revision -- Gauss, Green, and potential theory -- Dirichlet, potential theory, and Fourier series -- Riemann -- Riemann and complex function theory -- Riemann's later complex function theory -- Responses to Riemann's work -- Weierstrass -- Weierstrass's foundational results -- Revision { and assessment -- Uniform Convergence -- Integration and trigonometric series -- The fundamental theorem of the calculus -- The construction of the real numbers -- Implicit functions -- Towards Lebesgue's theory of integration -- Cantor, set theory, and foundations -- Topology -- Assessment. |
| Record Nr. | UNINA-9910300245303321 |
|
Gray Jeremy
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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