From Fermat to Minkowski: Lectures on the Theory of Numbers and Its Historical DevelopmentSpringer Science & Business Media, 1985 - 184 páginas This book arose from a course of lectures given by the first author during the winter term 1977/1978 at the University of Münster (West Germany). The course was primarily addressed to future high school teachers of mathematics; it was not meant as a systematic introduction to number theory but rather as a historically motivated invitation to the subject, designed to interest the audience in number-theoretical questions and developments. This is also the objective of this book, which is certainly not meant to replace any of the existing excellent texts in number theory. Our selection of topics and examples tries to show how, in the historical development, the investigation of obvious or natural questions has led to more and more comprehensive and profound theories, how again and again, surprising connections between seemingly unrelated problems were discovered, and how the introduction of new methods and concepts led to the solution of hitherto unassailable questions. All this means that we do not present the student with polished proofs (which in turn are the fruit of a long historical development); rather, we try to show how these theorems are the necessary consequences of natural questions. Two examples might illustrate our objectives. |
Conteúdo
The Beginnings | 1 |
Fermat | 5 |
Euler | 14 |
Lagrange | 32 |
Legendre | 57 |
Gauss | 64 |
Fourier | 102 |
Dirichlet | 109 |
From Hermite to Minkowski | 151 |
Preview Reduction Theory | 169 |
English Translation of Gausss Letter to Dirichlet November 1838 | 178 |
181 | |
Outras edições - Ver todos
From Fermat to Minkowski: Lectures on the Theory of Numbers and Its ... W. Scharlau,H. Opolka Visualização parcial - 2013 |
From Fermat to Minkowski: Lectures on the Theory of Numbers and Its ... W. Scharlau,H. Opolka Prévia não disponível - 2010 |
Termos e frases comuns
a₁ algebraic arithmetic ax² ay² b₁ Berlin bilinear space binary quadratic forms by² C. F. Gauss c₁ calculation Chapter class number formula coefficients compute congruence consequently consider continued fraction converges cy² cz² decomposition defined determinant Dirichlet discriminant Disquisitiones Arithmeticae divisor divisor of x² dy² equation x² Euler expansion Fermat finite Fourier function Gauss Gaussian sum Geometry Hence illus integral Jacobi Lagrange Lagrange's law of quadratic Legendre Lemma mathematicians mathematics matrix Minkowski modulo narrow class group natural number nontrivial number theory number-theoretical obtains P₁ polynomial positive prime element prime factorization prime number principal ideal domain problem proof proper equivalence classes properly equivalent prove quadratic number field quadratic reciprocity quadratic residue Re(s reduced form relatively prime representation solution of x² solvable specifically squares statement symmetric uniquely Zeta-function