## From Fermat to Minkowski: Lectures on the Theory of Numbers and Its Historical DevelopmentThis 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. |

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User Review - GalenWiley - LibraryThingThis 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 ... Read full review

#### LibraryThing Review

User Review - GalenWiley - LibraryThingThis 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 ... Read full review

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From Fermat to Minkowski: Lectures on the Theory of Numbers and Its ... W. Scharlau,H. Opolka Limited preview - 2013 |

From Fermat to Minkowski: Lectures on the Theory of Numbers and Its ... W. Scharlau,H. Opolka No preview available - 2010 |

### Common terms and phrases

2bxy algebraic arithmetic Berlin Bernoulli bilinear space binary quadratic forms C. F. Gauss calculation Chapter character class number formula coefficients compute congruence consequently consider continued fraction contradiction converges correspondence decomposition defined determinant Dirichlet discriminant Disquisitiones Arithmeticae divisor divisor of x2 equation x2 Euler expansion Fermat finite form ax2 Fourier function Gaussian sum Geometry Hence illus important integral Jacobi Lagrange Lagrange's lattice point theorem law of quadratic Legendre Lemma mathematicians mathematics matrix Minkowski mod4 modulo multiple narrow class group natural number nontrivial norm number theory number-theoretical obtains Obviously polynomial prime element prime factorization prime number principal ideal domain problem proper equivalence classes properly equivalent prove Q(Jd quadratic number field quadratic reciprocity quadratic residue reduced form relatively prime representation represented by v2 residue modulo solutions of x2 solvable specifically squares statement suffices to show symmetric tion uniquely written Zeta-function

### References to this book

Learn from the Masters Frank Swetz,John Fauvel,Bengt Johansson,Victor Katz,Otto Bekken No preview available - 1995 |