Einführung in die Zahlentheorie by Peter Bundschuh (auth.)

By Peter Bundschuh (auth.)

Das Buch gibt eine umfassende Darstellung der wichtigsten Grundlagen der elementaren Zahlentheorie; dabei wird die historische Entwicklung in st?rkerem Ma?e als ?blich ber?cksichtigt. Behandelt wird in den ersten f?nf Kapiteln (Teilbarkeit, Kongruenzen, Potenzreste und quadratische Reste, additive Probleme und diophantische Gleichungen, verschiedene Entwicklungen reeller Zahlen) etwa der Stoff einer einsemestrigen Einf?hrungsvorlesung. Dabei ergeben sich schon fr?h neue Probleme, die in sp?teren Kapiteln wieder aufgegriffen werden. So kommen bereits im ersten Kapitel arithmetische und Primzahlfragen zur Sprache, die in den beiden letzten (Transzendenz, Primzahlen) erheblich vertieft werden. In diesen Kapiteln soll der Leser beispielhaft lernen, wie sich die Zahlentheorie zur L?sung ihrer Probleme bisweilen anderer mathematischer Disziplinen bedient: Beide Kapitel zeigen die Leistungsf?higkeit analytischer Methoden bei zahlentheoretischen Fragestellungen. Eine weitere Aufgabe der vorliegenden Darstellung ist die Heranf?hrung des Lesers an das Studium vertiefender Literatur, die in den textual content eingearbeitet und am Ende des Buches zusammengestellt ist.

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Applications of nonstandard finite difference schemes by Ronald E Mickens

By Ronald E Mickens

This quantity should be divided into components: a only mathematical half with contributions on finance arithmetic, interactions among geometry and physics and diverse parts of arithmetic; one other half at the popularization of arithmetic and the placement of ladies in arithmetic Nonstandard finite distinction schemes / Ronald E. Mickens -- Nonstandard equipment for advection-diffusion response equations / Hristo V. Kojouharov and Benito M. Chen -- software of nonstandard finite alterations to resolve the wave equation and Maxwell's equations / James B. Cole -- Non-standard discretization tools for a few organic types / H. Al-Kahby, F. Dannan, and S. Elaydi -- An creation to numerical integrators keeping actual houses / Martin J. Gander and Rita Meyer-Spasche

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Real analysis: Theory of measure and integration by J Yeh

By J Yeh

This booklet provides a unified treatise of the speculation of degree and integration. within the surroundings of a normal degree area, each suggestion is outlined accurately and each theorem is gifted with a transparent and entire evidence with the entire proper information. Counter-examples are supplied to teach that convinced stipulations within the speculation of a theorem can't be easily dropped. The dependence of a theorem on prior theorems is explicitly indicated within the facts, not just to facilitate interpreting but additionally to delineate the constitution of the idea. The precision and readability of presentation make the publication a great textbook for a graduate direction in actual research whereas the wealth of themes handled additionally make the ebook a priceless reference paintings for mathematicians.

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Numbers by Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch,

By Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jürgen Neukirch, Alexander Prestel, Reinhold Remmert, John H. Ewing, H.L.S. Orde, K. Lamotke

Half A is filled with info at the genuine and intricate numbers and the elemental theorem of algebra with a lot old history. There also are extraordinary chapters with all kinds of data on pi and on p-adic numbers (which has not anything to do with anything within the book). partly B the authors unfastened themselves from the restrictions of classical quantity structures and research kind of number-like algebras. particularly, the privileged function of R,C,H,O is associated with the life n-square identities and the prospective dimensions of department algebras. half C treats a few chosen foundational issues: non-standard research, Conway's "games" method of the reals, set theory.

One may need that this booklet used to be "a vigorous tale approximately one thread of mathematics--the suggestion of 'number'-- ... equipped right into a historic narrative that leads the reader from old Egypt to the overdue 20th century" (English variation editor's preface). yet this can be not often the case. i assume it takes the mixed efforts of 8 authors to provide this sort of garbled and disorganised account, with such a lot of dead-end facet tracks, of a subject with such amazing inherent continuity, either ancient and logical. additionally, as in such a lot of different sleek books, the authors are essentially drawn to algebra and foundations, and their notion of historical past is tilted for this reason. Their worry of having their palms soiled with classical research signifies that they could purely point out, now not end up, the transcendence of pi, for example.

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