Number Theory

Download E-books Meine Zahlen, meine Freunde: Glanzlichter der Zahlentheorie (Springer-Lehrbuch) (German Edition) PDF

By Paulo Ribenboim

Paulo Ribenboim behandelt Zahlen in dieser außergewöhnlichen Sammlung von Übersichtsartikeln wie seine persönlichen Freunde. In leichter und allgemein zugänglicher Sprache berichtet er über Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer!), die klassischen Arbeiten von Gauß über binäre quadratische Formen, Eulers berühmtes primzahlerzeugendes Polynom, irrationale und transzendente Zahlen. Nach dem großen Erfolg von „Die Welt der Primzahlen" ist dies das zweite Buch von Paulo Ribenboim, das in deutscher Sprache erscheint.

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Number Theory

Download E-books Contributions to the History of Number Theory in the 20th Century (Heritage of European Mathematics) PDF

The twentieth century used to be a time of significant upheaval and nice development in arithmetic. with the intention to get the final photo of developments, advancements, and effects, it really is illuminating to ascertain their manifestations in the neighborhood, within the own lives and paintings of mathematicians who have been lively in this time. The college files of Göttingen harbor a wealth of papers, letters, and manuscripts from numerous generations of mathematicians--documents which inform the tale of the old advancements from an area perspective. This e-book bargains a few essays in line with records from Göttingen and elsewhere--essays that have now not but been incorporated within the author's accumulated works. those essays, autonomous from one another, are intended as contributions to the implementing mosaic of the historical past of quantity idea. they're written for mathematicians, yet there are not any targeted historical past requisites. The essays talk about the works of Abraham Adrian Albert, Cahit Arf, Emil Artin, Richard Brauer, Otto Grün, Helmut Hasse, Klaus Hoechsmann, Robert Langlands, Heinrich-Wolfgang Leopoldt, Emmy Noether, Abraham Robinson, Ernst Steinitz, Hermann Weyl, and others. A book of the ecu Mathematical Society (EMS). allotted in the Americas by means of the yank Mathematical Society.

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Number Theory

Download E-books A Comprehensive Treatment of q-Calculus PDF

By Thomas Ernst

To date, the theoretical improvement of q-calculus has rested on a non-uniform foundation. more often than not, the cumbersome Gasper-Rahman notation was once used, however the released works on q-calculus seemed varied looking on the place and by way of whom they have been written. This confusion of tongues not just advanced the theoretical improvement but additionally contributed to q-calculus ultimate a ignored mathematical box. This ebook overcomes those difficulties via introducing a brand new and fascinating notation for q-calculus in response to logarithms.For example, q-hypergeometric features are actually visually transparent and simple to track again to their hypergeometric mom and dad. With this new notation it's also effortless to determine the relationship among q-hypergeometric capabilities and the q-gamma functionality, anything that beforehand has been overlooked.

The ebook covers many issues on q-calculus, together with designated services, combinatorics, and q-difference equations. except an intensive evaluate of the ancient improvement of q-calculus, this ebook additionally offers the domain names of contemporary physics for which q-calculus is appropriate, reminiscent of particle physics and supersymmetry, to call only a few.​  

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Number Theory

Download E-books Ramanujan's Place in the World of Mathematics: Essays Providing a Comparative Study PDF

By Krishnaswami Alladi

This publication is a set of articles, all by means of the writer, at the Indian mathematical genius Srinivasa Ramanujan in addition to on a number of the maximum mathematicians through the background whose lifestyles and works have issues in universal with Ramanujan. It provides a different comparative learn of Ramanujan’s striking discoveries and noteworthy lifestyles and of the enormous contributions of assorted mathematical luminaries, a few of whom, like Ramanujan, overcame nice problems in lifestyles. within the ebook, a few features of Ramanujan’s contributions, corresponding to his outstanding formulae for the quantity pi, his pathbreaking paintings within the idea of walls, and his basic observations on quadratic kinds, are mentioned. eventually, the ebook describes a number of present efforts to make sure that the legacy of Ramanujan may be preserved and proceed to thrive sooner or later. hence the ebook is an enlightening learn of Ramanujan as a mathematician and a individual.

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Number Theory

Download E-books Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics (Problem Books in Mathematics) PDF

Mathematicians and non-mathematicians alike have lengthy been eager about geometrical difficulties, really those who are intuitive within the feel of being effortless to country, probably by means of an easy diagram. each one part within the publication describes an issue or a gaggle of similar difficulties. frequently the issues are in a position to generalization of edition in lots of instructions. The publication might be favored at many degrees and is meant for everybody from amateurs to investigate mathematicians.

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Number Theory

Download E-books Einführung in Algebra und Zahlentheorie (Springer-Lehrbuch) (German Edition) PDF

By Rainer Schulze-Pillot

Das Buch bietet eine neue Stoffzusammenstellung, die elementare Themen aus der Algebra und der Zahlentheorie verknüpft und für die Verwendung in Bachelorstudiengängen und modularisierten Lehramtsstudiengängen konzipiert ist. Es führt die abstrakten Konzepte der Algebra in stetem Kontakt mit konkreten Problemen der elementaren Zahlentheorie und mit Blick auf Anwendungen ein und bietet Ausblicke auf fortgeschrittene Themen. In beiden Gebieten wird ein Stand erreicht, der für Nichtspezialisten das nötige Handwerkszeug für die meisten Anwendungen (etwa in diskreter Mathematik, Kryptographie oder Signalverarbeitung) vermittelt, aber auch zu einer vertieften Beschäftigung mit Algebra und Zahlentheorie anregt und für diese eine gute Ausgangsbasis bildet.

Für die dritte Auflage wurden neben einer allgemeinen Überarbeitung und Fehlerkorrektur zahlreiche Beispiele und Aufgaben neu hinzugefügt. Ferner wird in einem neuen ergänzenden Abschnitt der Beweis der Sätze der linearen Algebra über Normalformen von Matrizen mit Hilfe des Elementarteilersatzes behandelt, da dieser schöne Beweis in Lehrbüchern der Linearen Algebra selten Platz findet.

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Number Theory

Download E-books Definitions, Solved and Unsolved Problems, Conjectures, and Theorems in Number Theory and Geometry PDF

By Florentin Smarandache

A suite of definitions, questions, and theorems edited by way of M. L. Perez, resembling Smarandache variety conjectures, difficulties, numerical bases, T-numbers, progressions, sequence, services, Non-Euclidean geometries, paradoxes (such as Smarandache Sorites Paradox that our obvious international consists through a totality of invisible particles), linguistic tautologies, Smarandache speculation that there's no pace barrier within the universe - which has been prolonged to SRM-theory.

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Number Theory

Download E-books The Solution of Equations in Integers PDF

2014 Reprint of 1961 version. complete facsimile of the unique version. no longer reproduced with Optical popularity software program. The booklet is dedicated to at least one of the main fascinating branches of quantity idea, the answer of equations in integers. the answer in integers of algebraic equations in additional than one unknown with indispensable coefficients is a such a lot tough challenge within the thought of numbers. The theoretical significance of equations with critical coefficients is sort of nice as they're heavily attached with many difficulties of quantity idea. in addition, those equations are often encountered in physics and they also are very important in perform. the weather of the speculation of equations with quintessential coefficients as provided during this booklet are compatible for broadening the mathematical outlook of high-school scholars and scholars of pedagogical institutes. a number of the major ends up in the speculation of the answer of equations in integers were given and proofs of the theorems concerned are provided after they are sufficiently easy.

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Number Theory

Download E-books Number Theory Through Inquiry (Maa Textbooks) (Mathematical Association of America Textbooks) PDF

By David C. Marshall, Michael Starbird

Quantity thought via Inquiry; is an leading edge textbook that leads scholars on a delicately guided discovery of introductory quantity idea. The ebook has both major objectives. One target is to aid scholars improve mathematical pondering talents, relatively, theorem-proving abilities. the opposite objective is to aid scholars comprehend many of the splendidly wealthy principles within the mathematical learn of numbers. This publication is suitable for an evidence transitions path, for an self reliant examine adventure, or for a path designed as an creation to summary arithmetic. Math or similar majors, destiny lecturers, and scholars or adults attracted to exploring mathematical principles all alone will take pleasure in ;Number conception via Inquiry.; quantity concept is the appropriate subject for an introduction-to-proofs path. each university scholar understands simple houses of numbers, and but the exploration of these well-known numbers leads us to a wealthy panorama of rules. quantity thought via Inquiry encompasses a rigorously prepared series of demanding situations that lead scholars to find principles approximately numbers and to find equipment of facts on their lonesome. it truly is designed for use with an educational strategy variously referred to as guided discovery or changed Moore process or Inquiry established studying (IBL). teachers fabrics clarify the academic approach. This kind of guide offers scholars a wholly varied adventure in comparison to a regular lecture direction. this is the influence of this adventure: scholars discover ways to imagine independently: they learn how to rely on their very own reasoning to figure out correct from incorrect; and theydevelop the principal, vital principles of introductory quantity thought all alone. From that have, they examine that they could in my opinion create vital rules. They advance an angle of private reliance and a feeling that they could imagine successfully approximately tough difficulties. those objectives are basic to the tutorial firm inside and past arithmetic.

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