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Arithmetic Tales: Advanced Edition (Universitext)

This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses.Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results.Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.

Arithmetic Tests for ages 10-11: Preparation for KS2 SATs

This teacher resource title is designed to match the style and contents of the Arithmetic Tests elements of the new format National Tests. One of the New Maths Arithmetic Tests series, the book provides all the practice your pupils need to build their confidence and boost their ability in the key skills of addition, subtraction, multiplication and division. The book contains forty-eight tests with matching answer pages, enabling teachers to provide short regular practice of non-contextual number questions. The answer pages provide clear answers and show the correct layout for column addition, column subtraction and column multiplication as well as short division and long division. Each book in the series includes 480 non-contextual number questions.

Arithmetic Tests for ages 6-7: Preparation for KS1 SATs

This teacher resource title is designed to match the style and contents of the Arithmetic Tests elements of the new format National Tests. One of the new Arithmetic Tests series, the book provides all the practice your pupils need to build their confidence and boost their ability in the key skills of addition, subtraction, multiplication and division. The book contains forty-eight tests with matching answer pages, enabling teachers to provide short regular practice of non-contextual number questions. The answer pages provide clear answers and show the correct layout for column addition and column subtraction. Each book in the series includes 480 non-contextual number questions.

Arithmetic Theory of Elliptic Curves: Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in Cetaro, Italy, July 12-19, 1997 (Lecture Notes in Mathematics #1716)

This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.

Arithmetical Aspects of the Large Sieve Inequality

This book is an elaboration of a series of lectures given at the Harish-Chandra Research Institute. The reader will be taken through a journey on the arithmetical sides of the large sieve inequality when applied to the Farey dissection. This will reveal connections between this inequality, the Selberg sieve and other less used notions like pseudo-characters and the $\Lambda_Q$-function, as well as extend these theories. One of the leading themes of these notes is the notion of so-called\emph{local models} that throws a unifying light on the subject. As examples and applications, the authors present, among other things, an extension of the Brun-Tichmarsh Theorem, a new proof of Linnik's Theorem on quadratic residues and an equally novel one of the Vinogradov three primes Theorem; the authors also consider the problem of small prime gaps, of sums of two squarefree numbers and several other ones, some of them being new, like a sharp upper bound for the number of twin primes $p$ that are such that $p+1$ is squarefree. In the end the problem of equality in the large sieve inequality is considered and several results in this area are also proved.

Arithmetical Functions (Grundlehren der mathematischen Wissenschaften #167)

The plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno Eckmann. My Introduction to Analytic Number Theory has appeared in the meanwhile, and this book may be looked upon as a sequel. It presupposes only a modicum of acquaintance with analysis and number theory. The arithmetical functions considered here are those associated with the distribution of prime numbers, as well as the partition function and the divisor function. Some of the problems posed by their asymptotic behaviour form the theme. They afford a glimpse of the variety of analytical methods used in the theory, and of the variety of problems that await solution. I owe a debt of gratitude to Professor Carl Ludwig Siegel, who has read the book in manuscript and given me the benefit of his criticism. I have improved the text in several places in response to his comments. I must thank Professor Raghavan Narasimhan for many stimulating discussions, and Mr. Henri Joris for the valuable assistance he has given me in checking the manuscript and correcting the proofs. K. Chandrasekharan July 1970 Contents Chapter I The prime number theorem and Selberg's method § 1. Selberg's fonnula . . . . . . 1 § 2. A variant of Selberg's formula 6 12 § 3. Wirsing's inequality . . . . . 17 § 4. The prime number theorem. .

Arithmetical Investigations: Representation Theory, Orthogonal Polynomials, and Quantum Interpolations (Lecture Notes in Mathematics)

In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.

Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1 (SpringerBriefs in Mathematics #0)

This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1. It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas. The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points. The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem. In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra. Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevant, open questions that may inspire future research. Graduate students and researchers working in algebraic geometry and commutative algebra will find this book to be a valuable contribution to the literature.

Arithmetics (Universitext)

Number theory is a branch of mathematics which draws its vitality from a rich historical background. It is also traditionally nourished through interactions with other areas of research, such as algebra, algebraic geometry, topology, complex analysis and harmonic analysis. More recently, it has made a spectacular appearance in the field of theoretical computer science and in questions of communication, cryptography and error-correcting codes. Providing an elementary introduction to the central topics in number theory, this book spans multiple areas of research. The first part corresponds to an advanced undergraduate course. All of the statements given in this part are of course accompanied by their proofs, with perhaps the exception of some results appearing at the end of the chapters. A copious list of exercises, of varying difficulty, are also included here. The second part is of a higher level and is relevant for the first year of graduate school. It contains an introduction to elliptic curves and a chapter entitled “Developments and Open Problems”, which introduces and brings together various themes oriented toward ongoing mathematical research. Given the multifaceted nature of number theory, the primary aims of this book are to: - provide an overview of the various forms of mathematics useful for studying numbers - demonstrate the necessity of deep and classical themes such as Gauss sums - highlight the role that arithmetic plays in modern applied mathematics - include recent proofs such as the polynomial primality algorithm - approach subjects of contemporary research such as elliptic curves - illustrate the beauty of arithmetic The prerequisites for this text are undergraduate level algebra and a little topology of Rn. It will be of use to undergraduates, graduates and phd students, and may also appeal to professional mathematicians as a reference text.

Arithmetik Abelscher Varietäten mit komplexer Multiplikation (Lecture Notes in Mathematics #1082)

Arithmetik, Algebra und Analysis

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Arithmetik und Algebra: Aufgaben

Arithmetik und Algebra (pdf): Arithmetik Und Algebra

Arithmetique des algebres de quaternions (Lecture Notes in Mathematics #800)

Arithmetische Funktionen

Dieses Buch bietet eine Einführung in die Theorie der arithmetischen Funktionen, welche zu den klassischen und dynamischen Gebieten der Zahlentheorie gehört. Das Buch enthält breitgefächerte Resultate, die für alle mit den Grundlagen der Zahlentheorie vertrauten Leser zugänglich sind. Der Inhalt geht weit über das Spektrum hinaus, mit dem die meisten Lehrbücher dieses Thema behandeln. Intensiv besprochen werden beispielsweise Ramanujan-Summen, Fourier-Zerlegungen arithmetischer Funktionen, Anzahl der Lösungen von Kongruenzen, Dirichlet-Reihen und verallgemeinerte Dirichlet-Faltungen sowie arithmetische Funktionen auf Gittern. Desweiteren sind viele bibliografische Anmerkungen sowie Verweise auf Originalliteratur aufgeführt. Mehr als 400 Übungsaufgaben bilden darüber hinaus einen wesentlichen Bestandteil für die Erschließung des Themas.

Arithmetische und geometrische Fähigkeiten von Schulanfängern: Eine empirische Untersuchung unter besonderer Berücksichtigung des Bereichs Muster und Strukturen (Dortmunder Beiträge zur Entwicklung und Erforschung des Mathematikunterrichts #3)

Theresa Deutscher stellt die Lernstände von Schulanfängerinnen und Schulanfängern inhaltlich umfassend und detailliert für die Grundideen der Arithmetik und der Geometrie dar. Als Datenbasis dienen klinische Einzelinterviews mit 108 Kindern, die sowohl qualitativ als auch quantitativ in Bezug auf unterschiedliche Schülergruppen ausgewertet werden.

Aritmetica: un approccio computazionale (Convergenze)

Il volume si propone di fornire una prima introduzione alla teoria elementare dei numeri, rivolta agli insegnanti (e ai futuri insegnanti) di matematica. Esso vuole costituire un invito e una preparazione per la lettura di opere più impegnative di cui c'è gran copia nella letteratura di lingua inglese e (ultimamente grazie proprio a Springer) una buona presenza anche in lingua italiana. Esso si caratterizza per avere una "approccio computazionale" cioè per favorire l'uso di un software (scegliendolo tra i più diffusi oggi in commercio) ai fini della costruzione di un laboratorio di calcolo.

Aritmetica, crittografia e codici (UNITEXT)

Il volume potrà essere utile ai docenti che intendano svolgere un corso su questi argomenti, la cui presenza sempre più viene richiesta nei corsi di laurea di matematica, fisica, informatica, ingnegneria.

ARM Assembly Language: Fundamentals and Techniques, Second Edition

Delivering a solid introduction to assembly language and embedded systems, ARM Assembly Language: Fundamentals and Techniques, Second Edition continues to support the popular ARM7TDMI, but also addresses the latest architectures from ARM, including Cortex�-A, Cortex-R, and Cortex-M processors-all of which have slightly different instruction sets, p

ARM Assembly Language: Fundamentals and Techniques, Second Edition

Delivering a solid introduction to assembly language and embedded systems, ARM Assembly Language: Fundamentals and Techniques, Second Edition continues to support the popular ARM7TDMI, but also addresses the latest architectures from ARM, including Cortex-A, Cortex-R, and Cortex-M processors-all of which have slightly different instruction sets, p

ARMA Model Identification (Springer Series in Statistics)

During the last two decades, considerable progress has been made in statistical time series analysis. The aim of this book is to present a survey of one of the most active areas in this field: the identification of autoregressive moving-average models, i.e., determining their orders. Readers are assumed to have already taken one course on time series analysis as might be offered in a graduate course, but otherwise this account is self-contained. The main topics covered include: Box-Jenkins' method, inverse autocorrelation functions, penalty function identification such as AIC, BIC techniques and Hannan and Quinn's method, instrumental regression, and a range of pattern identification methods. Rather than cover all the methods in detail, the emphasis is on exploring the fundamental ideas underlying them. Extensive references are given to the research literature and as a result, all those engaged in research in this subject will find this an invaluable aid to their work.

Armut im jungen Erwachsenenalter und der Wandel von Arbeitsmarkt, Wohlfahrtsstaat und Haushalten

Sebastian Link geht in diesem Buch der Frage nach, welche Auswirkungen mit dem Erwerbseinstiegsprozess verbundene Risiken (Arbeitslosigkeit, Niedriglohnbeschäftigung) und atypische Beschäftigungsverhältnisse auf die Armutsbetroffenheit junger Erwachsener in Deutschland haben. Mithilfe von Quer- und Längsschnittanalysen auf Basis des Sozio-Oekonomischen Panels zeigt er, dass nicht in erster Linie das gehäufte Auftreten von Erwerbsrisiken und atypischer Beschäftigung zu einem Armutsanstieg bei jungen Erwachsenen geführt hat, sondern die Verstärkung ihrer negativen finanziellen Folgen. Diese Verstärkung steht in einem Zusammenhang mit dem abnehmenden Schutz junger Erwachsener vor Armut durch Wohlfahrtsstaat und Haushalte.

Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom: (AMS-208) (Annals of Mathematics Studies #391)

The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physicsArnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom).This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

The Arnold-Gelfand Mathematical Seminars

Arnold Sommerfeld: Science, Life and Turbulent Times 1868-1951 (Springerbriefs In History Of Science And Technology Ser.)

The subject of the book is a biography of the theoretical physicist Arnold Sommerfeld (1868-1951). Although Sommerfeld is famous as a quantum theorist for the elaboration of the semi-classical atomic theory (Bohr-Sommerfeld model, Sommerfeld's fine-structure constant), his role in the history of modern physics is not confined to atoms and quanta. Sommerfeld left his mark in the history of mathematics, fluid mechanics, a number of physical subdisciplines and, in particular, as founder of a most productive "school" (Peter Debye, Wolfgang Pauli, Werner Heisenberg, Linus Pauling and Hans Bethe were his pupils, to name only the Nobel laureates among them). This biography is to a large extent based on primary source material (correspondence, diaries, unpublished manuscripts). It should be of particular interest to students who are keen to know more about the historical roots of modern science. Sommerfeld lived through turbulent times of German history (Wilhelmian Empire, Weimar Republic, Nazi period). His life, therefore, illustrates how science and scientists perform in changing social environments. From this perspective, the biography should also attract readers with a general interest in the history of science and technology.