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Arithmetic and Geometry
by Luis Dieulefait Gerd Faltings D. R. Heath-Brown Yu. V. Manin B. Z. Moroz Jean-Pierre WintenbergerThe 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.
Arithmetic and Geometry of K3 Surfaces and Calabi–Yau Threefolds (Fields Institute Communications #67)
by Matthias Schütt Radu Laza Noriko YuiIn recent years, research in K3 surfaces and Calabi-Yau varieties has seen spectacular progress from both arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics--in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi-Yau threefolds, held at the Fields Institute (August 16-25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi-Yau varieties. With the big variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi-Yau workshop started with 3 days of introductory lectures. A selection of 4 of these lectures is included in this volume. These lectures can be used as a starting point for the graduate students and other junior researchers, or as a guide to the subject.
Arithmetic and Geometry over Local Fields: VIASM 2018 (Lecture Notes in Mathematics #2275)
by Bruno Anglès Tuan Ngo DacThis volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.
Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces: Hyperbolicity in Montréal (CRM Short Courses)
by Marc-Hubert NicoleThis textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes:The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures;A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective;A systematic presentation and comparison between different notions of hyperbolicity, as an introduction to the Lang–Vojta conjectures in the projective case;An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasi-projective varieties.Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.
The Arithmetic of Elliptic Curves
by Joseph H. SilvermanThe theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
Arithmetic of Finite Fields: 5th International Workshop, WAIFI 2014, Gebze, Turkey, September 27-28, 2014. Revised Selected Papers (Lecture Notes in Computer Science #9061)
by Çetin Kaya Koç Sihem Mesnager Erkay SavaşThis book constitutes the refereed proceedings of the 5th International Workshop on the Arithmetic of Finite Field, WAIFI 2014, held in Gebze, Turkey, in September 2014. The 9 revised full papers and 43 invited talks presented were carefully reviewed and selected from 27 submissions. This workshop is a forum of mathematicians, computer scientists, engineers and physicists performing research on finite field arithmetic, interested in communicating the advances in the theory, applications, and implementations of finite fields. The workshop will help to bridge the gap between the mathematical theory of finite fields and their hardware/software implementations and technical applications.
Arithmetic of Quadratic Forms (Springer Monographs in Mathematics #109)
by Goro ShimuraThis book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
Arithmetic Optimization Techniques for Hardware and Software Design
by Ryan Kastner Anup Hosangadi Farzan FallahObtain better system performance, lower energy consumption, and avoid hand-coding arithmetic functions with this concise guide to automated optimization techniques for hardware and software design. High-level compiler optimizations and high-speed architectures for implementing FIR filters are covered, which can improve performance in communications, signal processing, computer graphics, and cryptography. Clearly explained algorithms and illustrative examples throughout make it easy to understand the techniques and write software for their implementation. Background information on the synthesis of arithmetic expressions and computer arithmetic is also included, making the book ideal for new-comers to the subject. This is an invaluable resource for researchers, professionals, and graduate students working in system level design and automation, compilers, and VLSI CAD.
Arithmetic Refresher (Dover Books on Mathematics)
by A. A. KlafThe farther we get from our grade school days, the easier it is to forget those operations and nuances of arithmetical computation that keep recurring in our daily lives: interest and discount problems, time-payment calculations, tax problems, and so on.This handy book is designed to streamline your methods and resharpen your calculation skills for a variety of situations. Starting with the most elementary operations, the book goes on to cover all basic topics and processes of arithmetic: addition, subtraction, multiplication, division, fractions, percentage, interest, ratio and proportion, denominate numbers, averages, etc. The text continues into other useful matters, such as powers and roots, logarithms, positive and negative numbers, harmonic progression, and introductory concepts of algebra.Entirely practical in approach and using an easy-to-follow question and answer style, this book covers a wide range of common knotty areas: filling and emptying receptacles, scales for models and maps, business and financial calculations (partial payment problems, compound interest, bank and sales discount, profit and loss problems, etc.), angle measurement, mixtures and solutions, graph and chart problems, and the like.The discussion contains numerous alternate and short-cut methods, such as quick ways to figure compound interest; to square a number from 1 to 100; to divide by 5, 25, 125, 99, etc.; to multiply two 2-digit numbers having the same figure in the tens place; and many more. These valuable tips, together with the huge fund of exercise problems (a total of 809, half of them answered in an appendix), help you to increase your computational proficiency and speed, and make this an extremely useful volume to have on your shelf at home or at work. Anyone who has to do any figuring at all -- housewife, merchant, student -- will profit from this refresher. Parents will find it an excellent source of material for helping children in school work.
Arithmetic Tales: Advanced Edition (Universitext)
by Olivier BordellèsThis 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 Tales (Universitext)
by Olivier Bordellès Véronique BordellèsNumber theory was once famously labeled the queen of mathematics by Gauss. The multiplicative structure of the integers in particular deals with many fascinating problems some of which are easy to understand but very difficult to solve. In the past, a variety of very different techniques has been applied to further its understanding. Classical methods in analytic theory such as Mertens' theorem and Chebyshev's inequalities and the celebrated Prime Number Theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum's theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included. Topics in Multiplicative Number Theory introduces offers a comprehensive introduction into these topics with an emphasis on analytic number theory. Since it requires very little technical expertise it will appeal to a wide target group including upper level undergraduates, doctoral and masters level students.
Arithmetic Work-text 5
by Judy HoweArithmetic 5 contains a variety of exercises involving new/review material in each lesson. The workbook includes 169 lessons (excluding tests). Supplementary Exercises and Homework Exercises. The handbook at the end of the book contains facts, rules, and measures which are given throughout the workbook. Although all new material is presented at top of a workbook page, the workbook is not designed to be used without a teacher. Arithmetic 5 Curriculum/Lesson Plans, available separately or as part of the Grade 5 Curriculum, and the Teacher Edition provide complete daily plans for teaching, reviewing, and testing. The Teacher Edition also includes solutions to all exercises in the text. Student Quizzes, Tests, and Speed Drills are correlated with the work-text.
Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1 (SpringerBriefs in Mathematics #0)
by Elena Guardo Adam Van TuylThis 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.
Arithmetische Funktionen
by Paul J. MccarthyDieses Buch bietet eine Einf#65533;hrung in die Theorie der arithmetischen Funktionen, welche zu den klassischen und dynamischen Gebieten der Zahlentheorie geh#65533;rt. Das Buch enth#65533;lt breitgef#65533;cherte Resultate, die f#65533;r alle mit den Grundlagen der Zahlentheorie vertrauten Leser zug#65533;nglich sind. Der Inhalt geht weit #65533;ber das Spektrum hinaus, mit dem die meisten Lehrb#65533;cher dieses Thema behandeln. Intensiv besprochen werden beispielsweise Ramanujan-Summen, Fourier-Zerlegungen arithmetischer Funktionen, Anzahl der L#65533;sungen von Kongruenzen, Dirichlet-Reihen und verallgemeinerte Dirichlet-Faltungen sowie arithmetische Funktionen auf Gittern. Desweiteren sind viele bibliografische Anmerkungen sowie Verweise auf Originalliteratur aufgef#65533;hrt. Mehr als 400 #65533;bungsaufgaben bilden dar#65533;ber hinaus einen wesentlichen Bestandteil f#65533;r die Erschlie#65533;ung des Themas.
The Arm: Inside the Billion-Dollar Mystery of the Most Valuable Commodity in Sports
by Jeff PassanYahoo’s lead baseball columnist offers an in-depth look at the most valuable commodity in sports—the pitching arm—and how its vulnerability to injury is hurting players and the game, from Little League to the majors.Every year, Major League Baseball spends more than $1.5 billion on pitchers—five times more than the salary of every NFL quarterback combined. Pitchers are the game’s lifeblood. Their import is exceeded only by their fragility. One tiny band of tissue in the elbow, the ulnar collateral ligament, is snapping at unprecedented rates, leaving current big league players vulnerable and the coming generation of baseball-playing children dreading the three scariest words in the sport: Tommy John surgery.Jeff Passan traveled the world for three years to explore in-depth the past, present, and future of the arm, and how its evolution left baseball struggling to wrangle its Tommy John surgery epidemic. He examined what compelled the Chicago Cubs to spend $155 million on one arm. He snagged a rare interview with Sandy Koufax, whose career was cut short by injury at thirty, and visited Japan to understand how another baseball-mad country treats its prized arms. And he followed two major league pitchers, Daniel Hudson and Todd Coffey, throughout their returns from Tommy John surgery. He exposes how the baseball establishment long ignored the rise in arm injuries and reveals how misplaced incentives across the sport stifle potential changes.Injuries to the UCL start as early as Little League. Without a drastic cultural shift, baseball will continue to lose hundreds of millions of dollars annually to damaged pitchers, and another generation of children will suffer the same problems that vex current players. Informative and hard-hitting, The Arm is essential reading for everyone who loves the game, wants to keep their children healthy, or relishes a look into how a large, complex institution can fail so spectacularly.
ARM Assembly Language: Fundamentals and Techniques, Second Edition
by William Hohl Christopher HindsDelivering 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
Armut im jungen Erwachsenenalter und der Wandel von Arbeitsmarkt, Wohlfahrtsstaat und Haushalten
by Sebastian LinkSebastian 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 Sommerfeld: Science, Life and Turbulent Times 1868-1951
by Michael EckertThe 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.
Arnon Avron on Semantics and Proof Theory of Non-Classical Logics (Outstanding Contributions to Logic #21)
by Ofer Arieli Anna ZamanskyThis book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics.Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic.
Around and Beyond the Square of Opposition (Studies in Universal Logic)
by Dale Jacquette Jean-Yves BéziauThe theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, sociology, physics. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory. The square of opposition from its origin in antiquity to the present day continues to exert a profound impact on the development of deductive logic. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists on the square from all over the world.
Around the World in Eighty Games: From Tarot to Tic-Tac-Toe, Catan to Chutes and Ladders, a Mathematician Unlocks the Secrets of the World's Greatest Games
by Marcus du SautoyA &“fun&” and &“unexpected&” (The Economist) global tour of the world&’s greatest games and the mathematics that underlies them Where should you move first in Connect 4? What is the best property in Monopoly? And how can pi help you win rock paper scissors? Spanning millennia, oceans and continents, countries and cultures, Around the World in Eighty Games gleefully explores how mathematics and games have always been deeply intertwined. Renowned mathematician Marcus du Sautoy investigates how games provided the first opportunities for deep mathematical insight into the world, how understanding math can help us play games better, and how both math and games are integral to human psychology and culture. For as long as there have been people, there have been games, and for nearly as long, we have been exploring and discovering mathematics. A grand adventure, Around the World in Eighty Games teaches us not just how games are won, but how they, and their math, shape who we are.
Arrival Infrastructures: Migration and Urban Social Mobilities
by Bruno Meeus Karel Arnaut Bas Van HeurThis volume introduces a strategic interdisciplinary research agenda on arrival infrastructures. Arrival infrastructures are those parts of the urban fabric within which newcomers become entangled on arrival, and where their future local or translocal social mobilities are produced as much as negotiated. Challenging the dominance of national normativities, temporalities, and geographies of “arrival,” the authors scrutinize the position and potential of cities as transnationally embedded places of arrival. Critically interrogating conceptions of migrant arrival as oriented towards settlement and integration, the volume directs attention to much more diverse migration trajectories that shape our cities today. Each chapter examines how migrants, street-level bureaucrats, local residents, and civil society actors build—with the resources they have at hand—the infrastructures that accommodate, channel, and govern arrival.
The Arrow Impossibility Theorem
by Kenneth J. Arrow Eric Maskin Prasanta K. Pattanaik Amartya Sen Joseph E. StiglitzKenneth Arrow's pathbreaking "impossibility theorem" was a watershed in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, nondictatorship, and independence. In this book, Amartya Sen and Eric Maskin explore the implications of Arrow's theorem. Sen considers its ongoing utility, exploring the theorem's value and limitations in relation to recent research on social reasoning, while Maskin discusses how to design a voting rule that gets us closer to the ideal -- given that achieving the ideal is impossible. The volume also contains a contextual introduction by social choice scholar Prasanta K. Pattanaik and commentaries from Joseph E. Stiglitz and Kenneth Arrow himself, as well as essays by Sen and Maskin outlining the mathematical proof and framework behind their assertions.
The Arrow Impossibility Theorem (Kenneth J. Arrow Lecture Series)
by Amartya Sen Eric MaskinKenneth J. Arrow's pathbreaking "impossibility theorem" was a watershed innovation in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, nondictatorship, and independence. <P><P>In this book Eric Maskin and Amartya Sen explore the implications of Arrow's theorem. Sen considers its ongoing utility, exploring the theorem's value and limitations in relation to recent research on social reasoning, and Maskin discusses how to design a voting rule that gets us closer to the ideal—given the impossibility of achieving the ideal. The volume also contains a contextual introduction by social choice scholar Prasanta K. Pattanaik and commentaries from Joseph E. Stiglitz and Kenneth J. Arrow himself, as well as essays by Maskin, Dasgupta, and Sen outlining the mathematical proof and framework behind their assertions.
Art and IR Theory: Visual Semiotic Games (Mathematics in Mind)
by Serdar Ş. GünerThis book examines the correspondence between international relations (IR) theories of structural realism and constructivism and paintings, notably the artwork of Mark Rothko and Jackson Pollock, in a game theory setting. This interdisciplinary approach, through the lens of game theory and semiotics, permits different, enriched interpretations of structural realism and constructivism. These theories constitute an axis of debate between social and systemic approaches to international politics, as well as an axis of differentiation between scientific realism and positivism as philosophies of science. As such, the interpretations explored in this book contribute to what we know about international relations, how semiotics intersect with strategic uncertainty, and explains these interactions in the proposed games model.The book’s use of game theory and semiotics generate ‘visual semiotic games’ (VSGs) that shed light on the debate axes through strategic uncertainty, interactions, and players’ interactive belief systems. VSGs will contribute to literature on experimental semiotics in the sense of players’ coordination behavior, beliefs, and artistic evaluations. The equilibria, interpreted through branches of philosophy of mind and theories of explanation, will reveal possibilities of agreement among players about which artwork representing the theory at hand is the best, opening innovative research perspectives for the discipline of IR theory.