# Search Results for "experiment-number-theory-oxford-graduate-texts-in-mathematics"

## Experimental Number Theory

**Author**: Fernando Rodriguez Villegas**Publisher:**Oxford University Press**ISBN:**0198528221**Category:**Mathematics**Page:**214**View:**2224

This graduate text shows how the computer can be used as a tool for research in number theory through numerical experimentation. Examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, are provided along with exercises and selected solutions.

## Modular Forms

*A Classical and Computational Introduction Second Edition*

**Author**: L J P Kilford**Publisher:**World Scientific Publishing Company**ISBN:**1783265477**Category:**Mathematics**Page:**252**View:**9144

Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it. This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

## A Classical Introduction to Modern Number Theory

**Author**: K. Ireland,M. Rosen**Publisher:**Springer Science & Business Media**ISBN:**1475717792**Category:**Mathematics**Page:**344**View:**1803

This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972. As with the first book the primary audience we envisage consists of upper level undergraduate mathematics majors and graduate students. We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra. A large portion of Chapters 1-11 can be read even without such background with the aid of a small amount of supplementary reading. The later chapters assume some knowledge of Galois theory, and in Chapters 16 and 18 an acquaintance with the theory of complex variables is necessary. Number theory is an ancient subject and its content is vast. Any intro ductory book must, of necessity, make a very limited selection from the fascinat ing array of possible topics. Our focus is on topics which point in the direction of algebraic number theory and arithmetic algebraic geometry. By a careful selection of subject matter we have found it possible to exposit some rather advanced material without requiring very much in the way oftechnical background. Most of this material is classical in the sense that is was dis covered during the nineteenth century and earlier, but it is also modern because it is intimately related to important research going on at the present time.

## Matroid Theory

*AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory, July 2-6, 1995, University of Washington, Seattle*

**Author**: Joseph Edmond Bonin**Publisher:**American Mathematical Soc.**ISBN:**0821805088**Category:**Mathematics**Page:**418**View:**5604

This volume contains the proceedings of the 1995 AMS-IMS-SIAM Joint Summer Research Conference on Matroid Theory held at the University of Washington, Seattle. The book features three comprehensive surveys that bring the reader to the forefront of research in matroid theory. Joseph Kung's encyclopedic treatment of the critical problem traces the development of this problem from its origins through its numerous links with other branches of mathematics to the current status of its many aspects. James Oxley's survey of the role of connectivity and structure theorems in matroid theory stresses the influence of the Wheels and Whirls Theorem of Tutte and the Splitter Theorem of Seymour. Walter Whiteley's article unifies applications of matroid theory to constrained geometrical systems, including the rigidity of bar-and-joint frameworks, parallel drawings, and splines. These widely accessible articles contain many new results and directions for further research and applications. The surveys are complemented by selected short research papers. The volume concludes with a chapter of open problems. Features self-contained, accessible surveys of three active research areas in matroid theory; many new results; pointers to new research topics; a chapter of open problems; mathematical applications; and applications and connections to other disciplines, such as computer-aided design and electrical and structural engineering.

## Women in Numbers 2: Research Directions in Number Theory

**Author**: Chantal David,Matilde Lalín, Michelle Manes**Publisher:**American Mathematical Soc.**ISBN:**1470410222**Category:**Mathematics**Page:**206**View:**1069

The second Women in Numbers workshop (WIN2) was held November 6-11, 2011, at the Banff International Research Station (BIRS) in Banff, Alberta, Canada. During the workshop, group leaders presented open problems in various areas of number theory, and working groups tackled those problems in collaborations begun at the workshop and continuing long after. This volume collects articles written by participants of WIN2. Survey papers written by project leaders are designed to introduce areas of active research in number theory to advanced graduate students and recent PhDs. Original research articles by the project groups detail their work on the open problems tackled during and after WIN2. Other articles in this volume contain new research on related topics by women number theorists. The articles collected here encompass a wide range of topics in number theory including Galois representations, the Tamagawa number conjecture, arithmetic intersection formulas, Mahler measures, Newton polygons, the Dwork family, elliptic curves, cryptography, and supercongruences. WIN2 and this Proceedings volume are part of the Women in Numbers network, aimed at increasing the visibility of women researchers' contributions to number theory and at increasing the participation of women mathematicians in number theory and related fields. This book is co-published with the Centre de Recherches Mathématiques.

## Discrete Symmetries and CP Violation

*From Experiment to Theory*

**Author**: Marco Sozzi**Publisher:**Oxford University Press**ISBN:**0199296669**Category:**Science**Page:**550**View:**8899

This book takes a fresh approach to the teaching of discrete symmetries which are central to fundamental physics: mirror symmetry, matter/anti-matter symmetry, and time reversal. It is self-contained and includes detailed discussions of relevant experiments - conveying some of the fascination and intellectual challenges of experimental physics.

## A Course in the Theory of Groups

**Author**: Derek Robinson**Publisher:**Springer Science & Business Media**ISBN:**1468401289**Category:**Mathematics**Page:**481**View:**472

" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.

## An Introduction to the Theory of Numbers

**Author**: Godfrey Harold Hardy,E. M. Wright,Roger Heath-Brown,Joseph Silverman**Publisher:**Oxford University Press**ISBN:**9780199219865**Category:**Mathematics**Page:**621**View:**5073

An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. This Sixth Edition has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter on one of the mostimportant developments in number theory -- modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader and the clarityof exposition is retained throughout making this textbook highly accessible to undergraduates in mathematics from the first year upwards.

## Algebraic Models in Geometry

**Author**: Yves Félix,John Oprea,Daniel Tanré**Publisher:**Oxford University Press**ISBN:**0199206511**Category:**Mathematics**Page:**460**View:**6376

In the past century, different branches of mathematics have become more widely separated. Yet, there is an essential unity to mathematics which still springs up in fascinating ways to solve interdisciplinary problems. This text provides a bridge between the subjects of algebraic topology, including differential topology, and geometry. It is a survey book dedicated to a large audience of researchers and graduate students in these areas. Containing a generalintroduction to the algebraic theory of rational homotopy and giving concrete applications of algebraic models to the study of geometrical problems, mathematicians in many areas will find subjects that are of interest to them in the book.

## Introduction to Banach Spaces and Algebras

**Author**: Graham R. Allan,Harold G. Dales**Publisher:**Oxford University Press**ISBN:**0199206538**Category:**Banach algebras**Page:**371**View:**2731

A graduate level text in functional analysis, with an emphasis on Banach algebras. Based on lectures given for Part III of the Cambridge Mathematical Tripos, the text will assume a familiarity with elementary real and complex analysis, and some acquaintance with metric spaces, analytic topology and normed spaces (but not theorems depending on Baire category, or any version of the Hahn-Banach theorem).

## Algebraic Number Theory

**Author**: Ian Stewart**Publisher:**Springer**ISBN:**9780412138409**Category:**Science**Page:**257**View:**1494

The title of this book may be read in two ways. One is 'algebraic number-theory', that is, the theory of numbers viewed algebraically; the other, 'algebraic-number theory', the study of algebraic numbers. Both readings are compatible with our aims, and both are perhaps misleading. Misleading, because a proper coverage of either topic would require more space than is available, and demand more of the reader than we wish to; compatible, because our aim is to illustrate how some of the basic notions of the theory of algebraic numbers may be applied to problems in number theory. Algebra is an easy subject to compartmentalize, with topics such as 'groups', 'rings' or 'modules' being taught in comparative isolation. Many students view it this way. While it would be easy to exaggerate this tendency, it is not an especially desirable one. The leading mathematicians of the nineteenth and early twentieth centuries developed and used most of the basic results and techniques of linear algebra for perhaps a hundred years, without ever defining an abstract vector space: nor is there anything to suggest that they suf fered thereby. This historical fact may indicate that abstrac tion is not always as necessary as one commonly imagines; on the other hand the axiomatization of mathematics has led to enormous organizational and conceptual gains.

## Differential Geometry

*Bundles, Connections, Metrics and Curvature*

**Author**: Clifford Henry Taubes**Publisher:**Oxford University Press**ISBN:**0199605882**Category:**Mathematics**Page:**298**View:**1323

Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.

## Algebraic Geometry and Arithmetic Curves

**Author**: Qing Liu,Reinie Erne**Publisher:**Oxford University Press**ISBN:**0191547808**Category:**Mathematics**Page:**592**View:**8169

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

## Exploring the Quantum

*Atoms, Cavities, and Photons*

**Author**: Serge Haroche,Jean-Michel Raimond**Publisher:**Oxford University Press**ISBN:**0198509146**Category:**Language Arts & Disciplines**Page:**605**View:**300

The quantum world obeys logic at odds with our common sense intuition. This weirdness is directly displayed in recent experiments juggling with isolated atoms and photons. They are reviewed in this book, combining theoretical insight and experimental description, and providing useful illustrations for learning and teaching of quantum mechanics.

## Mathematical Logic

**Author**: Ian Chiswell,Wilfrid Hodges**Publisher:**Oxford University Press on Demand**ISBN:**0198571003**Category:**Mathematics**Page:**250**View:**6386

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't becalculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assumingMatiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics andcomputer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic,Mathematics, Philosophy, and Computer Science.

## Algebraic Number Theory

**Author**: Serge Lang**Publisher:**Springer Science & Business Media**ISBN:**146120853X**Category:**Mathematics**Page:**357**View:**6603

This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms. "Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—-MATHEMATICAL REVIEWS

## Chemical Dynamics in Condensed Phases

*Relaxation, Transfer and Reactions in Condensed Molecular Systems*

**Author**: Abraham Nitzan**Publisher:**Oxford University Press**ISBN:**0198529791**Category:**Science**Page:**719**View:**2951

Graduate level textbook presenting some of the most fundamental processes that underlie physical, chemical and biological phenomena in complex condensed phase systems. Includes in-depth descriptions of relevant methodologies, and provides ample introductory material for readers of different backgrounds.

## An Introduction to Number Theory

**Author**: Harold M. Stark**Publisher:**Mit Press**ISBN:**9780262690607**Category:**Mathematics**Page:**347**View:**2147

The majority of students who take courses in number theory are mathematics majors who will not become number theorists. Many of them will, however, teach mathematics at the high school or junior college level, and this book is intended for those students learning to teach, in addition to a careful presentation of the standard material usually taught in a first course in elementary number theory, this book includes a chapter on quadratic fields which the author has designed to make students think about some of the "obvious" concepts they have taken for granted earlier. The book also includes a large number of exercises, many of which are nonstandard.

## Quantum Field Theory of Many-Body Systems

*From the Origin of Sound to an Origin of Light and Electrons*

**Author**: Xiao-Gang Wen**Publisher:**Oxford University Press on Demand**ISBN:**0198530943**Category:**Science**Page:**505**View:**2640

This book is a pedagogical and systematic introduction to new concepts and quantum field theoretical methods in condensed matter physics, which may have an impact on our understanding of the origin of light, electrons and other elementary particles in the universe. Emphasis is on clear physical principles, while at the same time bringing students to the fore of today's research.

## Intuitive Concepts in Elementary Topology

**Author**: B.H. Arnold**Publisher:**Courier Corporation**ISBN:**0486275760**Category:**Mathematics**Page:**192**View:**2638

Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.