# 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:**8961

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:**8804

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.

## 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:**3465

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.

## Stochastic Analysis and Diffusion Processes

**Author**: Gopinath Kallianpur,P Sundar**Publisher:**Oxford University Press**ISBN:**0199657076**Category:**Mathematics**Page:**352**View:**3876

Beginning with the concept of random processes and Brownian motion and building on the theory and research directions in a self-contained manner, this book provides an introduction to stochastic analysis for graduate students, researchers and applied scientists interested in stochastic processes and their applications.

## Algebraic Models in Geometry

**Author**: Yves Félix,John Oprea,Daniel Tanré**Publisher:**Oxford University Press on Demand**ISBN:**9780199206513**Category:**Mathematics**Page:**460**View:**3591

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.

## Partial differential equations in general relativity

**Author**: Alan D. Rendall**Publisher:**Oxford University Press, USA**ISBN:**9780199215409**Category:**Mathematics**Page:**279**View:**5654

A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role in research on general relativity. This is partly due to the growth of the field of numerical relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interest in general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partial differential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field of mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology.

## Reviews in Number Theory, 1984-96

*As Printed in Mathematical Reviews*

**Author**: N.A**Publisher:**Amer Mathematical Society**ISBN:**9780821809372**Category:**Mathematics**Page:**1012**View:**3179

These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.

## Groups Acting on Hyperbolic Space

*Harmonic Analysis and Number Theory*

**Author**: Juergen Elstrodt,Fritz Grunewald,Jens Mennicke**Publisher:**Springer Science & Business Media**ISBN:**9783540627456**Category:**Mathematics**Page:**524**View:**9889

This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n :::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the last century the group of isometries of these spaces was studied by Steiner, when he looked at the group generated by the inversions in spheres. The ge ometries underlying the hyperbolic spaces were of fundamental importance since Lobachevski, Bolyai and Gauß had observed that they do not satisfy the axiom of parallels. Already in the classical works several concrete coordinate models of hy perbolic 3-space have appeared. They make explicit computations possible and also give identifications of the full group of motions or isometries with well-known matrix groups. One such model, due to H. Poincare, is the upper 3 half-space IH in JR . The group of isometries is then identified with an exten sion of index 2 of the group PSL(2,

## The American Mathematical Monthly

*The Official Journal of the Mathematical Association of America*

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Mathematicians**Page:**N.A**View:**314