Number theory

Noncommutative differential geometry is a novel approach to geometry that is paving the way for exciting new directions in the development of mathematics and physics.

Integral geometry, known as geometric probability in the past, originated from Buffon's needle experiment.

This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions.

This introductory book uses the moving frame as a tool and develops Finsler geometry on the basis of the Chern connection and the projective sphere bundle.

Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.

This book is devoted to the structure of the Mandelbrot set - a remarkable and important feature of modern theoretical physics, related to chaos and fractals and simultaneously to analytical functions, Riemann surfaces, phase transitions and string theory.

In 1938, at the Institute for Advanced Study, E Hecke gave a series of lectures on his theory of correspondence between modular forms and Dirichlet series.

This volume is not an ordinary proceedings volume assembling papers submitted but a collection of prestigious survey papers on various subjects studied enthusiastically by experts all over the world.

The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday.

Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes.

This volume takes a look at the current state of the theory of foliations, with surveys and research articles concerning different aspects.

The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered.

This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a self-contained and accessible manner.

This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.

This important book presents all the major works of Professor Wen-Tsun Wu, a widely respected Chinese mathematician who has made great contributions in the fields of topology and computer mathematics throughout his research career.

In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest.

The theory of connections is central not only in pure mathematics (differential and algebraic geometry), but also in mathematical and theoretical physics (general relativity, gauge fields, mechanics of continuum media).

This unique volume, resulting from a conference at the Chern Institute of Mathematics dedicated to the memory of Xiao-Song Lin, presents a broad connection between topology and physics as exemplified by the relationship between low-dimensional topology and quantum field theory.

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory.

The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan.

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda's 60th birthday.

Figurate numbers have a rich history with many applications.

This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan.

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms.

The need of optimal partition arises from many real-world problems involving the distribution of limited resources to many users.

This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates.

The binomial transform is a discrete transformation of one sequence into another with many interesting applications in combinatorics and analysis.

This volume is the result of the author's many-years of research in this field.

This book is a comprehensive treatise on the partial toroidal and minimal compactifications of the ordinary loci of PEL-type Shimura varieties and Kuga families, and on the canonical and subcanonical extensions of automorphic bundles.

This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations.

This is a first-ever textbook written in English about the theory of modular forms and Jacobi forms of several variables.

This book is an introduction to the theory and application of modes - structures that capture the common underlying algebra of convex sets, affine spaces and certain ordered sets.

The material in this book is organized in such a way that the reader gets to significant applications quickly, and the emphasis is on the geometric understanding and use of new concepts.

This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics.

This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used.

This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities.

This book covers selected topics in geometry, algebra, calculus and probability theory.

Starting with the Zermelo-Fraenhel axiomatic set theory, this book gives a self-contained, step-by-step construction of real and complex numbers.

Novel and important applications of number theory to graph theory and vice versa had been made in the past decade.

Number Mosaics has little in common with most other books of recreational mathematics.

The aim of this book is to familiarize the reader with fundamental topics in number theory: theory of divisibility, arithmetrical functions, prime numbers, geometry of numbers, additive number theory, probabilistic number theory, theory of Diophantine approximations and algebraic number theory.

This book explains clearly and in detail the basic concepts and methods of calculations of the elementary theory of numbers.

In these lecture notes the student learns basic theorems of the subject (due to Sylow, Burnside, Schur and Frobenius).

Essentials of integral geometry in a homogenous space are presented and the focus is on the basic results and applications.

This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980.

Spinors are used extensively in physics.

Riemann-Finsler geometry is a subject that concerns manifolds with Finsler metrics, including Riemannian metrics.

This textbook presents the foundations of tensor calculus and the elements of tensor analysis.

Number theory is an important research field of mathematics.

This textbook presents an elementary introduction to number theory and its different aspects: approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory.