Number theory

This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics.

Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized.

It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections.

In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics.

Within the general framework of the dynamics of "e;large"e; groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions.

There have been exciting developments in the area of knot theory in recent years.

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 Wei-Liang Chow and Kuo-Tsai Chen Memorial Conference was proposed and held by Prof S S Chern in Nankai Institute of Mathematics.

This book constitutes the proceedings of the 2000 Howard conference on "e;Infinite Dimensional Lie Groups in Geometry and Representation Theory"e;.

This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century.

This book covers new ground on Fibonacci sequences and the well-known Fibonacci numbers.

This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory.

The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology.

This book is intended as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors.

This book provides a detailed description of a most important unsolved mathematical problem - the Goldbach conjecture.

The International Conference on Modern Mathematics and the International Symposium on Differential Geometry, in honor of Professor Su Buchin on the centenary of his birth, were held in September 2001 at Fudan University, Shanghai, China.

Energy of knots is a theory that was introduced to create a "e;canonical configuration"e; of a knot - a beautiful knot which represents its knot type.

A real matrix is positive semidefinite if it can be decomposed as A=BB'.

This volume covers a broad range of subjects in modern geometry and related branches of mathematics, physics and computer science.

Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades.

Though elementary in nature, this book deals with fundamental issues in mathematics - number, algebra, geometry (both Euclidean and non-Euclidean) and topology.

The Bernstein problem and the Plateau problem are central topics in the theory of minimal submanifolds.

This subject has been of great interest both to topologists and to number theorists.

The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on "e;Representation Theory of Lie Groups"e; from July 2002 to January 2003.

This unique book deals with the theory of Rozansky-Witten invariants, introduced by L Rozansky and E Witten in 1997.

In this volume, an abstract theory of 'forms' is developed, thus providing a conceptually satisfying framework for the classification of forms of Fermat equations.

The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin.

The physical properties of knotted and linked configurations in space have long been of interest to mathematicians.

This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago.

This volume presents a comprehensive collection of Wang Yuan's original important papers which are not available elsewhere, since the majority of the papers were published in China.

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms.

This volume contains a valuable collection of research articles by active and well-known mathematicians in differential geometry and mathematical physics, contributed to mark Professor Kouei Sekigawa's 60th birthday.

This is the first book on analytic hyperbolic geometry, fully analogous to analytic Euclidean geometry.

The Euclidean algorithm is one of the oldest in mathematics, while the study of continued fractions as tools of approximation goes back at least to Euler and Legendre.

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 is the first book on the theory of multiple zeta values since its birth around 1994.

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.