Geometry

Mathematics develops both due to demands of other sciences and due to its internal logic.

Projective geometry, and the Cayley-Klein geometries embedded into it, were originated in the 19th century.

The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering.

The general theory of relativity, as formulated by Albert Einstein in 1915, provided an astoundingly original perspective on the physical nature of gr- itation, showing that it could be understood as a feature of a curvature in the four-dimensional continuum of space-time.

The present text is an introduction to the theory of association schemes.

For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who revised it substantially for the English edition.

Absolute values and their completions -like the p-adic number fields- play an important role in number theory.

From the reviews of the hardcover edition: .

Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences.

The theory of groups and Lie algebras is interesting for many reasons.

Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures.

This book is the first comprehensive presentation of a central topic of stochastic geometry: random mosaics that are generated by Poisson processes of hyperplanes.

The NLAGA's Biennial International Research Symposium (NLAGA-BIRS) is intended to gather African expertises in Nonlinear Analysis, Geometry and their Applications with their international partners in a four days conference where new mathematical results are presented and discussed.

This textbook combines the history of synthetic geometry, centered on the years 1800-1855, with a theorem-proof exposition of the geometry developed in those years.

Although not so well known today, Book 4 of Pappus' Collection is one of the most important and influential mathematical texts from antiquity.

As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities.

Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject.

Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style.

Computer languages and computer graphics have become the primary modes of human-computer interaction.

Although geometry has been a flourishing discipline for millennia, most of it has seen either no practical applications or only esoteric ones.

In my last book, Geometry for Computer Graphics, I employed a mixture of algebra and vector analysis to prove many of the equations used in computer graphics.

Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity.

Geometric algebra (a Clifford Algebra) has been applied to different branches of physics for a long time but is now being adopted by the computer graphics community and is providing exciting new ways of solving 3D geometric problems.

The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries.

Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion.

Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions.

Focussing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD).

Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion.

Taking a direct route, "e;Essential Topology"e; brings the most important aspects of modern topology within reach of a second-year undergraduate student.

This book collects the lecture notes of the Summer School on Convex Geometry, held in Cetraro, Italy, from August 30th to September 3rd, 2021.

This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry.

This book focuses on the study of the volume of vector fields on Riemannian manifolds.

Algebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry.