Geometry

Self-contained, richly illustrated account of modern differential geometry applied to integral geometry.

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common?

This is the Proceedings of the ICM 2010 Satellite Conference on "e;Buildings, Finite Geometries and Groups"e; organized at the Indian Statistical Institute, Bangalore, during August 29 - 31, 2010.

This second edition of Alexander Soifer's How Does One Cut a Triangle?

Mathematical craftwork has become extremely popular, and mathematicians and crafters alike are fascinated by the relationship between their crafts.

Discussion of theory and applications of algebraic curves over finite fields with many rational points.

From reviews of the first edition:"e;In the world of mathematics, the 1980's might well be described as the "e;decade of the fractal"e;.

The problem of "e;Shortest Connectivity"e;, which is discussed here, has a long and convoluted history.

This book will be of great interest to researchers into algebraic topology.

Introduction to Recognition and Deciphering of Patterns is meant to acquaint STEM and non-STEM students with different patterns, as well as to where and when specific patterns arise.

- Follows a standard course curriculum.

This 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory.

Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincare Conjecture introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries.

The 100+ Series, Intro to Geometry, offers in-depth practice and review for challenging middle school math topics such as angles and triangles; graphing lines; and area, volume, and surface area.

This book consists of two parts.

This detailed exposition makes classical algebraic geometry accessible to the modern mathematician.

Ever since Lorensen and Cline published their paper on the Marching Cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data.

Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings.

This book studies the geometric theory of polynomials and rational functions in the plane.

This book is based on the proceedings of the Fifth Northeast Conference on General Topology and Applications, held at The College of Staten Island - The City University of New York.

One of the world's foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields.

Mathematical Analysis: Theory and Applications provides an overview of the most up-to-date developments in the field, presenting original contributions and surveys from a spectrum of respected academics.

This book provides a comprehensive account of a modern generalisation of differential geometry in which coordinates need not commute.

Commutative Ring Theory emerged as a distinct field of research in math- ematics only at the beginning of the twentieth century.

Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general.

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems.

This book represents the first synthesis of the considerable body of new research into positive definite matrices.

A one-stop introduction to the methods of ergodic theory applied to holomorphic iteration that is ideal for graduate courses.

A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school.

*; Lavishly illustrated with hundreds of detailed diagrams and technical illustrations exploring the evolution and importance of the starcut diagram *; Shows how the starcut diagram underlies the shaman's dance in China, the Vedic Fire Altar in India, Raphael frescoes, labyrinth designs, the Great Pyramid in Egypt, and the building of ancient cities *; Explains how the starcut diagram was used in building and design, how it relates to Pythagoras's Tetrakys, and how it contains knowledge of the Tree of Life As Malcolm Stewart reveals in this lavishly illustrated study, the simplesquare figure of the Starcut diagram, created only with circles, has extraordinary geometric properties.

In this third installment of his classic 'Foundations' trilogy, Michel Serres takes on the history of geometry and mathematics.

This volume introduces some recent developments in Arithmetic Geometry over local fields.

This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems.

Classical number theory is developed from scratch leading to geometric discrepancy theory, with Fourier analysis introduced along the way.

This monograph gives a short introduction to the relevant modern parts of discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements.

Differential geometry is the study of the curvature and calculus of curves and surfaces.

Unified introduction to algebra and geometry, emphasising links between the topics.

This volume arose from a semester at CIRM-Luminy on "e;Thermodynamic Formalism: Applications to Probability, Geometry and Fractals"e; which brought together leading experts in the area to discuss topical problems and recent progress.

Explores the development of the ellipse and presents mathematical concepts within a rich, historical context The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment.

The discovery of hyperbolic geometry, and the subsequent proof that this geometry is just as logical as Euclid's, had a profound in- fluence on man's understanding of mathematics and the relation of mathematical geometry to the physical world.

"e;Mirrors and Reflections"e; presents a systematic and elementary introduction to the properties of finite groups generated by reflections.

This volume contains the proceedings of the special session on Modern Methods in Continuum Theory presented at the 100th Annual Joint Mathematics Meetings held in Cincinnati, Ohio.

Simple enough for detailed study, rich enough to show interesting behavior, K3 surfaces illuminate core methods in algebraic geometry.

A 2007 graduate text on spectral methods with applications in fluid dynamics and engineering.

Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature.