Geometry

This brief presents a global perspective on the geometry of spaces of polynomials.

Differential geometry and topology have become essential tools for many theoretical physicists.

This book provides a comprehensive introduction to modern global variational theory on fibred spaces.

This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c).

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade.

This book is about three seemingly independent areas of mathematics: combinatorial group theory, the theory of Lie algebras and affine algebraic geometry.

The 2007 Abel Symposium took place at the University of Oslo in August 2007.

This original monograph investigates several unsolved problems that currently exist in coding theory.

This comprehensive introduction to algebraic complexity theory presents new techniques for analyzing P vs NP and matrix multiplication.

Ruled varieties are unions of a family of linear spaces.

Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases.

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.

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility.

The study of geometry can play an important role in stimulating mathematical imagination and intuition, particularly in its relation to algebra.

This book presents a comprehensive set of methods for quantifying geometric quantities such as the volume of a tumor, the total surface area of the alveoli in a lung, the length of plant roots, or of blood vessels, the number of neurons in a brain compartment, the connectivity number of trabecular bone, the mean size of grains in a rock, etc.

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The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together.

The author presents deterministic chaos from the standpoint of theoretical computer arithmetic, leading to universal properties described by symbolic dynamics.

Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories.

Geometric group theory is the study of the interplay between groups and the spaces they act on, and has its roots in the works of Henri Poincare, Felix Klein, J.

A collection of expository articles on modern topics in algebraic geometry, focusing on the geometry of algebraic spaces and stacks.

Focusing Your Attention The purpose of this book is Cat least) twofold.

This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014.

This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.

This new edition describes the space of quantum states and the theory of quantum entanglement from a geometric perspective.

A comprehensive treatment of Floer homology, based on the Seiberg–Witten equations, first published in 2007.

This updated and revised second edition of the leading reference volume on distance metrics includes a wealth of new material that reflects advances in a developing field now regarded as an essential tool in many areas of pure and applied mathematics.

With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem.

This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics- and in theoretical physics such as quantum field theory and string theory.

The first of a two-part volume, this collection offers a unifying vision of algebraic geometry, exploring its evolution over the last four decades as well as state-of-the art research.

The first fully self-contained introduction to geometric algebra by two leading experts in the field.

Die morphologischen Operatoren werden durch einfache mathematische Begriffe definiert und durch didaktische An- sätze und Illustrationen erklärt.

Dieses Buch gibt eine Einführung in die Algebraische Geometrie.

For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry.

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997.

Revised and updated, this second edition provides an accessible introduction to both chaotic dynamics and fractal geometry for readers with a calculus background.

Complex Finsler metrics appear naturally in complex analysis.

The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics.

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology.

This book is a unique collection of challenging geometry problems and detailed solutions that will build students' confidence in mathematics.

Systems of polynomial equations arise throughout mathematics, science, and engineering.

Traditionally, Lorentzian geometry has been used as a necessary tool to understand general relativity, as well as to explore new genuine geometric behaviors, far from classical Riemannian techniques.