Geometry

Lie Sphere Geometry provides a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space.

Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry.

This book is an exposition of the theoretical foundations of hyperbolic manifolds.

Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form.

This book can be seen as a continuation of Equations and Inequalities: El- ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series.

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.

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.

Originally written in Russian and used in the Gelfand Correspondence School, "e;Lines and Curves"e; has since become a classic: the exposition maintains mathematical rigor while balancing creative storytelling and unusual examples of geometric properties.

The author's lectures, "e;Contact Manifolds in Riemannian Geometry,"e; volume 509 (1976), in the Springer-Verlag Lecture Notes in Mathematics series have been out of print for some time and it seems appropriate that an expanded version of this material should become available.

Reflection Groups and their invariant theory provide the main themes of this book and the first two parts focus on these topics.

The aim of this book is to present certain fundamental facts in the theory of algebraic surfaces, defined over an algebraically closed field lk of arbitrary characteristic.

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.

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

Algebraic curves are the graphs of polynomial equations in two vari- 3 ables, such as y3 + 5xy2 = x + 2xy.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas- sical techniques of applied mathematics.

The present work grew out of a study of the Maslov class (e.

Written as a supplement to Marcel Berger's popular two-volume set, Geometry I and II (Universitext), this book offers a comprehensive range of exercises, problems, and full solutions.

Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry.

This book is based on the full year Ph.

This book is based on one-semester courses given at Harvard in 1984, at Brown in 1985, and at Harvard in 1988.

We wrote this book to introduce undergraduates to some interesting ideas in algebraic geometry and commutative algebra.

From the reviews: "e;A prominent research mathematician and a high school teacher have combined their efforts in order to produce a high school geometry course.

The main aim of this book is to introduce Lie groups and allied algebraic and geometric concepts to a robotics audience.

A geometry course based on this book was taught success- fully by Gene Murrow for several years.

Gain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's TRIGONOMETRY.

Trigonometry: A Complete Introduction is the most comprehensive yet easy-to-use introduction to Trigonometry.

"e;Mechanical Drawing"e; aims to provide a fundamental course on all theory, principles, and methods needed to create a practical working drawing.

This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks.

manifolds, transformation groups, and Lie algebras, as well as the basic concepts of visual topology.

The present volume is the culmination often years' work separately and joint- ly.

The problem of finding minimal surfaces, i.

In the early years of the 1980s, while I was visiting the Institute for Ad- vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon- ical p-adic counterpart of several variables.

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title.

From the Preface: "e;This book was written for the active reader.

From the reviews of the first edition: "e;There are many books on the history of mathematics in which mathematics is subordinated to history.

This textbook on homology and cohomology theory is geared towards the beginning graduate student.

The theory of hyperbolic groups has its starting point in a fundamental paper by M.

This volume presents a complete and self-contained description of new results in the theory of manifolds of nonpositive curvature.

This volume contains the original lecture notes presented by A.

After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit- ful again.

Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par- tition of M into curves, i.

Early one morning in April of 1987, the Chinese mathematician J.

In a broad sense Design Science is the grammar of a language of images rather than of words.

This is a book of "e;impressions"e; of a journey through the theory of com- plex algebraic curves.

These notes are an expanded and updated version of a course of lectures which I gave at King's College London during the summer term 1979.