Geometry

Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems.

This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems.

The aim of this book is to facilitate the use of Stokes' Theorem in applications.

This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra.

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject.

This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology.

The Kepler conjecture, one of geometry's oldest unsolved problems, was formulated in 1611 by Johannes Kepler and mentioned by Hilbert in his famous 1900 problem list.

Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues.

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 book is an enhanced version of an earlier Russian edition.

This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas.

In many applications of graph theory, graphs are regarded as geometric objects drawn in the plane or in some other surface.

Apollonius's Conics was one of the greatest works of advanced mathematics in antiquity.

In the Fall of 1975 we started a joint project with the ultimate goal of topo- logically classifying real algebraic sets.

The papers in this volume are an outgrowth of the lectures and informal discussions that took place during the workshop on "e;The Geometry of Hamiltonian Systems"e; which was held at MSRl from June 5 to 16, 1989.

This volume derives from a workshop on differential geometry, calculus of vari- ations, and computer graphics at the Mathematical Sciences Research Institute in Berkeley, May 23-25, 1988.

The main object of this book is to reorient and revitalize classical geometry in a way that will bring it closer to the mainstream of contemporary mathematics.

Intercropping is a method of sustaining or improving soil structure by growing two or more crops on the same field.

With the publication of this book I discharge a debt which our era has long owed to the memory of a great mathematician of antiquity: to pub- lish the /llost books"e; of the Conics of Apollonius in the form which is the closest we have to the original, the Arabic version of the Banu Musil.

A recent paper on subfactors of von Neumann factors has stimulated much research in von Neumann algebras.

Convex and discrete geometry is one of the most intuitive subjects in mathematics.

Based on a graduate course given at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes.

Our main purpose in this book is to present an English translation of Desargues' Rough Draft of an Essay on the results of taking plane sections of a cone (1639), the pamphlet with which the modem study of projective geometry began.

This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs.

Substances possessing heterogeneous microstructure on the nanometer and micron scales are scientifically fascinating and technologically useful.

The Fifty-Nine Icosahedra was originally published in 1938 as No.

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.

This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics.

On February 15-17, 1993, a conference on Large Scale Optimization, hosted by the Center for Applied Optimization, was held at the University of Florida.

Although the monograph Progress in Optimization I: Contributions from Aus- tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza- tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization.

Designs and Finite Geometries brings together in one place important contributions and up-to-date research results in this important area of mathematics.

Regenerative gas turbines are attractive alternatives to diesel engines and spark- ignition engines for automobiles and to diesel engines and combined-cycle en- gines for power generation.

This volume is an outgrowth of the research project "e;The Inverse Ga- lois Problem and its Application to Number Theory"e; which was carried out in three academic years from 1999 to 2001 with the support of the Grant-in-Aid for Scientific Research (B) (1) No.

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics, which sometimes do not cover the underlying geometric concepts in detail.

Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few.

In his "e;Geometrie"e; of 1637 Descartes achieved a monumental innovation of mathematical techniques by introducing what is now called analytic geometry.

"e;Spherical soap bubbles"e;, isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry.

Discrete geometry investigates combinatorial properties of configurations of geometric objects.

"e;The appearance of Grunbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists.

In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges.

There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography.

This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition.

A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum.

The present essay stems from a history of polyhedra from 1750 to 1866 written several years ago (as part of a more general work, not published).

This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non- Euclidean Geometry.

Transformation geometry is a relatively recent expression of the successful venture of bringing together geometry and algebra.

Geometry has been defined as that part of mathematics which makes appeal to the sense of sight; but this definition is thrown in doubt by the existence of great geometers who were blind or nearly so, such as Leonhard Euler.

Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry.