Book Description

The study of two-dimensional analytic geometry has gone in and out of fashion several times over the past century, however this classic field of mathematics has once again become popular due to the growing power of personal computers and the availability of powerful mathematical software systems, such as Mathematica, that can provide an
interactive environment for studying the field. By combining the power of Mathematica with an analytic geometry software system called Descarta2D, the author has succeeded in meshing an ancient field of study with modern computational tools, the result being a simple, yet powerful, approach to studying analytic geometry. Students, engineers and mathematicians alike who are interested in analytic geometry can use this book and software for the study, research or just plain enjoyment of analytic geometry.

Mathematica provides an attractive environment for studying analytic geometry. Mathematica supports both numeric and symbolic computations meaning that geometry problems can be solved for special cases using numbers, as well as general cases producing formulas. Mathematica also has good facilities for producing graphical plots which are useful for visualizing the graphs of two-dimensional geometry.

* A classic study in analytic geometry, complete with in-line Mathematica dialogs illustrating every concept as it is introduced
* Excellent theoretical presentation
*Fully explained examples of all key concepts
*Interactive Mathematica notebooks for the entire book
* Provides a complete computer-based environment for study of analytic geometry
* All chapters and reference material are provided on CD-ROM in addition to being printed in the book
* Complete software system: Descarta2D
* A software system, including source code, for the underlying computer implementation, called Descarta2D is provided
* Part VII of the book is a listing of the (30) Mathematica files supporting Descarta2D; the source code is also supplied on CD-ROM
* Explorations
* More than 120 challenging problems in analytic geometry are posed;Complete solutions are provided both as interactive Mathematica notebooks on CD-ROM and as printed material in the book
* Mathematica and Descarta2D Hints expand the reader's knowledge and understanding of Descarta2D and Mathematica
* Sortware developed with Mathematica 3.0 and is compatible with Mathematica 4.0
* Detailed reference manual
* Complete documentation for Descarta2D
* Fully integrated into the Mathematica Help Browser ... Read more

Book Description

This is the first account in book form of the theory of harmonic morphisms between Riemannian manifolds. Harmonic morphisms are maps which preserve Laplace's equation. They can be characterized as harmonic maps which satisfy an additional first order condition. Examples include harmonic functions, conformal mappings in the plane, and holomorphic functions with values in a Riemann surface. There are connections with many conepts in differential geometry, for example, Killing fields, geodesics, foliations, Clifford systems, twistor spaces, Hermitian structures, iso-parametric mappings, and Einstein metrics and also the Brownain pathpreserving maps of probability theory. Giving a complete account of the fundamental aspects of the subject, this book is self-contained, assuming only a basic knowledge of differential geometry. ... Read more

Book Description

This is the first comprehensive treatment of the geometry of complex hyperbolic space, a rich area of research with numerous connections to other branches of mathematics, including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie groups, and harmonic analysis. ... Read more

Book Description

This is a comprehensive treatment of Minkowski geometry. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterizations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces--a fascinating geometrical interplay among the various roles of the ball in Euclidean space.Later chapters deal with trigonometry and differential geometry in Minkowski spaces.The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. ... Read more

Book Description

A major flaw in semi-Riemannian geometry is a shortage ofsuitable types of maps between semi-Riemannian manifolds that willcompare their geometric properties. Here, a class of such maps calledsemi-Riemannian maps is introduced. The main purpose of this book isto present results in semi-Riemannian geometry obtained by theexistence of such a map between semi-Riemannian manifolds, as well asto encourage the reader to explore these maps. The first three chapters are devoted to the development of fundamentalconcepts and formulas in semi-Riemannian geometry which are usedthroughout the work. In Chapters 4 and 5 semi-Riemannian maps and suchmaps with respect to a semi-Riemannian foliation are studied. Chapter6 studies the maps from a semi-Riemannian manifold to 1-dimensionalsemi- Euclidean space. In Chapter 7 some splitting theorems areobtained by using the existence of a semi-Riemannian map. Audience: This volume will be of interest to mathematicians andphysicists whose work involves differential geometry, global analysis,or relativity and gravitation. ... Read more

Book Description

The focus in this book is on the theory of regulators and secondary invariants, with articles written and refereed by experts in their respective fields. A short historical and mathematical overview of the theory of regulators from its number theoretic origins, and its connections to analysis, topology, differential geometry, and algebra, is presented by the editors in the introduction, with key topics noted as follows: hyperbolic volume and the Borel regulator, the Chern-Simons invariant, the Bloch-Beilinson regulator, polylogarithms (classical and elliptic), p-adic analalogues, and analytic torsion.

Contributors include:D. Blasius, S. Bloch, C. Deninger, H. Esnault, H. Gangl, A. Goncharov, K. Khler, K. Knnemann, A. Levin, J. Lott, V. Maillot, J. Rogawski, and J. Wildeshaus.

This work is an outgrowth of a conference held at the Hebrew University in Jerusalem on "Regulators in Analysis, Geometry and Number Theory", and should appeal to a broad audience of graduate students and research mathematicians.

Series: Progress in Mathematics, Vol. 171 ... Read more

Book Description

This is the first text to be published on stochastic Finsleriangeometry.The theory is rigorously presented and several applicationsin ecology, evolution and epidemiology are described. Amongst thevarious topics covered are the role of curvature in Finsleriandiffusions, Nelson's stochastic mechanics, nonlinear (Finslerian)filtering and entropy production. Two appendices deal with,respectively, the stochastic Hodge theory of Finslerian harmonicforms, and the theory of 2-dimensional Finsler spaces. The latterplays an important role in the applications described in the text.Audience: This volume will be of interest to probabilists,applied mathematicians, mathematical biologists and geometers. It canalso be recommended as a supplementary graduate text. ... Read more

Book Description

In recent years, there has been tremendous progress on the interface of geometry and mathematical physics. This book reflects the expanded articles of several lectures in these areas delivered at the University of Adelaide, with an audience of primarily graduate students. The aim of this volume is to provide surveys of recent progress without assuming too much prerequisite knowledge and with a comprehensive bibliography, so that researchers and graduate students in geometry and mathematical physics will benefit. The contributors cover a number of areas in mathematical physics. Chapter 1 offers a self-contained derivation of the partition function of Chern-Simons gauge theory in the semiclassical approximation. Chapter 2 considers the algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory, including their relation to the braid group, quantum groups and infinite dimensional Lie algebras. Chapter 3 surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. Chapter 4 examines the variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds. Chapter 5 is a review of monopoles in non-Abelian gauge theories and the various approaches to understanding them. Chapter 6 covers much of the exciting recent developments in quantum cohomology, including relative Gromov-Witten invariant, birational geometry, naturality and mirror symmetry. Chapter 7 explains the physics origin of the Seiberg-Witten equations in four-manifold theory and a number of important concepts in quantum field theory, such as vacuum, mass gap, (super)symmetry, anomalies and duality. Contributors: D.H. Adam, P. Bouwknegt, A.L. Carey, A. Harris, E. Langmann, M.K. Murray, Y. Ruan, S. Wu D. H. Adams: Semiclassical Approximation in Chern-Simons Gauge Theory P. Bouwknegt: The Knizhnik-Zamolodchikov Equations A. L. Carey and E. Langmann: Loop Groups and Quantum Fields A. Harris: Some Applications of Variational Calculus in Hermitian Geometry M. K. Murray: Monopoles Y. Ruan: On Gromov-Witten Invariants and Quantum Cohomology S. Wu The Geometry and Physics of the Seiberg-Witten Equations ... Read more

Book Description

This fully revised and updated Second Edition of an incomparable reference text bridges the gap between modern differential geometry and the mathematical physics of general relativity by providing an invariant treatment of Lorentzian geometry -- reflecting the more complete understanding of Lorentzian geometry achieved since the publication of the previous edition. ... Read more

Reviews (1)

Okay book!
The book is a thouroguh cover of calculus, but doesn not have many good example problems to llok at.It is a good book, but if you're a person who needs to seee example problems, this book is not for you. ... Read more

Book Description

In these notes on "Projective Modules and Complete Intersections" an account on the recent developments in research on this subject is presented. The author's preference for the technique of Patching isotopic isomorphisms due to Quillen, formalized by Plumsted, over the techniques of elementary matrices is evident here. The treatment of Basic Element theory here incorporates Plumstead's idea of the "generalized dimension functions". These notes are highly selfcontained and should be accessible to any graduate student in commutative algebra or algebraic geometry. They include fully self-contained presentations of the theorems of Ferrand-Szpiro, Cowsik-Nori and the techniques of Lindel. ... Read more

Book Description

A translation of a Soviet text covering plane analytic geometry and solid analytic geometry. ... Read more

Reviews (2)

overall, pretty good book
The book did have some irritating mistakes in the back (no more than the average math book), but I give it a thumbs up for being pretty clear and readable throughout. Some problems I had using the book though are:

-it doesn't provide adequate examples, too few and not on the same level as the problems
-towards the end, it loses some coherence by splitting up related ideas into many formulas and notations.

Overall word, the book teaches pretty well, but a good teacher is really needed to wade through some of the book.

ehhhh
i am using this book in my cal 3 class at this very moment. there are many mistakes in the text and the answers in the back of the book are sometimes wrong or they are factored in a weird way. the text is very easy to understand and with all it's shortcomings i dig this book ... Read more

Book Description

This monograph deals with the Riemannian geometry of both symplectic and contact manifolds, with particular emphasis on the latter. The text is carefully presented. Topics unfold systematically from Chapter 1, which examines the generaltheory of symplectic manifolds. Principal circle bundles (Chapter 2) are then discussed as a prelude to the Boothby--Wang fibration of a compact regular contact manifold in Chapter 3, which deals with the general theory of contact manifolds. Chapter 4 focuses on the general setting of Riemannian metrics associated with both symplectic and contact structures, and Chapter 5 is devoted to integral submanifolds of the contact subbundle. Topics treated in the subsequent chapters include Sasakian manifolds, the important study of the curvature of contact metric manifolds, submanifold theory in both the K¿hler and Sasakian settings, tangent sphere bundles, curvature functionals, complex contact manifolds and 3 Sasakian manifolds. The book serves both as a general reference for mathematicians to the basic properties of symplectic and contact manifolds and as an excellent resource for graduate students and researchers in the Riemanniangeometric arena. The prerequisite for this text is a basic course in Riemannian geometry. ... Read more

Book Description

This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students. The techniques in this area borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic, and analytical geometry. In turn, these latter areas have been enriched over the years by the study of problems in several complex variables addressed here. The authors, M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, include extensive preliminary material to make the book accessible to nonspecialists.

One of the most important topics that the authors address here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds. They present the main results in this area with a novel and self-contained approach. The book also devotes considerable attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions. The authors also give a thorough comparison of the various nondegeneracy conditions for manifolds and mappings and present new geometric interpretations of these conditions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role and are presented in a setting that is both general and elementary. ... Read more

Reviews (1)

Excellent reference book for researchers in CR geometry
The book presents an excellent discussions on some of the most active research fields in the subject of several complex variables. It includes a fairly complete list of references and an accurate account of the historical backgrounds of the materials. ... Read more

Book Description

Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving.Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness.The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations.The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies. ... Read more

Reviews (1)

An Excellent Introductory Book on the Study of Curves
John W. Rutter's book is an excellent introduction to the fascinating study of curves. Most introductory books on differential and algebraic geometry are somewhat incomprehensible. Rutter's book is at a U.S. college undergraduate level with many examples and explanations of notions passed over in other introductions. His book is a very good companion to the fine book "Curves and Singularities" by Bruce and Giblin. I highly recommend this book to anyone wanting to learn more about beautiful and interesting world of curves. ... Read more

Book Description

This text assesses the various merits of Kelvin's structure, with regard to the problem of the division of three- dimensional space into cells of equal volume, and of that discovered by Weaire and Phelan. ... Read more

Reviews (1)

A century of work on this problem
William Kelvin is mostly remembered today for the attachment of his name to the absolute temperature scale, in recognition of his original work on low temperature research in the late 19th century.

But during his long career, he investigated many other outstanding problems of the time. One such problem is the subject of this book. The editors chose Kelvin's pioneering paper to kick off the book. They then summarised over a century's effort by selecting papers by other prominent scientists tackling the issue.

The book is good for a historical perspective. Though undoubtedly some will be attracted mainly by Kelvin's work. ... Read more