Invitation to Geometry

Author: Z. A. Melzak

Publisher: Courier Corporation

ISBN: 0486789489

Category: Mathematics

Page: 240

View: 1513

Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. The author emphasizes connections with calculus and simple mechanics, focusing on developing students' grasp of spatial relationships. Subjects include classical Euclidean material, polygonal and circle isoperimetry, conics and Pascal's theorem, geometrical optimization, geometry and trigonometry on a sphere, graphs, convexity, and elements of differential geometry of curves. Additional material may be conveniently introduced in several places, and each chapter concludes with exercises of varying degrees of difficulty.

An Invitation to Algebraic Geometry

Author: Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves

Publisher: Springer Science & Business Media

ISBN: 1475744978

Category: Mathematics

Page: 164

View: 4685

This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Invitations to Geometry and Topology

Author: Martin R. Bridson

Publisher: Oxford University Press on Demand

ISBN: 9780198507727

Category: Mathematics

Page: 327

View: 8620

This volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader's understanding and to guide them in exciting directions for future investigation. The editors, M.R. Bridson and S.M. Salamon, have each written an article and are accompanied by A.J. Berrick; M.C. Crabb and A.J.B Potter; M. Eastwood and J. Sawon; M.A. Guest; N.J. Hitchin and J.Seade.

An Invitation to Arithmetic Geometry

Author: Dino Lorenzini

Publisher: American Mathematical Soc.

ISBN: 0821802674

Category: Arithmetical algebraic geometry

Page: 397

View: 7875

Extremely carefully written, masterfully thought out, and skillfully arranged introduction ... to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. ... an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject ... a highly welcome addition to the existing literature. --Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject.

An Invitation to Noncommutative Geometry

Author: Matilde Marcolli

Publisher: World Scientific

ISBN: 9812814337

Category: Mathematics

Page: 506

View: 7928

This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulkenhaar); Lectures on Noncommutative Geometry (M Khalkhali); Noncommutative Bundles and Instantons in Tehran (G Landi & W D van Suijlekom); Lecture Notes on Noncommutative Algebraic Geometry and Noncommutative Tori (S Mahanta); Lectures on Derived and Triangulated Categories (B Noohi); Examples of Noncommutative Manifolds: Complex Tori and Spherical Manifolds (J Plazas); D-Branes in Noncommutative Field Theory (R J Szabo). Readership: Researchers in mathematical and theoretical physics, geometry and topology, algebra and number theory.

An Invitation to Web Geometry

Author: Jorge Vitorio Pereira,Luc Pirio

Publisher: Springer

ISBN: 3319145622

Category: Mathematics

Page: 213

View: 2620

This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern’s bound and Trépreau’s algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.

Invitation to Combinatorial Topology

Author: Maurice Fréchet,Ky Fan

Publisher: Courier Corporation

ISBN: 0486147886

Category: Mathematics

Page: 136

View: 3538

Elementary text, accessible to anyone with a background in high school geometry, covers problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, topological polygons, more. Includes 108 figures. 1967 edition.

Plateau's Problem

An Invitation to Varifold Geometry

Author: Frederick J. Almgren

Publisher: American Mathematical Soc.

ISBN: 0821827472

Category: Mathematics

Page: 78

View: 6580

There have been many wonderful developments in the theory of minimal surfaces and geometric measure theory in the past 25 to 30 years. Many of the researchers who have produced these excellent results were inspired by this little book--or by Fred Almgren himself. The book is indeed a delightful invitation to the world of variational geometry. A central topic is Plateau's Problem, which is concerned with surfaces that model the behavior of soap films. When trying to resolve the problem, however, one soon finds that smooth surfaces are insufficient: Varifolds are needed. With varifolds, one can obtain geometrically meaningful solutions without having to know in advance all their possible singularities. This new tool makes possible much exciting new analysis and many new results. Plateau's problem and varifolds live in the world of geometric measure theory, where differential geometry and measure theory combine to solve problems which have variational aspects. The author's hope in writing this book was to encourage young mathematicians to study this fascinating subject further. Judging from the success of his students, it achieves this exceedingly well.

An Introduction to Differential Geometry

Author: T. J. Willmore

Publisher: Courier Corporation

ISBN: 0486282104

Category: Mathematics

Page: 336

View: 7000

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

An Invitation to Quantum Cohomology

Kontsevich's Formula for Rational Plane Curves

Author: Joachim Kock,Israel Vainsencher

Publisher: Springer Science & Business Media

ISBN: 9780817644956

Category: Mathematics

Page: 162

View: 1674

Elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves Viewpoint is mostly that of enumerative geometry Emphasis is on examples, heuristic discussions, and simple applications to best convey the intuition behind the subject Ideal for self-study, for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory

An Invitation to 3-D Vision

From Images to Geometric Models

Author: Yi Ma,Stefano Soatto,Jana Kosecká,S. Shankar Sastry

Publisher: Springer Science & Business Media

ISBN: 0387217797

Category: Computers

Page: 528

View: 1638

This book introduces the geometry of 3-D vision, that is, the reconstruction of 3-D models of objects from a collection of 2-D images. It details the classic theory of two view geometry and shows that a more proper tool for studying the geometry of multiple views is the so-called rank consideration of the multiple view matrix. It also develops practical reconstruction algorithms and discusses possible extensions of the theory.

Invitation to Mathematics

Author: Konrad Jacobs

Publisher: Princeton University Press

ISBN: 9780691025285

Category: Mathematics

Page: 247

View: 6199

Based on a well-received course designed for philosophy students, this book is an informal introduction to mathematical thinking. The work will be rewarding not only for philosophers concerned with mathematical questions but also for serious amateur mathematicians with an interest in the "frontiers" as well as the foundations of mathematics. In what might be termed a sampler of the discipline, Konrad Jacobs discusses an unusually wide range of topics, including such items of contemporary interest as knot theory, optimization theory, and dynamical systems. Using Euclidean geometry and algebra to introduce the mathematical mode of thought, the author then turns to recent developments. In the process he offers what he calls a "Smithsonian of mathematical showpieces": the five Platonic Solids, the Mbius Strip, the Cantor Discontinuum, the Peano Curve, Reidemeister's Knot Table, the plane ornaments, Alexander's Horned Sphere, and Antoine's Necklace. The treatments of geometry and algebra are followed by a chapter on induction and one on optimization, game theory, and mathematical economics. The chapter on topology includes a discussion of topological spaces and continuous mappings, curves and knots, Euler's polyhedral formula for surfaces, and the fundamental group. The last chapter deals with dynamics and contains material on the Game of Life, circle rotation, Smale's "horseshoe," and stability and instability, among other topics.

A Bridge to Advanced Mathematics

Author: Dennis Sentilles

Publisher: Courier Corporation

ISBN: 0486277585

Category: Mathematics

Page: 416

View: 2053

This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.

An Introduction to the Theory of Elasticity

Author: R. J. Atkin,N. Fox

Publisher: Courier Corporation

ISBN: 0486150992

Category: Science

Page: 272

View: 6029

Accessible text covers deformation and stress, derivation of equations of finite elasticity, and formulation of infinitesimal elasticity with application to two- and three-dimensional static problems and elastic waves. 1980 edition.

Lectures on Hyperbolic Geometry

Author: Riccardo Benedetti,Carlo Petronio

Publisher: Springer Science & Business Media

ISBN: 9783540555346

Category: Mathematics

Page: 330

View: 6641

The core of the book is the study of the space of the hyperbolic manifolds endowed with the Chabauty and the geometric topology, and in particular the proof of the hypberbolic surgery theorem in dimension three, based on the representation of three-mainfolds as glued ideal tetrahedra. The development of this main theme requires setting a wide background forming the body of the book: the classical geometry of the hyperbolic space, the Fenchel-Nielsen parametrization of the Teichmüller space, Mostow's rigidity theorem, Margulis' lemma. As a conclusion some features of bounded cohomology, flat fiber bundles and amenable groups are mentioned.

An Invitation to Hypoelliptic Operators and Hörmander's Vector Fields

Author: Marco Bramanti

Publisher: Springer Science & Business Media

ISBN: 3319020870

Category: Mathematics

Page: 150

View: 1358

​Hörmander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients, which have been intensively studied since the late 1960s and are still an active field of research. This text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development.

An Invitation to Alexandrov Geometry

CAT(0) Spaces

Author: Stephanie Alexander,Vitali Kapovitch,Anton Petrunin

Publisher: Springer

ISBN: 9783030053116

Category: Mathematics

Page: 88

View: 8559

Aimed toward graduate students and research mathematicians, with minimal prerequisites this book provides a fresh take on Alexandrov geometry and explains the importance of CAT(0) geometry in geometric group theory. Beginning with an overview of fundamentals, definitions, and conventions, this book quickly moves forward to discuss the Reshetnyak gluing theorem and applies it to the billiards problems. The Hadamard–Cartan globalization theorem is explored and applied to construct exotic aspherical manifolds.