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Author: Z. A. Melzak Publisher: Courier Corporation ISBN: 0486789489 Category : Mathematics Languages : en Pages : 244
Book Description
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.
Author: Z. A. Melzak Publisher: Courier Corporation ISBN: 0486789489 Category : Mathematics Languages : en Pages : 244
Book Description
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.
Author: Karen E. Smith Publisher: Springer Science & Business Media ISBN: 1475744978 Category : Mathematics Languages : en Pages : 173
Book Description
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.
Author: Dino Lorenzini Publisher: American Mathematical Society ISBN: 1470467259 Category : Mathematics Languages : en Pages : 397
Book Description
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.
Author: Stephanie Alexander Publisher: Springer ISBN: 3030053121 Category : Mathematics Languages : en Pages : 95
Book Description
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.
Author: Frederick J. Almgren (Jr.) Publisher: American Mathematical Soc. ISBN: 0821827472 Category : Mathematics Languages : en Pages : 96
Book Description
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.
Author: Yi Ma Publisher: Springer Science & Business Media ISBN: 0387217797 Category : Computers Languages : en Pages : 542
Book Description
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.
Author: Jorge Vitório Pereira Publisher: Springer ISBN: 3319145622 Category : Mathematics Languages : en Pages : 229
Book Description
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.
Author: Maurice Fréchet Publisher: Courier Corporation ISBN: 0486147886 Category : Mathematics Languages : en Pages : 148
Book Description
An elementary text that can be understood by anyone with a background in high school geometry, Invitation to Combinatorial Topology offers a stimulating initiation to important topological ideas. This translation from the original French does full justice to the text's coherent presentation as well as to its rich historical content. Subjects include the problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, and topological polygons. Considerations of the topological classification of closed surfaces cover elementary operations, use of normal forms of polyhedra, reduction to normal form, and application to the geometric theory of functions. 1967 edition. 108 figures. Bibliography. Index.
Author: Matilde Marcolli Publisher: World Scientific ISBN: 9814475629 Category : Science Languages : en Pages : 515
Book Description
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.
Author: Joachim Kock Publisher: Springer Science & Business Media ISBN: 0817644954 Category : Mathematics Languages : en Pages : 162
Book Description
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
Author: Z. A. Melzak
Author: Z. A. Melzak
Author: Karen E. Smith
Author: Dino Lorenzini
Author: Stephanie Alexander
Author: Frederick J. Almgren (Jr.)
Author: Yi Ma
Author: Jorge Vitório Pereira
Author: Maurice Fréchet
Author: Matilde Marcolli
Author: Joachim Kock