Invitation to Geometry

Invitation to Geometry
Title Invitation to Geometry PDF eBook
Author Z. A. Melzak
Publisher Courier Corporation
Pages 244
Release 2014-01-15
Genre Mathematics
ISBN 0486789489

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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

An Invitation to Algebraic Geometry
Title An Invitation to Algebraic Geometry PDF eBook
Author Karen E. Smith
Publisher Springer Science & Business Media
Pages 173
Release 2013-03-09
Genre Mathematics
ISBN 1475744978

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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.

An Invitation to Arithmetic Geometry

An Invitation to Arithmetic Geometry
Title An Invitation to Arithmetic Geometry PDF eBook
Author Dino Lorenzini
Publisher American Mathematical Society
Pages 397
Release 2021-12-23
Genre Mathematics
ISBN 1470467259

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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.

Invitations to Geometry and Topology

Invitations to Geometry and Topology
Title Invitations to Geometry and Topology PDF eBook
Author Martin R. Bridson
Publisher
Pages 352
Release 2002
Genre Mathematics
ISBN 9780198507727

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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.

An Invitation to Alexandrov Geometry

An Invitation to Alexandrov Geometry
Title An Invitation to Alexandrov Geometry PDF eBook
Author Stephanie Alexander
Publisher Springer
Pages 95
Release 2019-05-08
Genre Mathematics
ISBN 3030053121

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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.

An Invitation to 3-D Vision

An Invitation to 3-D Vision
Title An Invitation to 3-D Vision PDF eBook
Author Yi Ma
Publisher Springer Science & Business Media
Pages 542
Release 2012-11-06
Genre Computers
ISBN 0387217797

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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.

Plateau's Problem

Plateau's Problem
Title Plateau's Problem PDF eBook
Author Frederick J. Almgren (Jr.)
Publisher American Mathematical Soc.
Pages 96
Release 1966
Genre Mathematics
ISBN 0821827472

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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.