Higher Geometry

Author : Frederick S. Woods
Publisher : Courier Corporation
Page : 442 pages
File Size : 46,7 Mb
Release : 2013-10-29
Category : Mathematics
ISBN : 9780486159560

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Higher Geometry by Frederick S. Woods Pdf

For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works. With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study of one-, two-, three-, and four-dimensional coordinated systems, the concepts they entail, and their associated geometrical elements. This study culminates with a discussion of n-dimensional geometry in an abstract sense, of which the earlier subjects form concrete illustrations. As each system of coordinates is introduced, the meaning of the linear and quadratic equations is studied, with principal emphasis on the interpretation of equations as well as on a knowledge of useful geometrical facts. The principle of duality is kept at the forefront, and the nature of imaginary elements and the conventional character of the locus of infinity, dependent upon the type of coordinates used, are carefully explained.

Author : Olivier Debarre
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 40,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475754063

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Higher-Dimensional Algebraic Geometry by Olivier Debarre Pdf

The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction.

Author : Thomas Peternell,Joichi Miyaoka
Publisher : Birkhäuser
Page : 221 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034888936

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Geometry of Higher Dimensional Algebraic Varieties by Thomas Peternell,Joichi Miyaoka Pdf

This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

Author : Nathan Scholfield
Publisher : Unknown
Page : 506 pages
File Size : 55,8 Mb
Release : 1845
Category : Geometry
ISBN : STANFORD:36105046444365

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Higher Geometry and Trigonometry by Nathan Scholfield Pdf

Author : Marcel Berger
Publisher : Springer Science & Business Media
Page : 831 pages
File Size : 47,9 Mb
Release : 2010-07-23
Category : Mathematics
ISBN : 9783540709978

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Geometry Revealed by Marcel Berger Pdf

Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended... In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations. Marcel Berger is t he author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.

Author : Frederick S. Woods
Publisher : Forgotten Books
Page : 437 pages
File Size : 41,7 Mb
Release : 2015-06-14
Category : Mathematics
ISBN : 1330071905

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Higher Geometry by Frederick S. Woods Pdf

Excerpt from Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry The present book is the outgrowth of lectures given at various times to students of the later undergraduate and earlier graduate years. It aims to present some of the general concepts and methods which are necessary for advanced work in algebraic geometry (as distinguished from differential geometry), but which are not now accessible to the student in any one volume, and thus to bridge the gap between the. usual text in analytic geometry and treatises or articles on special topics. With this object in view the author has assumed very little mathematical preparation on the part of the student beyond that acquired in elementary courses in calculus and plane analytic geometry. In addition it has been necessary to assume a slight knowledge of determinants, especially as applied to the solution of linear equations, such as may be acquired in a very short course on the subject. But it has not been assumed that the student has had a course in higher algebra, including matrices, linear substitutions, invariants, and similar topics, and no effort has been made to include a discussion of these subjects in the text. This restriction in the tools to be used necessitates at times modes of expression and methods of proof which are a little cumbersome, but the appeal to a larger number of readers seems to justify the occasional lack of elegance. In preparing the text one of the greatest problems has consisted in determining what matters to exclude. It is-obvious that an introduction to geometry cannot contain all that is known on any subject or even refer briefly to all general topics. The matter of selection is necessarily one of individual judgment. One large domain of geometry has been definitely excluded from the plan of the book; namely, that of differential geometry. In the field which is left the author cannot dare to hope that his choice of material will agree exactly with that which would be made by any other teacher. He hopes, however, that his choice has been sufficiently wise to make the book useful to many besides himself. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Olivier Debarre
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 42,9 Mb
Release : 2001-06-26
Category : Mathematics
ISBN : 0387952276

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Higher-Dimensional Algebraic Geometry by Olivier Debarre Pdf

The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction.

Author : Nikolaĭ Vladimirovich Efimov
Publisher : Unknown
Page : 566 pages
File Size : 49,9 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:49015000698168

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Higher Geometry by Nikolaĭ Vladimirovich Efimov Pdf

Author : Zhizhin, Gennadiy Vladimirovich
Publisher : IGI Global
Page : 286 pages
File Size : 47,8 Mb
Release : 2018-08-03
Category : Technology & Engineering
ISBN : 9781522569695

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The Geometry of Higher-Dimensional Polytopes by Zhizhin, Gennadiy Vladimirovich Pdf

The majority of the chemical elements form chemical compounds with molecules of higher dimension (i.e., substantially exceeding three). This fact is very important for the analysis of molecular interactions in various areas: nanomedicine, nanotoxicology, and quantum biology. The Geometry of Higher-Dimensional Polytopes contains innovative research on the methods and applications of the structures of binary compounds. It explores the study of geometry polytopes from a higher-dimensional perspective, taking into account the features of polytopes that are models of chemical compounds. While highlighting topics including chemical compounds, symmetry transformation, and DNA structures, this book is ideally designed for researchers, academicians, and students seeking current research on dimensions present in binary compounds.

Author : Frederick Shenstone Woods
Publisher : Palala Press
Page : 440 pages
File Size : 55,9 Mb
Release : 2018-02-15
Category : Mathematics
ISBN : 1377571599

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Higher Geometry: An Introduction to Advanced Methods in Analytic Geometry by Frederick Shenstone Woods Pdf

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Xinghe Zhou,Mingsheng Yang
Publisher : Unknown
Page : 0 pages
File Size : 44,7 Mb
Release : 2014
Category : Mathematics
ISBN : 1842657747

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Higher Geometry by Xinghe Zhou,Mingsheng Yang Pdf

This book provides an introduction to plane projective geometry and affine geometry. Its main contents involve projective plane, projective transformations, transformation groups and geometry, the projective and affine theories of conics, the historic development track of geometry and so on. The book is easy both to teach and to learn, which is typical of its well-knit system, refined content and colorful pictures. The book can act as text-book for undergraduates in maths' majors as well as reference book for faculty concerned.

Author : William Caspar Graustein
Publisher : Unknown
Page : 512 pages
File Size : 45,9 Mb
Release : 1930
Category : Geometry
ISBN : STANFORD:36105033274874

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Introduction to Higher Geometry by William Caspar Graustein Pdf

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 49,5 Mb
Release : 2005-08-09
Category : Mathematics
ISBN : 9780387255309

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The Four Pillars of Geometry by John Stillwell Pdf

This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises

Author : Felix Klein
Publisher : Springer
Page : 315 pages
File Size : 41,7 Mb
Release : 2016-06-29
Category : Education
ISBN : 9783662494455

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Elementary Mathematics from a Higher Standpoint by Felix Klein Pdf

These three volumes constitute the first complete English translation of Felix Klein’s seminal series “Elementarmathematik vom höheren Standpunkte aus”. “Complete” has a twofold meaning here: First, there now exists a translation of volume III into English, while until today the only translation had been into Chinese. Second, the English versions of volume I and II had omitted several, even extended parts of the original, while we now present a complete revised translation into modern English. The volumes, first published between 1902 and 1908, are lecture notes of courses that Klein offered to future mathematics teachers, realizing a new form of teacher training that remained valid and effective until today: Klein leads the students to gain a more comprehensive and methodological point of view on school mathematics. The volumes enable us to understand Klein’s far-reaching conception of elementarisation, of the “elementary from a higher standpoint”, in its implementation for school mathematics./div This volume II presents a paradigmatic realisation of Klein’s approach of elementarisation for teacher education. It is shown how the various geometries, elaborated particularly since the beginning of the 19th century, are revealed as becoming unified in a new restructured geometry. As Klein liked to stress: “Projective geometry is all geometry”. Non-Euclidean geometry proves to constitute a part of this unifying process. The teaching of geometry is discussed in a separate chapter, which provides moreover important information on the history of geometry teaching and an international comparison.

Author : Audun Holme
Publisher : Springer Science & Business Media
Page : 519 pages
File Size : 53,6 Mb
Release : 2010-09-23
Category : Mathematics
ISBN : 9783642144417

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Geometry by Audun Holme Pdf

This is a revised edition of the ?rst printing which appeared in 2002. The book is based on lectures at the University of Bergen, Norway.Over the years these lectures have covered many different aspects and facets of the wonderful ?eld of geometry. Consequently it has never been possible to give a full and ?nal account of geometry as such, at an undergraduatelevel: A carefully consideredselection has always been necessary. The present book constitutes the main central themes of these selections. One of the groups I am aiming at, is future teachers of mathematics. All too oftenthe textsdealingwith geometrywhichgo intothe syllabusforteacher-students present the material in ways which appear pedantic and formalistic, suppressing the very powerful and dynamic character of this old ?eld, which at the same time so young. Geometry is a ?eld of mathematical insight, research, history and source of artistic inspiration. And not least important, an integral part of our common cultural heritage.