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Author : Margaret Wiscamb Hutchinson
Publisher : Merrill Publishing Company
Page : 324 pages
File Size : 40,9 Mb
Release : 1972-01-01
Category : Geometry
ISBN : 0675094275
Author : Meridon Vestal Garner,B. G. Nunley
Publisher : Unknown
Page : 186 pages
File Size : 54,8 Mb
Release : 1971
Category : Geometria
ISBN : 0876203500
Here, explored in an intuitive manner, are the basic concepts of geometry required for effective teaching of elementary school mathematics. The text investigates the metric and non-metric properties of both plane and three-dimensional geometric figures. Also included is a study of plane coordinate geometry. Very precise mathematically, this text will serve as the basis for a more rigorous study of geometry. Answers to selected problems are also provided.
Author : Beauregard Stubblefield
Publisher : Unknown
Page : 280 pages
File Size : 43,8 Mb
Release : 1969
Category : Geometry
ISBN : PSU:000027307458
Author : Gail S. Konkle
Publisher : Unknown
Page : 268 pages
File Size : 51,5 Mb
Release : 1974
Category : Geometry
ISBN : UOM:49015000689126
Author : Melvin Hausner
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 43,5 Mb
Release : 2018-10-17
Category : Mathematics
ISBN : 9780486835396
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
Author : John L. Bell
Publisher : Cambridge University Press
Page : 7 pages
File Size : 44,9 Mb
Release : 2008-04-07
Category : Mathematics
ISBN : 9780521887182
A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.
Author : John Snygg
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 42,8 Mb
Release : 2011-12-09
Category : Mathematics
ISBN : 9780817682835
Differential geometry is the study of the curvature and calculus of curves and surfaces. A New Approach to Differential Geometry using Clifford's Geometric Algebra simplifies the discussion to an accessible level of differential geometry by introducing Clifford algebra. This presentation is relevant because Clifford algebra is an effective tool for dealing with the rotations intrinsic to the study of curved space. Complete with chapter-by-chapter exercises, an overview of general relativity, and brief biographies of historical figures, this comprehensive textbook presents a valuable introduction to differential geometry. It will serve as a useful resource for upper-level undergraduates, beginning-level graduate students, and researchers in the algebra and physics communities.
Author : Hajime Satō
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 45,9 Mb
Release : 1999
Category : Mathematics
ISBN : 0821810464
The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Möbius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.
Author : Imre Bárány,K. Böröczky
Publisher : Unknown
Page : 456 pages
File Size : 53,6 Mb
Release : 1997
Category : Geometry
ISBN : UOM:39015050320566
Author : Tristan Needham
Publisher : Princeton University Press
Page : 530 pages
File Size : 43,8 Mb
Release : 2021-07-13
Category : Mathematics
ISBN : 9780691203706
An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
Author : Gergely Ambrus,Imre Bárány,Károly J. Böröczky,Gábor Fejes Tóth,János Pach
Publisher : Springer
Page : 458 pages
File Size : 52,7 Mb
Release : 2018-11-03
Category : Mathematics
ISBN : 9783662574133
This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field. The readers will find a variety of modern topics and many fascinating open problems that may serve as starting points for research.
Author : Chris J. Isham
Publisher : Allied Publishers
Page : 308 pages
File Size : 43,8 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 8177643169
Author : J. Akiyama
Publisher : Springer Nature
Page : 642 pages
File Size : 51,7 Mb
Release : 2024
Category : Geometry
ISBN : 9789819986088
This book is written in a style that uncovers the mathematical theories hidden in our daily lives, using examples of patterns that appear in nature, arts, traditional crafts, as well as mathematical mechanics in architectural techniques. The authors believe that through conversations between students and mathematicians, readers may learn about the methods used by the originators of these theoriestheir trials, errors, and triumphsin reaching their various conclusions. The goal is to help readers refine their mathematical sense in terms of formulating valuable questions and pursuing them. In addition, the book aims to provide enjoyment in the application of mathematical principles to beautiful art and design by using examples that highlight the wonders and mysteries of these works found in our daily lives. To achieve these goals, the book tackles the latest exquisite results on polygons and polyhedra and the dynamic history of geometric research found around us. The term "intuitive geometry" was coined by Lszlo Fejes Tth and refers to the kind of geometry which, in Hilbert's words, can be explained to and appeal to the "man on the street." This book enables readers to enjoy intuitive geometry informally and instinctively. It does not require more than a high school level of knowledge but calls for a sense of wonder, intuition, and mathematical maturity. In this second edition, many new results, and elegant proofs on a variety of topics have been added, enhancing the books rich content even further.
Author : David Eisenbud,Joe Harris
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 43,9 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387226392
Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Author : Henri Cartan
Publisher : Courier Corporation
Page : 178 pages
File Size : 53,5 Mb
Release : 2012-07-06
Category : Mathematics
ISBN : 9780486139111
"Cartan's work provides a superb text for an undergraduate course in advanced calculus, but at the same time it furnishes the reader with an excellent foundation for global and nonlinear algebra."—Mathematical Review "Brilliantly successful."—Bulletin de l'Association des Professeurs de Mathematiques "The presentation is precise and detailed, the style lucid and almost conversational . . . clearly an outstanding text and work of reference."—Annales Cartan's Formes Differentielles was first published in France in 1967. It was based on the world-famous teacher's experience at the Faculty of Sciences in Paris, where his reputation as an outstanding exponent of the Bourbaki school of mathematics was first established. Addressed to second- and third-year students of mathematics, the material skillfully spans the pure and applied branches in the familiar French manner, so that the applied aspects gain in rigor while the pure mathematics loses none of its dignity. This book is equally essential as a course text, as a work of reference, or simply as a brilliant mathematical exercise.
