A Course in Modern Geometries

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Author: Judith N. Cederberg

Publisher: Springer Science & Business Media

ISBN: 1475738315

Category: Mathematics

Page: 233

View: 5125

A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 introduces Euclid's geometry and the basic ideas of non-Euclidean geometry. The synthetic approach of Chapters 1 - 2 is followed by the analytic treatment of transformations of the Euclidean plane in Chapter 3. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3 - 4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. Each chapter includes a list of suggested sources for applications and/or related topics.

Modern Geometries

Non-Euclidean, Projective, and Discrete

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Author: Michael Henle

Publisher: Pearson College Division

ISBN: 9780130323132

Category: Mathematics

Page: 389

View: 1935

Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.

A Survey of Classical and Modern Geometries

With Computer Activities

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Author: Arthur Baragar

Publisher: Pearson College Division

ISBN: N.A

Category: Mathematics

Page: 370

View: 1183

This book emphasizes the beauty of geometry using a modern approach. Models & computer exercises help readers to cultivate geometric intuition.Topics include Euclidean Geometry, Hand Constructions, Geometer's Sketch Pad, Hyperbolic Geometry, Tilings & Lattices, Spherical Geometry, Projective Geometry, Finite Geometry, and Modern Geometry Research.Ideal for geometry at an intermediate level.

Modern Geometry

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Author: David A. Thomas

Publisher: Brooks/Cole Publishing Company

ISBN: 9780534365509

Category: Mathematics

Page: 348

View: 4453

MODERN GEOMETRY was written to provide undergraduate and graduate level mathematics education students with an introduction to both Euclidean and non-Euclidean geometries, appropriate to their needs as future junior and senior high school mathematics teachers. MODERN GEOMETRY provides a systematic survey of Euclidean, hyperbolic, transformation, fractal, and projective geometries. This approach is consistent with the recommendations of the National Council of Teachers of Mathematics (NCTM), the International Society for Technology in Education (ISTE), and other professional organizations active in the preparation and continuing professional development of K-12 mathematics teachers.

Modern Geometry— Methods and Applications

Part II: The Geometry and Topology of Manifolds

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Author: B.A. Dubrovin,A.T. Fomenko,S.P. Novikov

Publisher: Springer Science & Business Media

ISBN: 9780387961620

Category: Mathematics

Page: 432

View: 6920

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.

Mechanical Theorem Proving in Geometries

Basic Principles

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Author: Wen-tsün Wu

Publisher: Springer Science & Business Media

ISBN: 9783211825068

Category: Computers

Page: 288

View: 907

This book is a translation of Professor Wu's seminal Chinese book of 1984 on Automated Geometric Theorem Proving. The translation was done by his former student Dongming Wang jointly with Xiaofan Jin so that authenticity is guaranteed. Meanwhile, automated geometric theorem proving based on Wu's method of characteristic sets has become one of the fundamental, practically successful, methods in this area that has drastically enhanced the scope of what is computationally tractable in automated theorem proving. This book is a source book for students and researchers who want to study both the intuitive first ideas behind the method and the formal details together with many examples.

Modern Geometry with Applications

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Author: George A. Jennings

Publisher: Springer Science & Business Media

ISBN: 1461208556

Category: Mathematics

Page: 204

View: 4861

This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.

An Essay on the Foundations of Modern Geometry

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Author: Bertrand Russell

Publisher: Courier Corporation

ISBN: 9780486495552

Category: Mathematics

Page: 224

View: 7014

The author, a Nobel Laureate and one of the 20th century's most important logicians, asks and answers basic questions about the intersection of philosophy and higher mathematics. 1897 edition.

Fundamentals of Modern Geometry for College Students

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Author: Honore P Mavinga

Publisher: Xulon Press

ISBN: 9781625093127

Category: Mathematics

Page: 206

View: 1385

This text presents the essential of affine, Euclidean, projective and hyperbolic geometries in a transformational perspective as inaugurated by F. Klein. It originated from the author's 2-volume textbook in French 'Geometrie Affine et Projective' Editions Ceda, Abidjan. It can be used as a one semester Modern Geometry course for second year college math students, especially those who are prospective high school mathematics teachers. The text starts with a concise historical development of geometry from the times of Thales and Euclid to the 20th century, highlighting significant discoveries in Geometry. Honore P. Mavinga is a Professor of Mathematics. He is a native of the Democratic Republic of the Congo. He received his Master's and Doctoral degree at the Universite Catholique de Louvain in Belgium and an extended study diploma from the Universite de Paris 5. Following his studies in Europe, he received a postdoctoral fellowship grant from the US state department for a semester at Princeton. He returned to Africa where he taught at Universite de Kinshasa (Congo) then at Universite d'Abidjan (Cote d' Ivoire). During that time he served as one of the 12 members of the board committee of the African Mathematical Union which held its initial Pan African Convention in Rabat (Morocco) in 1976. He also taught as visiting associate at the University of the South Sewanee Tennessee for one year and the next year at Cuttington College (Liberia). In 1989 he moved with his family to the USA where he taught at University of Wisconsin-Eau Claire, WI and more recently at Liberty University in Virginia. Honore Mavinga confessed Christ publicly during the campaign 'Explo '84' sponsored by the Campus Crusade for Christ in Abidjan. He also enjoys cooking and singing.

College Geometry

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Author: Howard Whitley Eves,Howard Eves

Publisher: Jones & Bartlett Learning

ISBN: 9780867204759

Category: Mathematics

Page: 370

View: 4294

Mathematics

Modern Geometry

An Elementary Treatise on the Geometry of the Triangle and the Circle

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Author: Roger Arthur Johnson

Publisher: N.A

ISBN: N.A

Category: Geometry, Modern

Page: 319

View: 1069

Von Fermat bis Minkowski

Eine Vorlesung über Zahlentheorie und ihre Entwicklung

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Author: W. Scharlau,H. Opolka

Publisher: Springer-Verlag

ISBN: 3642618499

Category: Mathematics

Page: 226

View: 446

Unvergängliche Geometrie

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Author: H.S. Coxeter

Publisher: Springer-Verlag

ISBN: 3034851510

Category: Juvenile Nonfiction

Page: 558

View: 4586

Journey Into Geometries

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Author: Marta Sved

Publisher: Cambridge University Press

ISBN: 9780883855003

Category: Mathematics

Page: 182

View: 1391

Informal introduction into the non-Euclidean geometries through a series of dialogues involving Alice in Wonderland.