Author : Marcel Berger
Publisher : Springer Science & Business Media
Release :2009-01-21
Total pages :432
Language : EN, FR, DE, ES
ISBN : 3540116583

Volume I of this 2-volume textbook provides a lively and readable presentation of large parts of classical geometry. For each topic the author presents an esthetically pleasing and easily stated theorem - although the proof may be difficult and concealed. The mathematical text is illustrated with figures, open problems and references to modern literature, providing a unified reference to geometry in the full breadth of its subfields and ramifications.

Author : Serge Lang,Gene Murrow
Publisher : Springer Science & Business Media
Release :2013-04-17
Total pages :394
Language : EN, FR, DE, ES
ISBN : 9781475720228

At last: geometry in an exemplary, accessible and attractive form! The authors emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications. They also show students the fundamental concepts and the difference between important results and minor technical routines. Altogether, the text presents a coherent high school curriculum for the geometry course, naturally backed by numerous examples and exercises.

Author : V. V. Prasolov, V. M. Tikhomirov
Publisher : American Mathematical Soc.
Release :2001-06-12
Total pages :257
Language : EN, FR, DE, ES
ISBN : 9781470425432

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Author : Marcel Berger
Publisher : Springer Science & Business Media
Release :2009-01-21
Total pages :406
Language : EN, FR, DE, ES
ISBN : 3540170154

This is the second of a two-volume textbook that provides a very readable and lively presentation of large parts of geometry in the classical sense. For each topic the author presents a theorem that is esthetically pleasing and easily stated, although the proof may be quite hard and concealed. Yet another strong trait of the book is that it provides a comprehensive and unified reference source for the field of geometry in the full breadth of its subfields and ramifications.

Author : Michele Audin
Publisher : Springer Science & Business Media
Release :2002-09-19
Total pages :361
Language : EN, FR, DE, ES
ISBN : 3540434984

Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michle Audin, professor at the University of Strasbourg, has written a book allowing them to remedy this situation and, starting from linear algebra, extend their knowledge of affine, Euclidean and projective geometry, conic sections and quadrics, curves and surfaces. It includes many nice theorems like the nine-point circle, Feuerbach's theorem, and so on. Everything is presented clearly and rigourously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for most of the exercises are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master's level to discover geometry and deepen their knowledge and understanding.

Author : Simon Kirwan Donaldson,S. K. Donaldson,P. B. Kronheimer
Publisher : Oxford University Press
Release :1990
Total pages :440
Language : EN, FR, DE, ES
ISBN : 0198502699

This book provides the first lucid and accessible account to the modern study of the geometry of four-manifolds. It has become required reading for postgraduates and research workers whose research touches on this topic. Pre-requisites are a firm grounding in differential topology, andgeometry as may be gained from the first year of a graduate course. The subject matter of this book is the most significant breakthrough in mathematics of the last fifty years, and Professor Donaldson won a Fields medal for his work in the area. The authors start from the standpoint that thefundamental group and intersection form of a four-manifold provides information about its homology and characteristic classes, but little of its differential topology. It turns out that the classification up to diffeomorphism of four-manifolds is very different from the classification of unimodularforms and that the study of this question leads naturally to the new Donaldson invariants of four-manifolds. A central theme of this book is that the appropriate geometrical tools for investigating these questions come from mathematical physics: the Yang-Mills theory and anti-self dual connectionsover four-manifolds. One of the many consquences of this theory is that 'exotic' smooth manifolds exist which are homeomorphic but not diffeomorphic to (4, and that large classes of forms cannot be realized as intersection forms whereas distinct manifolds may share the same form. These result havehad far-reaching consequences in algebraic geometry, topology, and mathematical physics, and will continue to be a mainspring of mathematical research for years to come.

Author : John R. Silvester
Publisher : Oxford University Press on Demand
Release :2001
Total pages :313
Language : EN, FR, DE, ES
ISBN : 0198508255

''This book is densely packed with useful and interesting geometrical insights whilst the written style is engaging and often amusing... John Silvester has written a work of quality and substance and I strongly recommended it for use by anyone seeking to extend their knowledge of geometry beyond the A level stage. As one who is intrigued by geometry, I shall certainly keep my copy permanently close to hand'' -The Mathematical GazetteThis book offers a guided tour of geometry from euclid through to algebraic geometry. It shows how mathematicians use a variety of techniques to tackle problems , and it links geometry to other branches of mathematics. Many problems and examples are included to aid understanding.

Author : Clayton W. Dodge
Publisher : Courier Corporation
Release :2004
Total pages :295
Language : EN, FR, DE, ES
ISBN : 0486434761

This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.

Author : Bonnie Leech
Publisher : The Rosen Publishing Group, Inc
Release :2009-12-15
Total pages :32
Language : EN, FR, DE, ES
ISBN : 1404260730

Introduces famous figures in the history of geometry and explains the principles that they proposed.

Author : T. A. Sarasvati Amma
Publisher : Motilal Banarsidass Publ.
Release :1999
Total pages :277
Language : EN, FR, DE, ES
ISBN : 8120813448

This book is a geometrical survey of the Sanskrit and Prakrt scientific and quasi-scientific literature of India, beginning with the Vedic literature and ending with the early part of the 17th century. It deals in detail with the Sulbasutras in the Vedic literature, with the mathematical parts of Jaina Canonical works and of the Hindu Siddhantas and with the contributions to geometry made by the astronomer mathematicians Aryabhata I & II, Sripati, Bhaskara I & II, Sangamagrama Madhava, Paramesvara, Nilakantha, his disciples and a host of others. The works of the mathematicians Mahavira, Sridhara and Narayana Pandita and the Bakshali Manuscript have also been studied. The work seeks to explode the theory that the Indian mathematical genius was predominantly algebraic and computational and that it eschewed proofs and rationales. There was a school in India which delighted to demonstrate even algebraical results geometrically. In their search for a sufficiently good approximation for the value of pie Indian mathematicians had discovered the tool of integration. Which they used equally effectively for finding the surface area and volume of a sphere and in other fields. This discovery of integration was the sequel of the inextricable blending of geometry and series mathematics.