Topics In Geometry

Author : Robert Bix
Publisher : Elsevier
Page : 538 pages
File Size : 55,8 Mb
Release : 2016-02-20
Category : Mathematics
ISBN : 9781483296463

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Topics in Geometry by Robert Bix Pdf

This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered. The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.

Author : O. Bottema
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 44,7 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9780387781310

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Topics in Elementary Geometry by O. Bottema Pdf

This small book, translated into English for the first time, has long been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained over the past years. There are 27 independent chapters on a wide range of topics in elementary plane Euclidean geometry, at a level just beyond what is usually taught in a good high school or college geometry course. The selection of topics is intelligent, varied, and stimulating, and the author provides many thought-provoking ideas.

Author : Peter W. Michor
Publisher : American Mathematical Soc.
Page : 510 pages
File Size : 46,9 Mb
Release : 2008
Category : Geometry, Differential
ISBN : 9780821820032

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Topics in Differential Geometry by Peter W. Michor Pdf

"This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.

Author : Károly Bezdek
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 42,5 Mb
Release : 2010-06-23
Category : Mathematics
ISBN : 9781441906007

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Classical Topics in Discrete Geometry by Károly Bezdek Pdf

Geometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory.

Author : Tullio Ceccherini-Silberstein,Michele D'Adderio
Publisher : Springer Nature
Page : 468 pages
File Size : 47,9 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030881092

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Topics in Groups and Geometry by Tullio Ceccherini-Silberstein,Michele D'Adderio Pdf

This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

Author : Maria Moszynska
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 50,5 Mb
Release : 2006-11-24
Category : Mathematics
ISBN : 9780817644512

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Selected Topics in Convex Geometry by Maria Moszynska Pdf

Examines in detail those topics in convex geometry that are concerned with Euclidean space Enriched by numerous examples, illustrations, and exercises, with a good bibliography and index Requires only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory Can be used for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization

Author : Arnaldo Garcia,Henning Stichtenoth
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 54,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9781402053344

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Topics in Geometry, Coding Theory and Cryptography by Arnaldo Garcia,Henning Stichtenoth Pdf

The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.

Author : J. A. Thorpe
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261537

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Elementary Topics in Differential Geometry by J. A. Thorpe Pdf

In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.

Author : Richard Rusczyk
Publisher : Aops Incorporated
Page : 557 pages
File Size : 46,7 Mb
Release : 2007-07-01
Category : Juvenile Nonfiction
ISBN : 1934124087

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Introduction to Geometry by Richard Rusczyk Pdf

Author : Glasby,Marion K. Glasby,Symancyk
Publisher : Kendall/Hunt Publishing Company
Page : 80 pages
File Size : 55,8 Mb
Release : 1986-11-01
Category : Geometry
ISBN : 0840342055

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Basic Geometry Topics by Glasby,Marion K. Glasby,Symancyk Pdf

Author : R. Lazarsfeld,Ven
Publisher : Birkhäuser
Page : 51 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034893480

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Topics in the Geometry of Projective Space by R. Lazarsfeld,Ven Pdf

The main topics discussed at the D. M. V. Seminar were the connectedness theorems of Fulton and Hansen, linear normality and subvarieties of small codimension in projective spaces. They are closely related; thus the connectedness theorem can be used to prove the inequality-part of Hartshorne's conjecture on linear normality, whereas Deligne's generalisation of the connectedness theorem leads to a refinement of Barth's results on the topology of varieties with small codimension in a projective space. The material concerning the connectedness theorem itself (including the highly surprising application to tamely ramified coverings of the projective plane) can be found in the paper by Fulton and the first author: W. Fulton, R. Lazarsfeld, Connectivity and its applications in algebraic geometry, Lecture Notes in Math. 862, p. 26-92 (Springer 1981). It was never intended to be written out in these notes. As to linear normality, the situation is different. The main point was an exposition of Zak's work, for most of which there is no reference but his letters. Thus it is appropriate to take an extended version of the content of the lectures as the central part of these notes.

Author : María A. Cañadas-Pinedo,José Luis Flores,Francisco J. Palomo
Publisher : Springer
Page : 273 pages
File Size : 52,5 Mb
Release : 2018-03-06
Category : Mathematics
ISBN : 9783319662909

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Lorentzian Geometry and Related Topics by María A. Cañadas-Pinedo,José Luis Flores,Francisco J. Palomo Pdf

This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.

Author : Pavel Pech
Publisher : World Scientific
Page : 252 pages
File Size : 40,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812709424

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Selected Topics in Geometry with Classical Vs. Computer Proving by Pavel Pech Pdf

This textbook presents various automatic techniques based on Gr”bner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects ? which cannot be easily done with a ruler and compass.Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically ? without using computer where possible ? so that readers can compare the strengths and weaknesses of both approaches.

Author : Evan Chen
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 52,7 Mb
Release : 2021-08-23
Category : Education
ISBN : 9781470466206

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Euclidean Geometry in Mathematical Olympiads by Evan Chen Pdf

This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.

Author : Howard Levi
Publisher : Unknown
Page : 104 pages
File Size : 44,7 Mb
Release : 1975
Category : Electronic
ISBN : OCLC:613359574

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Topics in Geometry by Howard Levi Pdf