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$119.00 $90.32
21. Affine and Projective Geometry
$164.00 $151.25
22. The Symbolic Universe: Geometry
$182.36 list($120.00)
23. Geometry of Linear 2-Normed Spaces
$82.00 $81.98
24. Least Action Principle of Crystal
$89.95 $75.51
25. Hyperbolic Manifolds and Discrete
$165.00
26. Complex Hyperbolic Geometry (Oxford
$88.00 $60.00
27. Euclidean and Non-Euclidean Geometries
$100.00
28. Contact Geometry and Nonlinear
$19.00
29. Non-Euclidean Geometry in the
$99.00 $78.97
30. Geometric Asymptotics for Nonlinear
$19.50 list($133.00)
31. Some Novel Types of Fractal Geometry
$94.95 $81.56
32. Generalized Cauchy-Riemann Systems
list($65.00)
33. Foundations of Euclidean and Non-Euclidean
$31.25 $26.98
34. Journey into Geometries (Spectrum)
$169.95
35. Noncommutative Algebra And Geometry
$8.95 $5.85
36. Introductory Non-Euclidean Geometry
$11.53 list($16.95)
37. The Elements of Non-Euclidean
$107.34 list($113.00)
38. A History of Non-Euclidean Geometry

21. Affine and Projective Geometry
by M. K.Bennett
list price: $119.00
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Asin: 0471113158
Catlog: Book (1995-08-04)
Publisher: Wiley-Interscience
Sales Rank: 989198
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Book Description

An important new perspective on AFFINE AND PROJECTIVE GEOMETRY

This innovative book treats math majors and math education students to a fresh look at affine and projective geometry from algebraic, synthetic, and lattice theoretic points of view.

Affine and Projective Geometry comes complete with ninety illustrations, and numerous examples and exercises, covering material for two semesters of upper-level undergraduate mathematics. The first part of the book deals with the correlation between synthetic geometry and linear algebra. In the second part, geometry is used to introduce lattice theory, and the book culminates with the fundamental theorem of projective geometry.

While emphasizing affine geometry and its basis in Euclidean concepts, the book:

  • Builds an appreciation of the geometric nature of linear algebra
  • Expands students' understanding of abstract algebra with its nontraditional, geometry-driven approach
  • Demonstrates how one branch of mathematics can be used to prove theorems in another
  • Provides opportunities for further investigation of mathematics by various means, including historical references at the ends of chapters

Throughout, the text explores geometry's correlation to algebra in ways that are meant to foster inquiry and develop mathematical insights whether or not one has a background in algebra. The insight offered is particularly important for prospective secondary teachers who must major in the subject they teach to fulfill the licensing requirements of many states. Affine and Projective Geometry's broad scope and its communicative tone make it an ideal choice for all students and professionals who would like to further their understanding of things mathematical. ... Read more


22. The Symbolic Universe: Geometry and Physics 1890-1930
list price: $164.00
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Asin: 0198500882
Catlog: Book (1999-09-01)
Publisher: Oxford University Press
Sales Rank: 2013152
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Book Description

Physics was transformed between 1890 and 1930, and this volume provides a detailed history of the era and emphasizes the key role of geometrical ideas. Topics include the application of n-dimensional differential geometry to mechanics and theoretical physics, the philosophical questions on the reality of geometry, and the nature of geometry and its connections with psychology, special relativity, Hilbert's efforts to axiomatize relativity, and Emmy Noether's work on physics. ... Read more


23. Geometry of Linear 2-Normed Spaces
by Raymond W. Freese, Yeol Je Cho
list price: $120.00
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Asin: 1590330196
Catlog: Book (2001)
Publisher: Nova Science Publishers
Sales Rank: 3257802
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24. Least Action Principle of Crystal Formation of Dense Packing Type & the Proof of Kepler's Conjecture
by Wu Yi Hsiang, Wu-Yi Hisiang
list price: $82.00
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Asin: 9810246706
Catlog: Book (2002-03-15)
Publisher: World Scientific Publishing Company
Sales Rank: 2864535
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25. Hyperbolic Manifolds and Discrete Groups
by Michael Kapovich
list price: $89.95
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Asin: 0817639047
Catlog: Book (2000-11-15)
Publisher: Birkhauser
Sales Rank: 1148907
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Book Description

Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout is on the "Big Monster," i.e., on Thurston's hyperbolization theorem, which has not only completely changed the landscape of 3-dimensional topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book presents the first complete proof of Thurston's hyperbolization theorem in the "generic case" and an outline of Otal's proof of the hyperbolization theorem for manifolds fibered over the circle.This important work contains an extended treatment of the theory of Kleinian groups and group actions on trees, including such key topics as:* the Kazhdan--Margulis--Zassenhaus theorem* the Klein and Maskit combination theorems* the Mostow rigidity theorem* the Douady--Earle extension theorem for homeomorphisms of the circle* the smoothness theorem for representation varieties of Kleinian groups* the Ahlfors finiteness theorem* the Brooks deformation theorem* characterization of pseudo-Anosov homeomorphisms* compactification of character varieties via group actions on trees ... Read more


26. Complex Hyperbolic Geometry (Oxford Mathematical Monographs)
by William M. Goldman
list price: $165.00
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Asin: 019853793X
Catlog: Book (1999-04-01)
Publisher: Oxford University Press
Sales Rank: 381206
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Book Description

This is the first comprehensive treatment of the geometry of complex hyperbolic space, a rich area of research with numerous connections to other branches of mathematics, including Riemannian geometry, complex analysis, symplectic and contact geometry, Lie groups, and harmonic analysis. ... Read more


27. Euclidean and Non-Euclidean Geometries
by Helena Noronha
list price: $88.00
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Asin: 013033717X
Catlog: Book (2002-01-15)
Publisher: Prentice Hall
Sales Rank: 467772
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Amazon.com

What's so sacred about parallel lines? Students and general readers who want a solid grounding in the fundamentals of space would do well to let M. Helena Noronha's Euclidean and Non-Euclidean Geometries be their guide. Noronha, professor of mathematics at California State University, Northridge, breaks geometry down to its essentials and shows students how Riemann, Lobachevsky, and the rest built their own by re-evaluating the parallel postulate. Each chapter devotes itself to rigorous study of one topic: neutral geometry, Euclidean 3-space, hyperbolic geometry, and more reveal themselves to the reader through the author's clear analyses and proofs. Problem sets help the student become comfortable with techniques and reach the conclusions through their own work, gaining a visceral understanding impossible through passive reading. Little mathematical background is needed beyond a bit of set theory, calculus, and a willingness to persevere. --Rob Lightner ... Read more


28. Contact Geometry and Nonlinear Differential Equations (Encyclopedia of Mathematics and its Applications)
by Alexei Kushner, Valentin Lychagin, Vladimir Roubtsov
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Asin: 0521824761
Catlog: Book (2005-09-30)
Publisher: Cambridge University Press
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Book Description

Growing interest in the use of symmetry methods in applied mathematics has triggered this comprehensive overview of the differential geometric view of the subject. Beginning with a background chapter on calculus on manifolds, the book proceeds to more advanced topics and applications, especially concerning singularities of the Monge-Ampere equations that describe phenomena in geophysical fluid dynamics. Many applications areas are covered, and computer code is included for implementing some of the techniques described. ... Read more


29. Non-Euclidean Geometry in the Theory of Automorphic Functions (History of Mathematics, V. 17)
by Jacques Hadamard
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Asin: 0821820303
Catlog: Book (1999-09-01)
Publisher: American Mathematical Society
Sales Rank: 1728032
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30. Geometric Asymptotics for Nonlinear PDE. I
by V. P. Maslov, G. A. Omelyanov
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Asin: 0821821091
Catlog: Book (2001-08-01)
Publisher: American Mathematical Society
Sales Rank: 3333300
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Book Description

The study of asymptotic solutions to nonlinear systems of partialdifferential equations is a very powerful tool in the analysisof such systems and their applications in physics, mechanics,and engineering. In the present book, the authors propose a newpowerful method of asymptotic analysis of solutions, which canbe successfully applied in the case of the so-called "smoothedshock waves", i.e., nonlinear waves which vary fast in aneighborhood of the front and slowly outside of thisneighborhood. The proposed method, based on the study ofgeometric objects associated to the front, can be viewed as ageneralization of the geometric optics (or WKB) method forlinear equations. This volume offers to a broad audience asimple and accessible presentation of this new method.

The authors present many examples originating from problems ofhydrodynamics, nonlinear optics, plasma physics, mechanics ofcontinuum, and theory of phase transitions (free boundaryproblems). In the examples, characterized by smoothing ofsingularities due to dispersion or diffusion, asymptoticsolutions in the form of distorted solitons, kinks, breathers,or smoothed shock waves are constructed. By a unified rule, ageometric picture is associated with each physical problem thatallows for obtaining tractable asymptotic formulas and providesa geometric interpretation of the physical process. Included aremany figures illustrating the various physical effects. ... Read more


31. Some Novel Types of Fractal Geometry (Oxford Mathematical Monographs)
by Stephen Semmes
list price: $133.00
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Asin: 0198508069
Catlog: Book (2000-04-01)
Publisher: Oxford University Press
Sales Rank: 2297194
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32. Generalized Cauchy-Riemann Systems with a Singular Point
by Z. D. Usmanov, Zafar Dzuraevich Usmanov
list price: $94.95
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Asin: 0582292808
Catlog: Book (1997-04-29)
Publisher: Addison Wesley Longman
Sales Rank: 2581504
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Book Description

A theory of generalized Cauchy-Riemann systems with polar singularities of order not less than one is presented and its application to study of infinitesimal bending of surfaces having positive curvature and an isolated flat point is given. The book contains results of investigations obtained by the author and his collaborators. ... Read more


33. Foundations of Euclidean and Non-Euclidean Geometry (Pure and Applied Mathematics (Marcel Dekker))
by Richard L. Faber
list price: $65.00
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Asin: 0824717481
Catlog: Book (1983-01-01)
Publisher: Marcel Dekker Inc Pod
Sales Rank: 2344491
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34. Journey into Geometries (Spectrum)
by Marta Sved
list price: $31.25
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Asin: 0883855003
Catlog: Book (1997-07)
Publisher: The Mathematical Association of America
Sales Rank: 935649
Average Customer Review: 5.0 out of 5 stars
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Book Description

This unique book gives an informal introduction into the non-Euclidean geometries through a series of dialogues between a somewhat grown-up Alice (of Looking Glass fame), her uncle Lewis Carroll, and a visitor from the twentieth century, Dr Whatif. In the story, Lewis Carroll's geometrical beliefs are cast into the Euclidean mould, Dr Whatif asks the penetrating and controversial questions, and Alice acts as a mediator and interested participant. The book is intentionally more mathematical than Lewis Carroll's books, but for those of us who enjoyed Alice's earlier adventures there are many interesting flashbacks to those inimitable characters: the Red Queen, Tweedle-Dum and his twin brother, the Mad Hatter ... The text is filled with humour, wit, and verses of poetry. Part 1 contains the story in six chapters, each of which concludes with a problem set; Part 2 is more mathematical, and looks at the axiom systems, and gives solutions to the problems. The presentation, with its old-time borders, script headings, and cartoon drawings evokes the spirit of the original Alice. ... Read more

Reviews (1)

5-0 out of 5 stars Another magical journey through the wonderland of geometry
One cannot say that Lewis Carroll would be pleased, since he helps with the narration of this account of some additional travels of his darling Alice. Many of the other original Wonderland characters also help Dr. WhatIf and him explain and illustrate a wide variety of geometric problems.
Although the author does an excellent job in presenting difficultconcepts, this is not a textbook, Thinkof it as an excursion into thewonderland of advanced geometry. Experts will frolic, amateurs with grinand eventually understand and beginners will smile right up to the point(pun intended), where they get lost.
Problems are given at the end ofeach chapter and detailed solutions appear in the back of the book. Apartial list of the topics covered includes inversions, reflections, ahyperbolic T-party, hyperbolic geometry, and projections. Verse with adecidedly Carrollean flavor appears throughout the text.
A joy toread and even better the second time through, it is a fitting sequel to theoriginal adventures.

Published in Journal of RecreationalMathematics, reprinted with permission. ... Read more


35. Noncommutative Algebra And Geometry
list price: $169.95
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Asin: 082472349X
Catlog: Book (2005-08-29)
Publisher: CRC Press
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36. Introductory Non-Euclidean Geometry
by Henry Parker Manning
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Asin: 0486442624
Catlog: Book (2005-02-18)
Publisher: Dover Publications
Sales Rank: 374664
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Book Description

An elementary introduction to the two most important non-Euclidean geometries, hyperbolic and elliptic, this undergraduate-level text presents an extremely simple and direct account of a tremendously important branch of mathematics.
... Read more

37. The Elements of Non-Euclidean Geometry (Dover Books on Mathematics)
by D. M.Y. Sommerville
list price: $16.95
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Asin: 0486442225
Catlog: Book (2005-04-12)
Publisher: Dover Publications
Sales Rank: 275614
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Book Description

This volume became the standard text in the field almost immediately upon its original publication. Renowned for its lucid yet meticulous exposition, it can be appreciated by anyone familiar with high school algebra and geometry. Its arrangement follows the traditional pattern of plane and solid geometry, allowing students to follow the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to such advanced topics as inversion and transformations. Although geared toward undergraduates, it treats such topics as the relation between parataxy and parallelism, the absolute measure, the pseudosphere, and Gauss’ proof of the defect-area theorem. 1914 ed. 133 figures.
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38. A History of Non-Euclidean Geometry : Evolution of the Concept of a Geometric Space (Studies in the History of Mathematics and Physical Sciences)
by Boris A. Rosenfeld, Hardy Grant
list price: $113.00
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Asin: 0387964584
Catlog: Book (1988-09-07)
Publisher: Springer
Sales Rank: 2996860
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Book Description

This book is an investigation of the mathematical and philosophical factors underlying the discovery of the concept of noneuclidean geometries, and the subsequent extension of the concept of space. Chapters one through five are devoted to the evolution of the concept of space, leading up to chapter six which describes the discovery of noneuclidean geometry, and the corresponding broadening of the concept of space. The author goes on to discuss concepts such as multidimensional spaces and curvature, and transformation groups. The book ends with a chapter describing the applications of nonassociative algebras to geometry. ... Read more


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