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High Quality Content by WIKIPEDIA articles! In incidence geometry, the De Bruijn-Erdős theorem, originally published by Nicolaas Govert de Bruijn and Paul Erdős (1948), states a lower bound on the number of lines determined by n points in a projective plane. By duality, this is also a bound on the number of intersection points determined by a configuration of lines. Although the proof given by De Bruijn and Erdős is combinatorial, De Bruijn and Erdős noted in their paper that the analogous (Euclidean) result is a consequence of the Sylvester-Gallai theorem, by an induction on the number of points. ... Read more

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Students will find all the information covered in the standard textbooks--and more--explained clearly and concisely in this powerful study tool. Unusually detailed, it elucidates all the most difficult-to-grasp concepts that class studies and texts sometimes gloss over. The hundreds of problems with fully explained solutions illuminate important points and teach students sound problem-solving skills. Ideal, also, for independent study. ... Read more

Customer Reviews (6)

nice seller
The Seller was very nice. He communicated me quickly and he does not leave a problem or a miscommunication behind. Thanks

A practicalelementary introduction to classical differential geometry
After so many years, this book continues to be a valuable introduction to the differential geometry (DG) of curves and surfaces in euclidean 3 dimensional space, quite clear and efficient for self study, since it combines theory and problems. It reviews the necessary calculus needed.Then it goes into curves and the Frenet equations (little attention is given to plane curves) and continues with surfaces. There one finds an excellent introductory exposition of curvature and assymptotic lines, (including Meusnier, Euler, Rodrigues andBeltrami-Enneper theorems) as well as geodesic curvature, geodesics and Gauss curvature. No mention of parallel transport though (this you can find in Stoker Differential Geometry (Wiley Classics Library),in Goetz Introduction to Differential Geometry (Addison-Wesley Series in Mathematics),Millman-Parker Elements of Differential Geometry's, do Carmo Differential Geometry of Curves and Surfaces or Klingenberg's A Course in Differential Geometry (Graduate Texts in Mathematics), all of them introductory books on DG too. No global properties of curves are given, but we find a clean proof of Liebmann's theorem characterising compact connected surfaces of constant curvatureas spheres (without assuming its orientabilty) and a rather sketchy proof of Gauss-Bonnet theorem. Many proofs of theoretical properties appear as problems. Practical questions are easy or not too hard to solve. If you really don't know the subject, this is a perfect start, alone or combinedwith those previously cited works or withStruik's classicalLectures on Classical Differential Geometry: Second Edition,or Oprea Curves and Surfaces (Graduate Studies in Mathematics) (Applied DG) or Montiel-Ros' recent book Differential Geometry and its Applications (Classroom Resource Materials) (Mathematical Association of America Textbooks). Other problem books on DG are rare. I will mentionFedenko's (Mir-Moscow) (similar to M. Lipschutz's)and Mishchenko-Solovyev-Fomenko (Problems in DG and Topology, Mir- Moscow).

Slightly Subpar for Mathematical Topics in the Schaum Outline Series
While the few solved problems have been carefully selected, and the topics covered continue to reflect Martin Lipschultz normal high standards of exposition, overall this volume is a sub par effort for topics in this series.

The problem lies with the progression of topics, and the erratic treatment -- both of which seem to lack rhyme or reason and leaves the reader with no sense of continuity or cohesion to the substance: Why not, for instance, have "vectors" and "vector functions of a real variable," followed by "vector functions of a vector variable?" And why throw topology right into the middle of this mix? Was it only to get to the idea of Homeomorphisms? If so, should this not have been done much earlier on in the book, maybe even as early as the very first chapter, providing a smoother transition to vector functions of higher mathematical forms?Or better yet, perhaps the author should have merely mentioned the importance of elementary topology, in passing, and then referred the reader to an introductory topology textbook, or as a last resort, he could have added topology as an appendix? But not just toss it in the middle unexpectedly without explanation in an almost completely disconnected fashion. This smattering of topology just seemed so much out of place here. And in any case, it surely was insufficient to tie down the concepts needed to build the necessary bridge between topology and differential geometry. Yes, it did help in understanding the parametric representations of surfaces, but the reader still "was on his own" and had to hustle mightily to make the intended connections.

As well, throughout the book, the lurching back and forth leaves the reader without any sense of coherence on which to build confidence in either the theory of these many complex topics, or problem-solving in the field of differential geometry, more generally. Thus I would argue at the very least that this volume should be relabeled "Selected Topics in Differential Geometry," or better yet "Eclectic Topics in Differential Geometry.'

Its real merit is as a supplement only: neither as a text, nor as a robust basis for developing skills beyond the basics for solving problems in Differential Geometry.

Still, since there is so little basic material available in the field, this remains a useful, even if not an entirely valuable, resource. Three stars.

Differential Geometry review
I have found this to be an excellent addition to my library.

Good as a basic textbook and a source of solve problems
This book is intended to assist upper level undergraduate and graduate students in their understanding of differential geometry, which is the study of geometry using calculus.Usually students study differential geometry in reference to its use in relativity. I personally have a rather oddball application for the subject - modeling of curved geometry for computer graphics applications. The fundamental concepts are presented for curves and surfaces in three-dimensional Euclidean space to add to the intuitive nature of the material.
The book presumes very little in the way of background and thus starts out with the basic theory of vectors and vector calculus of a single variable in the first two chapters. The following three chapters discuss the concept and theory of curves in three dimensions including selected topics in the theory of contact.
Great care is given to the definition of a surface so that the reader has a firm foundation in preparation for further study in modern differential geometry. Thus, there is some background material in analysis and in point set topology in Euclidean spaces presented in chapters 6 and 7. The definition of a surface is detailed in chapter eight. Chapters 9 and 10 are devoted to the theory of the non-intrinsic geometry of a surface. This includes an introduction to tensor methods and selected topics in the global geometry of surfaces. The last chapter of the outline presents the basic theory of the intrinsic geometry of surfaces in three-dimensional Euclidean space.
Exercises are primarily in the form of proofs, and there are plenty of worked examples. Since the examples are kept to no more than three dimensions, the outline contains plenty of good instructive diagrams that illustrate key concepts. This Schaum's outline has quite a bit of instruction in it past the bare required minimum, but you might still want a good primary textbook. My personal favorite is Pressley's "Elementary Differential Geometry". Overall I find this to be a very good outline and source of solved problems on the subject and I highly recommend it. ... Read more

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This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem. ... Read more

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Package (in clear plastic stretch wrap) of five identical soft cover CONNECTED MATHEMATICS Looking For Pythagoras student books. The ISBN for each of these books is 0-13-053078-6. There are 79 pages in each book. ... Read more

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High Quality Content by WIKIPEDIA articles! Kakutani's theorem is a result in geometry named after Shizuo Kakutani. It states that every convex body in 3-dimensional space has a circumscribed cube, i.e. a cube all whose faces touch the body. The result was further generalized by Yamabe and Yujobô to higher dimension, and by Floyd to other circumscribed parallelepipeds. Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujirō Shimizu. Early in his career he spent two years at the Institute for Advanced Study in Princeton at the invitation of the German mathematician Hermann Weyl. While there, he also met John von Neumann. ... Read more

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High Quality Content by WIKIPEDIA articles! Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is, any polyhedral net formed by unfolding the faces of the polyhedron onto a flat surface, together with gluing instructions describing which faces should be connected to each other, uniquely determines the shape of the original polyhedron. For instance, if six squares are connected together in the pattern of a cube, then they must form a cube: there is no convex polyhedron with six square faces connected in the same way that does not have the same shape. ... Read more

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High Quality Content by WIKIPEDIA articles! In the context of discrete geometry, Beck's theorem may refer to several different results, two of which are given below. Both appeared, alongside several other important theorems, in a well-known paper by József Beck. The two results described below primarily concern lower bounds on the number of lines determined by a set of points in the plane. (Any line containing at least two points of point set is said to be determined by that point set.) The Erdős-Beck theorem is a variation of a classical result by L.M. Kelly and W.O.J. Moser involving configurations of n points of which at most n−k are collinear, for some 0 ... Read more

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High Quality Content by WIKIPEDIA articles! In the mathematical field of differential geometry, Euler's theorem is a result on the curvature of curves on a surface. The theorem establishes the existence of principal curvatures and associated principal directions which give the directions in which the surface curves the most and the least. The theorem is named for Leonard Euler who proved the theorem in (Euler 1760). More precisely, let M be a surface in three-dimensional Euclidean space, and p a point on M. A normal plane through p is a plane passing through the point p containing the normal vector to M. Through each (unit) tangent vector to M at p, there passes a normal plane PX which cuts out a curve in M. ... Read more

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High Quality Content by WIKIPEDIA articles! Leonhard Euler (15 April 1707 - 18 September 1783) was a pioneering Swiss mathematician and physicist who spent most of his life in Russia and Germany.Euler made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. ... Read more

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This book constitutes the strictly refereed post-workshop proceedings of the Second International Workshop on Automated Deduction in Geometry, ADG'98, held in Beijing, China in August 1998. The 14 revised papers presented were selected from the papers accepted for the workshop after careful reviewing. The papers address all current issues in the area, in particular automated geometry theorem proving, automated geometry problem solving, plane Euclidean reasoning, Clifford algebraic methods for geometric reasoning, decomposing algebraic varieties, applciations in computer vision, mechanical CAGD, etc. ... Read more

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This text is intended for a brief course in geometry or a supplement for any mathematics course that includes some coverage of basic geometry. No previous exposure to geometry is assumed. This textbook can be used effectively in the classroom, math-lab, and/or for self study. Many examples have been included with complete explanations. All the skills required to pass the geometry sections of the TASP, ELM, CLAST, and other college-level academic skills tests are presented. ... Read more

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Straightforward, Simple
Delivers what it claims.It gives you a straightforward, simple approach to basic plane and solid geometry.Good for review, or if you are interested in getting through a standardized test.Not designed for deep understanding. ... Read more

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The Novikov Conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) in September, 1993, on the subject of `Novikov Conjectures, Index Theorems and Rigidity'. They are intended to give a snapshot of the status of work on the Novikov Conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry, analysis. ... Read more