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Geometry : Geometry
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Geometry
This text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students.These books cover the basics of mathematics in a clear and simple format – the style Gelfand was known for internationally.Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and practice the material at their own pace without a class. Geometry takes a different approach to presenting basic geometry for high-school students and others new to the subject. Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions.Illustrations and problems are abundant throughout, and readers are encouraged to draw figures and “move” them in the plane, allowing them to develop and enhance their geometrical vision, imagination, and creativity.Chapters are structured so that only certain operations and the instruments to perform these operations are available for drawing objects and figures on the plane.This structure corresponds to presenting, sequentially, projective, affine, symplectic, and Euclidean geometries, all the while ensuring students have the necessary tools to follow along. Geometry is suitable for a large audience, which includes not only high school geometry students, but also teachers and anyone else interested in improving their geometrical vision and intuition, skills useful in many professions.Similarly, experienced mathematicians can appreciate the book’s unique way of presenting plane geometry in a simple form while adhering to its depth and rigor. “Gelfand was a great mathematician and also a great teacher.The book provides an atypical view of geometry. Gelfand gets to the intuitive core of geometry, to the phenomena of shapes and how they move in the plane, leadingus to a better understanding of what coordinate geometry and axiomatic geometry seek to describe.” - Mark Saul, PhD, Executive Director, Julia Robinson Mathematics Festival“The subject matter is presented as intuitive, interesting and fun. No previous knowledge of the subject is required. Starting from the simplest concepts and by inculcating in the reader the use of visualization skills, [and] after reading the explanations and working through the examples, you will be able to confidently tackle the interesting problems posed. I highly recommend the book to any person interested in this fascinating branch of mathematics.” - Ricardo Gorrin, a student of the Extended Gelfand Correspondence Program in Mathematics (EGCPM)
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Beautiful Geometry
If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind.As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each.With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity.The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics.
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Make - Geometry
Geometry, of all the branches of mathematics, is the one that is most easily visualized by making something.However, it is all too easy to reduce it to reams of formulas to memorize and proofs to replicate.This book aims to take geometry back to its practical roots with 3D printed models and puzzles as well as demonstrations with household objects like flashlights and paper towel tubes. This is not a traditional geometry textbook, but rather builds up understanding of geometry concepts while also bringing in elements of concepts normally learned much later.Some of the models are counterintuitive, and figuring out how and why they work will both entertain and give insights.Two final chapters suggesting open-ended projects in astronomy and physics, and art and architecture, allow for deeper understanding and integration of the learning in the rest of the book.
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Differential Geometry
This textbook provides a concise introduction to the differential geometry of curves and surfaces in three-dimensional space, tailored for undergraduate students with a solid foundation in mathematical analysis and linear algebra. The book emphasizes the geometric content of the subject, aiming to quickly cover fundamental topics such as the isoperimetric inequality and the Gauss–Bonnet theorem.This approach allows the author to extend beyond the typical content of introductory books and include additional important geometric results, such as curves and surfaces of constant width, the classification of complete surfaces of non-negative constant curvature, and Hadamard's theorem on surfaces of non-positive curvature.This range of topics offers greater variety for an introductory course.
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Noncommutative Geometry
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes.Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.
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Algebraic Geometry
Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P.Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years.In 1972 he moved to California where he is now Professor at the University of California at Berkeley.He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles.His current research interest is the geometry of projective varieties and vector bundles.He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively.Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons.He has travelled widely, speaks several foreign languages, and is an experienced mountain climber.He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.
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