General

This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful...

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...

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...

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just...

In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a...

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

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This book presents a course in the geometry of convex polytopes in arbitrary dimension, suitable for an advanced undergraduate or beginning graduate student. The book starts with the basics of polytope theory. Schlegel and Gale diagrams are introduced as...

Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary...

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In an age of digital precision, Folded Paper Geometry brings design back to its most fundamental tool--your hands. It explores the beauty, simplicity and ingenuity of geometric structures through the act of folding, revealing how single sheets of paper...

In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space...

This book is based on an information-theoretic result according to which optimal information is associated with e-dimensionality. Drawing on the principle that nature chooses optimal solutions, it demonstrates that noninteger dimensionality provides a...

This book, taking a holistic view of geometry, introduces the reader to axiomatic, algebraic, analytic and differential geometry. Starting with an informal introduction to non-Euclidean plane geometries, the book develops the theory to put them on a...

Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without...

This three-volume collection is devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are...

In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success,...

The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying...

A classic title based on lectures given at Harvard University during the academic year 1960-1961 by one of the luminaries in the mathematical world. This timeless book addresses standard material and includes exercise throughout.Book InformationISBN...

William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way...

Sigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several...

In this highly recommended high school text by two eminent scholars, the authors deduce plane Euclidean geometry by utilizing only five fundamental postulates. Incorporation of the system of real numbers in three of the five postulates of this geometry...

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of...

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Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a...

Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of...

This volume contains the proceedings of the AMS Western Sectional Meeting on Algebraic Structures in Knot Theory held on May 6-7, 2023, at California State University, Fresno, California. Modern knot theory includes the study of a diversity of different...

The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and...

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The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

This volume contains the proceedings of the AMS Special Session on Recent Advanced in Differential Geometry, held virtually on April 1-2, 2023, and the Tenth Congress of Romanian Mathematicians Special Session on Recent Advances in the Geometry of...

Trigonometry: From Theory to Application introduces the basics of trigonometry and key areas of practice, fully considering in straightforward, pragmatic terms the characterization of triangles, coordinate transport, and coordinate systems, with emphasis...

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian...

This volume contains the proceedings of the mini-workshop on Topological Complexity and Related Topics, held from February 28-March 5, 2016, at the Mathematisches Forschungsinstitut Oberwolfach.Topological complexity is a numerical homotopy invariant,...

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This book provides a systematic treatment of the main results on the Morse index of minimal submanifolds of Riemannian manifolds. After an introductory chapter reviewing the necessary material, this book provides a survey of the basic properties of the...

Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct...