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Praise for George Francis's A Topological Picturebook: Bravo to Springer for reissuing this unique and beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, but also shows the new generation what ``hands on'' really means. - John Stillwell, University of San Francisco The Topological Picturebook has taught a whole generation of mathematicians to draw, to see, and to think. - Tony Robbin, artist and author of Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought The classic reference for how to present topological information visually, full of amazing hand-drawn pictures of complicated surfaces. - John Sullivan, Technische Universitat Berlin A Topological Picturebook lets students see topology as the original discoverers conceived it: concrete and visual, free of the formalism that burdens conventional textbooks. - Jeffrey Weeks, author of The Shape of Space A Topological Picturebook is a visual feast for anyone concerned with mathematical images. Francis provides exquisite examples to build one's "visualization muscles". At the same time, he explains the underlying principles and design techniques for readers to create their own lucid drawings. - George W. Hart, Stony Brook University In this collection of narrative gems and intriguing hand-drawn pictures, George Francis demonstrates the chicken-and-egg relationship, in mathematics, of image and text. Since the book was first published, the case for pictures in mathematics has been won, and now it is time to reflect on their meaning. A Topological Picturebook remains indispensable. - Marjorie Senechal, Smith College and co-editor of the Mathematical Intelligencer.

Mathematics. --- Topology. --- Geometry. --- Mathématiques --- Géométrie --- Topologie --- Topology --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Graphic methods --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Graphic methods. --- Topologie. Méthodes graphiques. --- Topologie. Grafische methoden. --- Polyhedra --- Set theory --- Algebras, Linear --- Euclid's Elements --- Géometrie --- Infographie --- Topology - Graphic methods.

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This book covers the necessary topics for learning the basic properties of complex manifolds and their submanifolds, offering an easy, friendly, and accessible introduction into the subject while aptly guiding the reader to topics of current research and to more advanced publications. The book begins with an introduction to the geometry of complex manifolds and their submanifolds and describes the properties of hypersurfaces and CR submanifolds, with particular emphasis on CR submanifolds of maximal CR dimension. The second part contains results which are not new, but recently published in some mathematical journals. The final part contains several original results by the authors, with complete proofs. Key features of "CR Submanifolds of Complex Projective Space": - Presents recent developments and results in the study of submanifolds previously published only in research papers. - Special topics explored include: the Kähler manifold, submersion and immersion, codimension reduction of a submanifold, tubes over submanifolds, geometry of hypersurfaces and CR submanifolds of maximal CR dimension. - Provides relevant techniques, results and their applications, and presents insight into the motivations and ideas behind the theory. - Presents the fundamental definitions and results necessary for reaching the frontiers of research in this field. This text is largely self-contained. Prerequisites include basic knowledge of introductory manifold theory and of curvature properties of Riemannian geometry. Advanced undergraduates, graduate students and researchers in differential geometry will benefit from this concise approach to an important topic.

Mathematics. --- Differential Geometry. --- Global Analysis and Analysis on Manifolds. --- Several Complex Variables and Analytic Spaces. --- Global analysis. --- Differential equations, partial. --- Global differential geometry. --- Mathématiques --- Géométrie différentielle globale --- CR submanifolds. --- Cauchy-Riemann submanifolds --- Submanifolds, CR --- Manifolds (Mathematics) --- Cauchy-Riemann equations. --- Functions of several complex variables. --- CR submanifolds --- Mathematics --- Geometry --- Physical Sciences & Mathematics --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Functions of complex variables. --- Differential geometry. --- Topology. --- Geometry, Differential --- Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Partial differential equations --- Differential geometry --- Complex variables --- Elliptic functions --- Functions of real variables --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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Topological bifurcation theory is one of the most essential topics in mathematics. This book contains original bifurcation results for the existence of oscillations and chaotic behaviour of differential equations and discrete dynamical systems under variation of involved parameters. Using topological degree theory and a perturbation approach in dynamical systems, a broad variety of nonlinear problems are studied, including: non-smooth mechanical systems with dry frictions; weakly coupled oscillators; systems with relay hysteresis; differential equations on infinite lattices of Frenkel-Kontorova and discretized Klein-Gordon types; blue sky catastrophes for reversible dynamical systems; buckling of beams; and discontinuous wave equations. Precise and complete proofs, together with concrete applications with many stimulating and illustrating examples, make this book valuable to both the applied sciences and mathematical fields, ensuring the book should not only be of interest to mathematicians but to physicists and theoretically inclined engineers interested in bifurcation theory and its applications to dynamical systems and nonlinear analysis.

Mathematics. --- Analysis. --- Topology. --- Dynamical Systems and Ergodic Theory. --- Mechanics. --- Vibration, Dynamical Systems, Control. --- Global analysis (Mathematics). --- Differentiable dynamical systems. --- Vibration. --- Mathématiques --- Analyse globale (Mathématiques) --- Dynamique différentiable --- Topologie --- Mécanique --- Vibration --- Bifurcation theory. --- Bifurcation theory --- Topology --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Mathematics --- Calculus --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Mathematical analysis. --- Analysis (Mathematics). --- Dynamics. --- Ergodic theory. --- Dynamical systems. --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Differential equations, Nonlinear --- Stability --- Numerical solutions --- Classical Mechanics. --- Cycles --- Mechanics --- Sound --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- 517.1 Mathematical analysis --- Mathematical analysis --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal