Download or read book Basic Concepts of the Theory of Geometric Objects written by M. Kucharzewski and published by . This book was released on 1964 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1988 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.
Download or read book Theory of the Geometric Object written by Albert Nijenhuis and published by . This book was released on 1952 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book From Groups to Geometry and Back written by Vaughn Climenhaga and published by American Mathematical Soc.. This book was released on 2017-04-07 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.
Download or read book Topics in Geometric Group Theory written by Pierre de la Harpe and published by University of Chicago Press. This book was released on 2000-09-15 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.
Download or read book Basic Concepts of Synthetic Differential Geometry written by R. Lavendhomme and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's theorem; the synthetic view of global action, going as far as the Weil characteristic homomorphism; the systematic account of structured Lie objects, such as Riemannian, symplectic, or Poisson Lie objects; the view of global Lie algebras as Lie algebras of a Lie group in the synthetic sense; and lastly the synthetic construction of symplectic structure on the cotangent bundle in general. Thus while the book is limited to a naive point of view developing synthetic differential geometry as a theory in itself, the author nevertheless treats somewhat advanced topics, which are classic in classical differential geometry but new in the synthetic context. Audience: The book is suitable as an introduction to synthetic differential geometry for students as well as more qualified mathematicians.
Download or read book Methods of Geometric Analysis in Extension and Trace Problems written by Alexander Brudnyi and published by Springer Science & Business Media. This book was released on 2011-10-07 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a comprehensive exposition of extension results for maps between different geometric objects and of extension-trace results for smooth functions on subsets with no a priori differential structure (Whitney problems). The account covers development of the area from the initial classical works of the first half of the 20th century to the flourishing period of the last decade. Seemingly very specific these problems have been from the very beginning a powerful source of ideas, concepts and methods that essentially influenced and in some cases even transformed considerable areas of analysis. Aside from the material linked by the aforementioned problems the book also is unified by geometric analysis approach used in the proofs of basic results. This requires a variety of geometric tools from convex and combinatorial geometry to geometry of metric space theory to Riemannian and coarse geometry and more. The necessary facts are presented mostly with detailed proofs to make the book accessible to a wide audience.
Download or read book Lectures on Functional Equations and Their Applications written by J. Aczel and published by Courier Corporation. This book was released on 2006-02-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.
Download or read book Number Shape Symmetry written by Diane L. Herrmann and published by CRC Press. This book was released on 2012-10-18 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.
Download or read book Encyclopaedia of Mathematics set written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1994-02-28 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.
Download or read book Arithmetic and Geometry Around Galois Theory written by Pierre Dèbes and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.
Download or read book On the theory of the geometric object written by Jean Aroldus Schouten and published by . This book was released on 1937 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in the Geometric Theory of Linear Systems written by Robert Hermann and published by . This book was released on 1984 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.
Download or read book Catalog of Copyright Entries Third Series written by Library of Congress. Copyright Office and published by . This book was released on 1965 with total page 1400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The record of each copyright registration listed in the Catalog includes a description of the work copyrighted and data relating to the copyright claim (the name of the copyright claimant as given in the application for registration, the copyright date, the copyright registration number, etc.).
Download or read book M Theory and Quantum Geometry written by Lárus Thorlacius and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantization of geometrical objects. The majority of lectures at the Advanced Study Institute on Quantum Ge ometry in Akureyri was on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary par ticles and interactions. The geometric concept of one-dimensional extended objects, or strings, has always been at the core of superstring theory but in recent years the focus has shifted to include also higher-dimensional ob jects, so called D-branes, which play a key role in the non-perturbative dynamics of the theory. A related development has seen the strong coupling regime of a given string theory identified with the weak coupling regime of what was previ ously believed to be a different theory, and a web of such" dualities" that interrelates all known superstring theories has emerged. The resulting uni fied theoretical framework, termed M-theory, has evolved at a rapid pace in recent years.
Download or read book Basic Concepts of Geometry written by Walter Prenowitz and published by Rowman & Littlefield. This book was released on 2012-10-04 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: No descriptive material is available for this title.
