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New Spaces In Mathematics
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Book Synopsis New Spaces in Mathematics: Volume 1 by : Mathieu Anel
Download or read book New Spaces in Mathematics: Volume 1 written by Mathieu Anel and published by Cambridge University Press. This book was released on 2021-04-01 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.
Book Synopsis New Spaces in Mathematics and Physics 2 Volume Hardback Set: Formal and Conceptual Reflections by : Mathieu Anel
Download or read book New Spaces in Mathematics and Physics 2 Volume Hardback Set: Formal and Conceptual Reflections written by Mathieu Anel and published by . This book was released on 2020-11-30 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Spaces in Physics: Volume 2 by : Mathieu Anel
Download or read book New Spaces in Physics: Volume 2 written by Mathieu Anel and published by Cambridge University Press. This book was released on 2021-04-01 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. This volume covers a broad range of topics in mathematical physics, including noncommutative geometry, supergeometry, derived symplectic geometry, higher geometric quantization, intuitionistic quantum logic, problems with the continuum description of spacetime, twistor theory, loop quantum gravity, and geometry in string theory. It is addressed primarily to mathematical physicists and mathematicians, but also to historians and philosophers of these disciplines.
Book Synopsis New Foundations for Physical Geometry by : Tim Maudlin
Download or read book New Foundations for Physical Geometry written by Tim Maudlin and published by . This book was released on 2014-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Book Synopsis New Foundations in Mathematics by : Garret Sobczyk
Download or read book New Foundations in Mathematics written by Garret Sobczyk and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
Download or read book Spectral Spaces written by Max Dickmann and published by Cambridge University Press. This book was released on 2019-03-21 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.
Book Synopsis A New Look at Geometry by : Irving Adler
Download or read book A New Look at Geometry written by Irving Adler and published by Courier Corporation. This book was released on 2013-10-03 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richly detailed survey of the evolution of geometrical ideas and development of concepts of modern geometry: projective, Euclidean, and non-Euclidean geometry; role of geometry in Newtonian physics, calculus, relativity. Over 100 exercises with answers. 1966 edition.
Book Synopsis A Vector Space Approach to Geometry by : Melvin Hausner
Download or read book A Vector Space Approach to Geometry written by Melvin Hausner and published by Courier Dover Publications. This book was released on 2018-10-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fascinating exploration of the correlation between geometry and linear algebra, this text also offers elementary explanations of the role of geometry in other branches of math and science. 1965 edition.
Book Synopsis Spaces: An Introduction to Real Analysis by : Tom L. Lindstrøm
Download or read book Spaces: An Introduction to Real Analysis written by Tom L. Lindstrøm and published by American Mathematical Soc.. This book was released on 2017-11-28 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spaces is a modern introduction to real analysis at the advanced undergraduate level. It is forward-looking in the sense that it first and foremost aims to provide students with the concepts and techniques they need in order to follow more advanced courses in mathematical analysis and neighboring fields. The only prerequisites are a solid understanding of calculus and linear algebra. Two introductory chapters will help students with the transition from computation-based calculus to theory-based analysis. The main topics covered are metric spaces, spaces of continuous functions, normed spaces, differentiation in normed spaces, measure and integration theory, and Fourier series. Although some of the topics are more advanced than what is usually found in books of this level, care is taken to present the material in a way that is suitable for the intended audience: concepts are carefully introduced and motivated, and proofs are presented in full detail. Applications to differential equations and Fourier analysis are used to illustrate the power of the theory, and exercises of all levels from routine to real challenges help students develop their skills and understanding. The text has been tested in classes at the University of Oslo over a number of years.
Book Synopsis Topological Spaces by : Gerard Buskes
Download or read book Topological Spaces written by Gerard Buskes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.
Book Synopsis The Shape of Space by : Jeffrey R. Weeks
Download or read book The Shape of Space written by Jeffrey R. Weeks and published by CRC Press. This book was released on 2001-12-12 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
Book Synopsis An Introduction to Hilbert Space and Quantum Logic by : David W. Cohen
Download or read book An Introduction to Hilbert Space and Quantum Logic written by David W. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically, nonclassical physics developed in three stages. First came a collection of ad hoc assumptions and then a cookbook of equations known as "quantum mechanics". The equations and their philosophical underpinnings were then collected into a model based on the mathematics of Hilbert space. From the Hilbert space model came the abstaction of "quantum logics". This book explores all three stages, but not in historical order. Instead, in an effort to illustrate how physics and abstract mathematics influence each other we hop back and forth between a purely mathematical development of Hilbert space, and a physically motivated definition of a logic, partially linking the two throughout, and then bringing them together at the deepest level in the last two chapters. This book should be accessible to undergraduate and beginning graduate students in both mathematics and physics. The only strict prerequisites are calculus and linear algebra, but the level of mathematical sophistication assumes at least one or two intermediate courses, for example in mathematical analysis or advanced calculus. No background in physics is assumed.
Book Synopsis Topological Methods in Euclidean Spaces by : Gregory L. Naber
Download or read book Topological Methods in Euclidean Spaces written by Gregory L. Naber and published by Courier Corporation. This book was released on 2012-08-29 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensive development of such topics as elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, and the Stone-Weierstrass Theorem. New section of solutions to selected problems.
Book Synopsis New Spaces in Physics by : Mathieu Anel
Download or read book New Spaces in Physics written by Mathieu Anel and published by Cambridge University Press. This book was released on 2021-04 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this graduate-level book, leading researchers explore various new notions of 'space' in mathematical physics.
Book Synopsis Shapes, Space, and Symmetry by : Alan Holden
Download or read book Shapes, Space, and Symmetry written by Alan Holden and published by Courier Corporation. This book was released on 1991-01-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains structure of nine regular solids and many semiregular solids and demonstrates how they can be used to explain mathematics. Instructions for cardboard models. Over 300 illustrations. 1971 edition.
Book Synopsis Vector Spaces and Matrices by : Robert M. Thrall
Download or read book Vector Spaces and Matrices written by Robert M. Thrall and published by Courier Corporation. This book was released on 2014-01-15 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students receive the benefits of axiom-based mathematical reasoning as well as a grasp of concrete formulations. Suitable as a primary or supplementary text for college-level courses in linear algebra. 1957 edition.
Book Synopsis Normal Topological Spaces by : Richard A. Alo
Download or read book Normal Topological Spaces written by Richard A. Alo and published by Cambridge University Press. This book was released on 2009-01-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text bridges the gap existing in the field of set theoretical topology between the introductory texts and the more specialised monographs. The authors review fit developments in general topology and discuss important new areas of research and the importance of defining a methodology applicable to this active field of mathematics. The concept of normal cover and related ideas is considered in detail, as are the characterisations of normal spaces, collectionwise normal spaces and their interrelationships with paracompact spaces (and other weaker forms of compactness). Various methods of embedding subspaces are studied, before considering newer concepts such as M-spaces and their relationships with established ideas. These ideas are applied to give new results pertaining to the extension of continuous vector-valued functions. Wallman-Frink compactifications and realcompactifications are also studied to assist in unifying the ideas through the use of the more general L-filter.
