New Spaces in Mathematics: Volume 1
New Spaces in Mathematics: Volume 1

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04-01

Total Pages: 602

ISBN-13: 1108848214

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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.

New Spaces in Physics: Volume 2
New Spaces in Physics: Volume 2

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04-01

Total Pages: 438

ISBN-13: 1108848206

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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.

New Foundations for Physical Geometry
New Foundations for Physical Geometry

Author: Tim Maudlin

Publisher:

Published: 2014-02

Total Pages: 374

ISBN-13: 0198701306

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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.

New Foundations in Mathematics
New Foundations in Mathematics

Author: Garret Sobczyk

Publisher: Springer Science & Business Media

Published: 2012-10-26

Total Pages: 373

ISBN-13: 0817683852

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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.

Spectral Spaces
Spectral Spaces

Author: Max Dickmann

Publisher: Cambridge University Press

Published: 2019-03-21

Total Pages: 652

ISBN-13: 1107146720

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Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.

Topological Spaces
Topological Spaces

Author: Gerard Buskes

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 321

ISBN-13: 1461206650

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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.

A New Look at Geometry
A New Look at Geometry

Author: Irving Adler

Publisher: Courier Corporation

Published: 2013-10-03

Total Pages: 420

ISBN-13: 0486320499

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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.

A Vector Space Approach to Geometry
A Vector Space Approach to Geometry

Author: Melvin Hausner

Publisher: Courier Dover Publications

Published: 2018-10-17

Total Pages: 417

ISBN-13: 0486835391

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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.

New Spaces in Mathematics
New Spaces in Mathematics

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04

Total Pages: 601

ISBN-13: 1108490638

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In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.