Sketches of an elephant: a topos theory compendium, Johnstone, Peter T. (reader In The Foundations Of Mathematics, University Of Cambridge, Cambridge, Uk)
Автор: Hatcher A. Название: Algebraic topology ISBN: 0521795400 ISBN-13(EAN): 9780521795401 Издательство: Cambridge Academ Рейтинг: Цена: 40120.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.
Автор: Daniel Huybrechts Название: The Geometry of Cubic Hypersurfaces ISBN: 1009280007 ISBN-13(EAN): 9781009280006 Издательство: Cambridge Academ Рейтинг: Цена: 73910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.
Автор: Clara Loh Название: Exploring Formalisation ISBN: 3031146484 ISBN-13(EAN): 9783031146480 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Нет в наличии. Описание: This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean. After a quick introduction to Lean, the basic techniques of human-readable formalisation are introduced, illustrated by simple examples on maps, induction and real numbers. Subsequently, typical design options are discussed and brought to life through worked examples in the setting of simplicial complexes (a higher-dimensional generalisation of graph theory). Finally, the book demonstrates how current research in algebraic and geometric topology can be formalised by means of suitable abstraction layers. Informed by the author's recent teaching and research experience, this book allows students and researchers to quickly get started with formalising and checking their proofs. The core material of the book is accessible to mathematics students with basic programming skills. For the final chapter, familiarity with elementary category theory and algebraic topology is recommended.
Автор: Isaac Goldbring Название: Ultrafilters Throughout Mathematics ISBN: 1470469618 ISBN-13(EAN): 9781470469610 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 71060.00 T Наличие на складе: Поставка под заказ. Описание: Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to a wide variety of topics. The first part of the book deals solely with ultrafilters; the second part presents the classical ultraproduct construction.
Автор: John Milnor Название: Topology from the Differentiable Viewpoint ISBN: 0691048339 ISBN-13(EAN): 9780691048338 Издательство: Wiley Рейтинг: Цена: 47520.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Chmutov Название: Introduction to Vassiliev Knot Invariants ISBN: 1107020832 ISBN-13(EAN): 9781107020832 Издательство: Cambridge Academ Рейтинг: Цена: 53960.00 T Наличие на складе: Есть Описание: This detailed exposition of a relatively recent development in knot theory, namely, the theory of Vassiliev knot invariants, is intended to serve both as a textbook for readers with little background in this area, and as a guide to some of the more advanced material.
Автор: Afra J. Zomorodian Название: Topology for Computing ISBN: 0521836662 ISBN-13(EAN): 9780521836661 Издательство: Cambridge Academ Рейтинг: Цена: 116160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book presents the basic concepts from the emerging field of computational topology that combines topology theory with the power of computing to solve problems in diverse fields. Written from a computer science perspective, the book enables non-specialists to grasp the ideas and so participate in current research in computational topology.
Автор: Hans-Christian Hege; Konrad Polthier; Gerik Scheue Название: Topology-Based Methods in Visualization II ISBN: 3540886052 ISBN-13(EAN): 9783540886051 Издательство: Springer Рейтинг: Цена: 107130.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Visualization research aims at providing insight into large, complicated data. Topological methods stand out by their solid mathematical ground guiding the algorithmic analysis and its presentation among the various visualization techniques. This book contains papers from the second workshop on `Topology-Based Methods in Visualization`.
Автор: Thurston, William P. Название: Three-dimensional geometry and topology ISBN: 0691083045 ISBN-13(EAN): 9780691083049 Издательство: Wiley Рейтинг: Цена: 116160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning, but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book develops some of the power of geometry in two and three dimensions, and the strong connection of geometry with topology.
Автор: Adams, Colin , Flapan, Erica , Henrich, Allison Название: Concise Encyclopedia of Knot Theory ISBN: 1138297844 ISBN-13(EAN): 9781138297845 Издательство: Taylor&Francis Рейтинг: Цена: 224570.00 T Наличие на складе: Невозможна поставка. Описание: This books provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications edited and contributed to by top researchers in the field of knot theory. The articles in this book are accessible to both undergrads and researchers.
Автор: Dey, Tamal Krishna (purdue University, Indiana) Wang, Yusu (university Of California, San Diego) Название: Computational topology for data analysis ISBN: 1009098160 ISBN-13(EAN): 9781009098168 Издательство: Cambridge Academ Рейтинг: Цена: 52790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data in applied domains. This comprehensive text covers the current state of the field for students in mathematics and computer science, providing a computational and algorithmic foundation for techniques in TDA.
Автор: Schultz, Patrick Spivak, David I. Название: Temporal type theory ISBN: 3030007030 ISBN-13(EAN): 9783030007034 Издательство: Springer Рейтинг: Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This innovative monograph explores a new mathematical formalism in higher-order temporal logic for proving properties about the behavior of systems. Developed by the authors, the goal of this novel approach is to explain what occurs when multiple, distinct system components interact by using a category-theoretic description of behavior types based on sheaves. The authors demonstrate how to analyze the behaviors of elements in continuous and discrete dynamical systems so that each can be translated and compared to one another. Their temporal logic is also flexible enough that it can serve as a framework for other logics that work with similar models.
The book begins with a discussion of behavior types, interval domains, and translation invariance, which serves as the groundwork for temporal type theory. From there, the authors lay out the logical preliminaries they need for their temporal modalities and explain the soundness of those logical semantics. These results are then applied to hybrid dynamical systems, differential equations, and labeled transition systems. A case study involving aircraft separation within the National Airspace System is provided to illustrate temporal type theory in action.
Researchers in computer science, logic, and mathematics interested in topos-theoretic and category-theory-friendly approaches to system behavior will find this monograph to be an important resource. It can also serve as a supplemental text for a specialized graduate topics course.
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