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Smooth Manifolds and Observables

Posted By: AvaxGenius
Date: 9 Jan 2024 22:35:45
Smooth Manifolds and Observables

Smooth Manifolds and Observables by Jet Nestruev
English | PDF (True) | 2003 | 226 Pages | ISBN : 0387955437 | 3.3 MB

This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
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General Topology II: Compactness, Homologies of General Spaces

Posted By: AvaxGenius
Date: 19 Sep 2022 17:09:24
General Topology II: Compactness, Homologies of General Spaces

General Topology II: Compactness, Homologies of General Spaces by A. V. Arhangel’skii
English | PDF | 1996 | 265 Pages | ISBN : 3642770320 | 47.4 MB

This volume of the Encyclopaedia consists of two independent parts. The first contains a survey of results related to the concept of compactness in general topology. It highlights the role that compactness plays in many areas of general topology. The second part is devoted to homology and cohomology theories of general spaces. Special emphasis is placed on the method of sheaf theory as a unified approach to constructions of such theories. Both authors have succeeded in presenting a wealth of material that is of interest to students and researchers in the area of topology. Each part illustrates deep connections between important mathematical concepts. Both parts reflect a certain new way of looking at well known facts by establishing interesting relationships between specialized results belonging to diverse areas of mathematics.
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Difference Algebra (Repost)

Posted By: AvaxGenius
Date: 30 Apr 2022 08:31:17
Difference Algebra (Repost)

Difference Algebra by Alexander Levin
English | PDF | 2008 | 528 Pages | ISBN : 1402069464 | 4.4 MB

Difference algebra grew out of the study of algebraic difference equations with coefficients from functional fields in much the same way as the classical algebraic geometry arose from the study of polynomial equations with numerical coefficients. The first stage of the development of the theory is associated with its founder J. F. Ritt (1893 - 1951) and R. Cohn whose book Difference Algebra (1965) remained the only fundamental monograph on the subject for many years.
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Universal Algebra, Algebraic Logic, and Databases

Posted By: AvaxGenius
Date: 6 Jul 2021 11:59:43
Universal Algebra, Algebraic Logic, and Databases

Universal Algebra, Algebraic Logic, and Databases by B. Plotkin
English | PDF | 1994 | 445 Pages | ISBN : 0792326652 | 41 MB

Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications.
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Sheaves in Geometry and Logic: A First Introduction to Topos Theory

Posted By: AvaxGenius
Date: 1 Jul 2021 04:51:12
Sheaves in Geometry and Logic: A First Introduction to Topos Theory

Sheaves in Geometry and Logic: A First Introduction to Topos Theory by Saunders Mac Lane
English | PDF | 1994 | 642 Pages | ISBN : 0387977104 | 51.5 MB

We dedicate this book to the memory of J. Frank Adams. His clear insights have inspired many mathematicians, including both of us. In January 1989, when the first draft of our book had been completed, we heard the sad news of his untimely death.
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Modern Algebra and the Rise of Mathematical Structures: Second revised edition

Posted By: AvaxGenius
Date: 22 Nov 2020 22:15:19
Modern Algebra and the Rise of Mathematical Structures: Second revised edition

Modern Algebra and the Rise of Mathematical Structures: Second revised edition by Leo Corry
English | PDF | 2004 | 463 Pages | ISBN : 3764370025 | 64.1 MB

The notion of a mathematical structure is among the most pervasive ones in twentieth-century mathematics. Modern Algebra and the Rise of Mathematical Structures describes two stages in the historical development of this notion: first, it traces its rise in the context of algebra from the mid-nineteenth century to its consolidation by 1930, and then it considers several attempts to formulate elaborate theories after 1930 aimed at elucidating, from a purely mathematical perspective, the precise meaning of this idea.
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Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups (Repost)

Posted By: AvaxGenius
Date: 21 Mar 2020 23:09:43
Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups (Repost)

Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups by José Bueso
English | PDF | 2003 | 307 Pages | ISBN : 9048163285 | 22.51 MB

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them.
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Graphs on Surfaces and Their Applications

Posted By: AvaxGenius
Date: 21 Mar 2020 22:47:50
Graphs on Surfaces and Their Applications

Graphs on Surfaces and Their Applications by Sergei K. Lando
English | PDF | 2004 | 463 Pages | ISBN : 3540002030 | 3.89 MB

Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research.
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