Solitons, Geometry, and Topology: On the Crossroad

Solitons, Geometry, and Topology: On the Crossroad PDF Author: V. M. Buchstaber
Publisher: American Mathematical Soc.
ISBN: 9780821806661
Category : Geometry
Languages : en
Pages : 204

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Solitons, Geometry, and Topology: On the Crossroad

Solitons, Geometry, and Topology: On the Crossroad PDF Author: V. M. Buchstaber
Publisher: American Mathematical Soc.
ISBN: 9780821806661
Category : Geometry
Languages : en
Pages : 204

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Extrinsic Geometry of Convex Surfaces

Extrinsic Geometry of Convex Surfaces PDF Author: Alekseĭ Vasilʹevich Pogorelov
Publisher: American Mathematical Soc.
ISBN: 9780821886618
Category : Mathematics
Languages : en
Pages : 680

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Methods of Information Geometry

Methods of Information Geometry PDF Author: Shun-ichi Amari
Publisher: American Mathematical Soc.
ISBN: 9780821843024
Category : Computers
Languages : en
Pages : 220

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Book Description
Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis.

Introduction to the Theory of Linear Nonselfadjoint Operators

Introduction to the Theory of Linear Nonselfadjoint Operators PDF Author: Israel Gohberg
Publisher: American Mathematical Soc.
ISBN: 9780821886502
Category : Mathematics
Languages : en
Pages : 402

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Modular Forms and Hecke Operators

Modular Forms and Hecke Operators PDF Author: A. N. Andrianov
Publisher: American Mathematical Soc.
ISBN: 1470418681
Category :
Languages : en
Pages : 346

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Book Description
he concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups.Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.

Geometric Theory of Functions of a Complex Variable

Geometric Theory of Functions of a Complex Variable PDF Author: Gennadiĭ Mikhaĭlovich Goluzin
Publisher: American Mathematical Soc.
ISBN: 9780821886557
Category : Functions of complex variables
Languages : en
Pages : 690

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Introduction to Topology

Introduction to Topology PDF Author: V. A. Vasilʹev
Publisher: American Mathematical Soc.
ISBN: 0821821628
Category : Mathematics
Languages : en
Pages : 165

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Book Description
This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on itsstyle. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have importantgeneralizations are presented."

Generalized Cohomology

Generalized Cohomology PDF Author: Akira Kōno
Publisher: American Mathematical Soc.
ISBN: 9780821835142
Category : Mathematics
Languages : en
Pages : 276

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Book Description
Aims to give an exposition of generalized (co)homology theories that can be read by a group of mathematicians who are not experts in algebraic topology. This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.

Geometry

Geometry PDF Author: V. V. Prasolov
Publisher: American Mathematical Soc.
ISBN: 1470425432
Category : Mathematics
Languages : en
Pages : 274

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Book Description
This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Distribution of Zeros of Entire Functions

Distribution of Zeros of Entire Functions PDF Author: Boris I_Akovlevich Levin
Publisher: American Mathematical Soc.
ISBN: 0821845055
Category : Mathematics
Languages : en
Pages : 542

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Book Description