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Author: Viktor Vasilʹevich Prasolov Vladimir Mikhaĭlovich Tikhomirov
Publisher: American Mathematical Soc.
ISBN: 9780821897973
Category : Mathematics
Languages : en
Pages : 276
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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.
Author: Viktor Vasilʹevich Prasolov Vladimir Mikhaĭlovich Tikhomirov
Publisher: American Mathematical Soc.
ISBN: 9780821897973
Category : Mathematics
Languages : en
Pages : 276
Get Book
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.
Author: Gennadiĭ Mikhaĭlovich Goluzin
Publisher: American Mathematical Soc.
ISBN: 9780821886557
Category : Functions of complex variables
Languages : en
Pages : 690
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Book Description
Author: Takashi Sakai
Publisher: American Mathematical Soc.
ISBN: 9780821889565
Category : Mathematics
Languages : en
Pages : 378
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Book Description
This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.
Author: Olʹga A. Ladyženskaja
Publisher: American Mathematical Soc.
ISBN: 9780821815731
Category : Mathematics
Languages : en
Pages : 74
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Book Description
Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Author: V. M. Zolotarev
Publisher: American Mathematical Soc.
ISBN: 0821845195
Category : Mathematics
Languages : en
Pages : 298
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Book Description
This is the first book specifically devoted to a systematic exposition of the essential facts known about the properties of stable distributions. In addition to its main focus on the analytic properties of stable laws, the book also includes examples of the occurrence of stable distributions in applied problems and a chapter on the problem of statistical estimation of the parameters determining stable laws. A valuable feature of the book is the author's use of several formally different ways of expressing characteristic functions corresponding to these laws.
Author: Alekseĭ Vasilʹevich Pogorelov
Publisher: American Mathematical Soc.
ISBN: 9780821886618
Category : Mathematics
Languages : en
Pages : 680
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Book Description
Author: Naum Ilʹich Akhiezer
Publisher: American Mathematical Soc.
ISBN: 9780821809006
Category : Mathematics
Languages : en
Pages : 237
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Book Description
Presents the theory of elliptic functions and its applications. Suitable primarily for engineers who work with elliptic functions, this work is also intended for those with background in the elements of mathematical analysis and the theory of functions contained in the first two years of mathematics and physics courses at the college level.
Author: Masaya Yamaguchi
Publisher: American Mathematical Soc.
ISBN: 9780821805374
Category : Mathematics
Languages : en
Pages : 104
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Book Description
This book aims at providing a handy explanation of the notions behind the self-similar sets called "fractals" and "chaotic dynamical systems". The authors emphasize the beautiful relationship between fractal functions (such as Weierstrass's) and chaotic dynamical systems; these nowhere-differentiable functions are generating functions of chaotic dynamical systems. These functions are shown to be in a sense unique solutions of certain boundary problems. The last chapter of the book treats harmonic functions on fractal sets.
Author: Ichirō Shigekawa
Publisher: American Mathematical Soc.
ISBN: 9780821826263
Category : Mathematics
Languages : en
Pages : 202
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Book Description
This book offers a concise introduction to stochastic analysis, particularly the Malliavin calculus. A detailed description is given of all technical tools necessary to describe the theory, such as the Wiener process, the Ornstein-Uhlenbeck process, and Sobolev spaces. Applications of stochastic cal
Author: M. G. Goluzina
Publisher: American Mathematical Soc.
ISBN: 9780821897386
Category : Mathematics
Languages : en
Pages : 386
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Book Description
This book is intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area. It differs from other problem books in the greater difficulty of the problems, some of which are well-known theorems in analysis. Nonetheless, no special preparation is required to solve the majority of the problems. Brief but detailed solutions to most of the problems are given in the second part of the book. This book is unique in that the authors have aimed to systematize a range of problems that are found in sources that are almost inaccessible (especially to students) and in mathematical folklore.
