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The Geometry of Celestial Mechanics

The Geometry of Celestial Mechanics Author Hansjörg Geiges
ISBN-10 9781107125407
Release 2016-03-24
Pages 236
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A first course in celestial mechanics emphasising the variety of geometric ideas that have shaped the subject.

The Block Theory of Finite Group Algebras

The Block Theory of Finite Group Algebras Author Markus Linckelmann
ISBN-10 9781108589215
Release 2018-05-24
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This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

Groups Languages and Automata

Groups  Languages and Automata Author Derek F. Holt
ISBN-10 9781108211048
Release 2017-02-23
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Fascinating connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Automata can be used in group theory to encode complexity, to represent aspects of underlying geometry on a space on which a group acts, and to provide efficient algorithms for practical computation. There are also many applications in geometric group theory. The authors provide background material in each of these related areas, as well as exploring the connections along a number of strands that lead to the forefront of current research in geometric group theory. Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group. This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research students in (geometric) group theory.

Riemann Surfaces and Algebraic Curves

Riemann Surfaces and Algebraic Curves Author Renzo Cavalieri
ISBN-10 9781316798935
Release 2016-09-26
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Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

Fourier Analysis with Applications

Fourier Analysis with Applications Author Adrian Constantin
ISBN-10 9781107044104
Release 2016-05-21
Pages 379
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Fourier analysis aims to decompose functions into a superposition of simple trigonometric functions, whose special features can be exploited to isolate specific components into manageable clusters before reassembling the pieces. This two-volume text presents a largely self-contained treatment, comprising not just the major theoretical aspects (Part I) but also exploring links to other areas of mathematics and applications to science and technology (Part II). Following the historical and conceptual genesis, this book (Part I) provides overviews of basic measure theory and functional analysis, with added insight into complex analysis and the theory of distributions. The material is intended for both beginning and advanced graduate students with a thorough knowledge of advanced calculus and linear algebra. Historical notes are provided and topics are illustrated at every stage by examples and exercises, with separate hints and solutions, thus making the exposition useful both as a course textbook and for individual study.

Dispersive Partial Differential Equations

Dispersive Partial Differential Equations Author M. Burak Erdoğan
ISBN-10 9781316694589
Release 2016-05-03
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The area of nonlinear dispersive partial differential equations (PDEs) is a fast developing field which has become exceedingly technical in recent years. With this book, the authors provide a self-contained and accessible introduction for graduate or advanced undergraduate students in mathematics, engineering, and the physical sciences. Both classical and modern methods used in the field are described in detail, concentrating on the model cases that simplify the presentation without compromising the deep technical aspects of the theory, thus allowing students to learn the material in a short period of time. This book is appropriate both for self-study by students with a background in analysis, and for teaching a semester-long introductory graduate course in nonlinear dispersive PDEs. Copious exercises are included, and applications of the theory are also presented to connect dispersive PDEs with the more general areas of dynamical systems and mathematical physics.

The Mathematical Mechanic

The Mathematical Mechanic Author Mark Levi
ISBN-10 9780691154565
Release 2012
Pages 186
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In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.

Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics Author V.I. Arnol'd
ISBN-10 9781475720631
Release 2013-04-09
Pages 520
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This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.

Finite Geometry and Combinatorial Applications

Finite Geometry and Combinatorial Applications Author Simeon Ball
ISBN-10 9781107107991
Release 2015-07-02
Pages 295
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A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.

The Scientific Legacy of Poincar

The Scientific Legacy of Poincar  Author Éric Charpentier
ISBN-10 9780821847183
Release 2010
Pages 391
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Henri Poincare (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. He created new mathematical branches, such as algebraic topology, dynamical systems, and automorphic functions, and he opened the way to complex analysis with several variables and to the modern approach to asymptotic expansions. He revolutionized celestial mechanics, discovering deterministic chaos. In physics, he is one of the fathers of special relativity, and his work in the philosophy of sciences is illuminating. For this book, about twenty world experts were asked to present one part of Poincare's extraordinary work. Each chapter treats one theme, presenting Poincare's approach, and achievements, along with examples of recent applications and some current prospects. Their contributions emphasize the power and modernity of the work of Poincare, an inexhaustible source of inspiration for researchers, as illustrated by the Fields Medal awarded in 2006 to Grigori Perelman for his proof of the Poincare conjecture stated a century before. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, or physics, or more generally by anyone who likes mathematical and physical ideas. Rather than presenting detailed proofs, the main ideas are explained, and a bibliography is provided for those who wish to understand the technical details.

Reversibility in Dynamics and Group Theory

Reversibility in Dynamics and Group Theory Author Anthony G. O'Farrell
ISBN-10 9781107442887
Release 2015-05-28
Pages 292
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An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.

Hyperbolic Geometry

Hyperbolic Geometry Author Birger Iversen
ISBN-10 9780521435086
Release 1992-12-17
Pages 298
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Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.

Euclid s Phaenomena

Euclid s Phaenomena Author Euclid
ISBN-10 9780821840726
Release 1996
Pages 132
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This book contains a translation and study of ""Euclid's Phaenomena"", a work which once formed part of the mathematical training of astronomers from Central Asia to Western Europe. Included is an introduction that sets Euclid's geometry of the celestial sphere, and its application to the astronomy of his day, into its historical context for readers not already familiar with it. So no knowledge of astronomy or advanced mathematics is necessary for an understanding of the work. The book shows mathematical astronomy shortly before the invention of trigonometry, which allowed the calculation of exact results and the subsequent composition of ""Ptolemy's Almagest"".""The Phaenomena"" itself begins with an introduction (possibly not by Euclid) followed by eighteen propositions set out in geometrical style about how arcs of the zodiacal circle move across the sky. The astronomical application is to the small arc of that circle occupied by the Sun, but the Sun is not mentioned. This work and the (roughly) contemporaneous treatises of Autolycus and Aristarchos form a corpus of the oldest extant works on mathematical astronomy. Together with ""Euclid's Optics"", one has the beginnings of the history of science as an application of mathematics.

Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society Author
ISBN-10 UCSD:31822020214870
Release 1903
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Bulletin of the American Mathematical Society has been writing in one form or another for most of life. You can find so many inspiration from Bulletin of the American Mathematical Society also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Bulletin of the American Mathematical Society book for free.

Register of Vanderbilt University Announcement

Register of Vanderbilt University     Announcement    Author Vanderbilt University
ISBN-10 UOM:39015076283608
Release 1930
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Register of Vanderbilt University Announcement has been writing in one form or another for most of life. You can find so many inspiration from Register of Vanderbilt University Announcement also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Register of Vanderbilt University Announcement book for free.

Mathematics and Its History

Mathematics and Its History Author John Stillwell
ISBN-10 9781441960528
Release 2010-08-02
Pages 662
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From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

The Emergence of the American Mathematical Research Community 1876 1900

The Emergence of the American Mathematical Research Community  1876 1900 Author Karen Hunger Parshall
ISBN-10 0821809075
Release 1994
Pages 500
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This volume traces the transformation of the United States from a mathematical backwater to a major presence during the quarter-century from 1876 to 1900. Presenting a detailed study of the major figures involved in this transformation, it focuses on the three most influential individuals--the British algebraist James Joseph Sylvester, the German standard-bearer Felix Klein, and the American mathematician Eliakim Hastings Moore--and on the principal institutions with which they were associated--the Johns Hopkins University, Gottingen University, and the University of Chicago. This book further analyzes the research traditions these men and their institutions represented, the impact they had on the second generation of American mathematical researchers, and the role of the American Mathematical Society in these developments. This is the first work ever written on the history of American mathematics during this period and one of the few books that examines the historical development of American mathematics from a wide perspective. By placing the development of American mathematics within the context of broader external factors affecting historical events, the authors show how the character of American research was decisively affected by the surrounding scientific, educational, and social contexts of the period. Aimed at a general mathematical audience and at historians of science, this book contains an abundance of unpublished archival material, numerous rare photographs, and an extensive bibliography.