Peter Grassmann's Books

Introduction to Strings and Branes

By: Peter West

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Introduction to Strings and Branes

By: Peter West

Detailed, step-by-step introduction to the theoretical foundations of strings and branes, essential reading for graduate students and researchers.

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723

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Cambridge University Press

Published Date

ISBN 10

0521817471

ISBN 13

9780521817479

Introduction to the Functional Renormalization Group

By: Peter Kopietz,Lorenz Bartosch,Florian Schütz

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Introduction to the Functional Renormalization Group

By: Peter Kopietz,Lorenz Bartosch,Florian Schütz

The renormalization group (RG) has nowadays achieved the status of a meta-theory, which is a theory about theories. The theory of the RG consists of a set of concepts and methods which can be used to understand phenomena in many different ?elds of physics, ranging from quantum ?eld theory over classical statistical mechanics to nonequilibrium phenomena. RG methods are particularly useful to understand phenomena where ?uctuations involving many different length or time scales lead to the emergence of new collective behavior in complex many-body systems. In view of the diversity of ?elds where RG methods have been successfully applied, it is not surprising that a variety of apparently different implementations of the RG idea have been proposed. Unfortunately, this makes it somewhat dif?cult for beginners to learn this technique. For example, the ?eld-theoretical formulation of the RG idea looks at the ?rst sight rather different from the RG approach pioneered by Wilson, the latter being based on the concept of the effective action which is ite- tively calculated by successive elimination of the high-energy degrees of freedom. Moreover, the Wilsonian RG idea has been implemented in many different ways, depending on the particular problem at hand, and there seems to be no canonical way of setting up the RG procedure for a given problem.

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383

Publisher

Springer

Published Date

ISBN 10

3642050948

ISBN 13

9783642050947

Bosonization of Interacting Fermions in Arbitrary Dimensions

By: Peter Kopietz

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Bosonization of Interacting Fermions in Arbitrary Dimensions

By: Peter Kopietz

The author presents in detail a new non-perturbative approach to the fermionic many-body problem, improving the bosonization technique and generalizing it to dimensions d1 via functional integration and Hubbard--Stratonovich transformations. In Part I he clearly illustrates the approximations and limitations inherent in higher-dimensional bosonization and derives the precise relation with diagrammatic perturbation theory. He shows how the non-linear terms in the energy dispersion can be systematically included into bosonization in arbitrary d, so that in d1 the curvature of the Fermi surface can be taken into account. Part II gives applications to problems of physical interest. The book addresses researchers and graduate students in theoretical condensed matter physics.

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263

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Springer Science & Business Media

Published Date

ISBN 10

3540684956

ISBN 13

9783540684954

Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering

By: Peter Russer

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Electromagnetics, Microwave Circuit and Antenna Design for Communications Engineering

By: Peter Russer

If you're looking for a clear, comprehensive overview of basic electromagnetics principles and applications to antenna and microwave circuit design for communications, this authoritative book is your best choice. Including concise explanations of all required mathematical concepts needed to fully comprehend the material, the book is your complete resource for understanding electromagnetics in current, emerging and future broadband communication systems, as well as high-speed analogue and digital electronic circuits and systems.

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444

Publisher

Artech House

Published Date

ISBN 10

1580535321

ISBN 13

9781580535328

A Mathematician and His Mathematical Work

Selected Papers of S.S. Chern

By: Shiing-Shen Chern,G. Tian,Peter Li

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A Mathematician and His Mathematical Work

Selected Papers of S.S. Chern

By: Shiing-Shen Chern,G. Tian,Peter Li

This volume is about the life and work of Shiing-Shen Chern (1911-), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988.

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734

Publisher

World Scientific

Published Date

ISBN 10

9810223854

ISBN 13

9789810223854

Riemannian Geometry

By: Peter Petersen

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Riemannian Geometry

By: Peter Petersen

This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in disguise); an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus integrated into the text, allowing for an early treatment of the Sphere theorem using a forgotten proof by Berger; recent results regarding manifolds with positive curvature.

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412

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Springer Science & Business Media

Published Date

ISBN 10

0387294031

ISBN 13

9780387294032

Path Integrals and Anomalies in Curved Space

By: Fiorenzo Bastianelli,Peter van Nieuwenhuizen

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Path Integrals and Anomalies in Curved Space

By: Fiorenzo Bastianelli,Peter van Nieuwenhuizen

This book introduces path integrals, a powerful method for describing quantum phenomena, and then uses them to compute anomalies in quantum field theories. An advanced text for researchers and graduate students of quantum field theory and string theory, it also provides a stand-alone introduction to path integrals in quantum mechanics.

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Cambridge University Press

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ISBN 10

1139456849

ISBN 13

9781139456845

Methods of Algebraic Geometry in Control Theory: Part II

Multivariable Linear Systems and Projective Algebraic Geometry

By: Peter Falb

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Methods of Algebraic Geometry in Control Theory: Part II

Multivariable Linear Systems and Projective Algebraic Geometry

By: Peter Falb

Control theory represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems. Algebraic geometry may, in an elementary way, be viewed as the study of the structure and properties of the solutions of systems of algebraic equations. The aim of this book is to provide access to the methods of algebraic geometry for engineers and applied scientists through the motivated context of control theory" .* The development which culminated with this volume began over twenty-five years ago with a series of lectures at the control group of the Lund Institute of Technology in Sweden. I have sought throughout to strive for clarity, often using constructive methods and giving several proofs of a particular result as well as many examples. The first volume dealt with the simplest control systems (i.e., single input, single output linear time-invariant systems) and with the simplest algebraic geometry (i.e., affine algebraic geometry). While this is quite satisfactory and natural for scalar systems, the study of multi-input, multi-output linear time invariant control systems requires projective algebraic geometry. Thus, this second volume deals with multi-variable linear systems and pro jective algebraic geometry. The results are deeper and less transparent, but are also quite essential to an understanding of linear control theory. A review of * From the Preface to Part 1. viii Preface the scalar theory is included along with a brief summary of affine algebraic geometry (Appendix E).

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382

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Springer Science & Business Media

Published Date

ISBN 10

1461215641

ISBN 13

9781461215646

Quantum Theory

A Mathematical Approach

By: Peter Bongaarts

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Quantum Theory

A Mathematical Approach

By: Peter Bongaarts

This book was inspired by the general observation that the great theories of modern physics are based on simple and transparent underlying mathematical structures – a fact not usually emphasized in standard physics textbooks – which makes it easy for mathematicians to understand their basic features. It is a textbook on quantum theory intended for advanced undergraduate or graduate students: mathematics students interested in modern physics, and physics students who are interested in the mathematical background of physics and are dissatisfied with the level of rigor in standard physics courses. More generally, it offers a valuable resource for all mathematicians interested in modern physics, and all physicists looking for a higher degree of mathematical precision with regard to the basic concepts in their field.

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460

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Springer

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ISBN 10

3319095617

ISBN 13

9783319095615

Newtonian Electrodynamics

By: Peter Graneau,Neal Graneau

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Newtonian Electrodynamics

By: Peter Graneau,Neal Graneau

The book deals with the resurgence of nineteenth century electromagnetism in physics and electrical engineering. It describes a series of important experiments, and new technologies based on these experiments, which cannot be explained by and analyzed with the modern relativistic electrodynamics of the twentieth century. The Newtonian electrodynamics of Coulomb, Ampere, Neumann, and Kirchhoff, which was current from 1750 to 1900, is fully reviewed and greatly extended to deal with contemporary research on exploding wires, railguns and other electromagnetic accelerators, jet propulsion in liquid metals, arc plasma explosions, capillary fusion, and lightning phenomena. Much of the book is based on the atomic definition of the Amperian current element. Finite element techniques for solving many electrodynamic problems are described.

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310

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World Scientific

Published Date

ISBN 10

9810226810

ISBN 13

9789810226817

Abel's Proof

An Essay on the Sources and Meaning of Mathematical Unsolvability

By: Peter Pesic

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Abel's Proof

An Essay on the Sources and Meaning of Mathematical Unsolvability

By: Peter Pesic

The intellectual and human story of a mathematical proof that transformed our ideas about mathematics. In 1824 a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancé. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra—which even Newton resisted—and the gradual acceptance of the usefulness and perhaps even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.

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222

Publisher

MIT Press

Published Date

ISBN 10

0262338955

ISBN 13

9780262338950

Lectures on Number Theory

By: Peter Gustav Lejeune Dirichlet,Richard Dedekind

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Lectures on Number Theory

By: Peter Gustav Lejeune Dirichlet,Richard Dedekind

Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions.

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297

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American Mathematical Soc.

Published Date

ISBN 10

0821820176

ISBN 13

9780821820179

Condition

The Geometry of Numerical Algorithms

By: Peter Bürgisser,Felipe Cucker

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Condition

The Geometry of Numerical Algorithms

By: Peter Bürgisser,Felipe Cucker

This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance ---regarding both stability and complexity--- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming.

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567

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642388965

ISBN 13

9783642388965

Sievers' Law and the History of Semivowel Syllabicity in Indo-European and Ancient Greek

By: Peter Barber

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Sievers' Law and the History of Semivowel Syllabicity in Indo-European and Ancient Greek

By: Peter Barber

This book investigates how semivowels were realized in Indo-European and in early Greek. More specifically, it examines the extent to which Indo-European *i and *y were independent phonemes, in what respects their alternation was predictable, and how this situation changed as Indo-European developed into Greek. The comprehensive and chronologically sensitive nature of this study, together with its careful assessment of what is inherited and what is innovative, enables substantive conclusions to be drawn regarding the behaviour of semivowels at various stages in the history of Greek and in Indo-European itself.

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455

Publisher

OUP Oxford

Published Date

ISBN 10

0191501867

ISBN 13

9780191501869

Fundamentals of Computer Graphics

By: Steve Marschner,Peter Shirley

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Fundamentals of Computer Graphics

By: Steve Marschner,Peter Shirley

Drawing on an impressive roster of experts in the field, Fundamentals of Computer Graphics, Fourth Edition offers an ideal resource for computer course curricula as well as a user-friendly personal or professional reference. Focusing on geometric intuition, the book gives the necessary information for understanding how images get onto the screen by using the complementary approaches of ray tracing and rasterization. It covers topics common to an introductory course, such as sampling theory, texture mapping, spatial data structure, and splines. It also includes a number of contributed chapters from authors known for their expertise and clear way of explaining concepts. Highlights of the Fourth Edition Include: Updated coverage of existing topics Major updates and improvements to several chapters, including texture mapping, graphics hardware, signal processing, and data structures A text now printed entirely in four-color to enhance illustrative figures of concepts The fourth edition of Fundamentals of Computer Graphics continues to provide an outstanding and comprehensive introduction to basic computer graphic technology and theory. It retains an informal and intuitive style while improving precision, consistency, and completeness of material, allowing aspiring and experienced graphics programmers to better understand and apply foundational principles to the development of efficient code in creating film, game, or web designs. Key Features Provides a thorough treatment of basic and advanced topics in current graphics algorithms Explains core principles intuitively, with numerous examples and pseudo-code Gives updated coverage of the graphics pipeline, signal processing, texture mapping, graphics hardware, reflection models, and curves and surfaces Uses color images to give more illustrative power to concepts

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Page Count

771

Publisher

CRC Press

Published Date

ISBN 10

1315360209

ISBN 13

9781315360201

Introduction to Supersymmetry

By: Peter G. O. Freund,Peter George Oliver Freund

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Introduction to Supersymmetry

By: Peter G. O. Freund,Peter George Oliver Freund

A brief introductory description of the new physical and mathematical ideas involved in formulating supersymmetric theories. The basic ideas are worked out in low space dimensionalities and techniques where the formulae do not obscure the concepts.

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168

Publisher

Cambridge University Press

Published Date

ISBN 10

052135675X

ISBN 13

9780521356756

The Mongols and the West

1221-1410

By: Peter Jackson

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The Mongols and the West

1221-1410

By: Peter Jackson

The Mongols had a huge impact on medieval Europe and the Islamic world. This book provides a comprehensive survey of contacts between the Catholic West and the Mongol world-empire from the first appearance of Chinggis Khan’s armies in 1221 down to the death of Tamerlane (1405) and the battle of Tannenberg (1410). This book considers the Mongols as allies as well as conquerors; the perception of them in the West; the papal response to the threat (and opportunity) they presented; the fate of the Frankish principalities in the Holy Land in the path of the Mongol onslaught; Western European embassies and missions to the East; and the impact of the Mongols on the expanding world view of the maturing Middle Ages. For courses in crusading history and medieval European history.

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449

Publisher

Routledge

Published Date

ISBN 10

131787899X

ISBN 13

9781317878995

Topological Topics

Articles on Algebra and Topology Presented to Professor P J Hilton in Celebration of His Sixtieth Birthday

By: Peter Hilton

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Topological Topics

Articles on Algebra and Topology Presented to Professor P J Hilton in Celebration of His Sixtieth Birthday

By: Peter Hilton

Professor Peter Hilton is one of the best known mathematicians of his generation. He has published almost 300 books and papers on various aspects of topology and algebra. The present volume is to celebrate the occasion of his sixtieth birthday. It begins with a bibliography of his work, followed by reviews of his contributions to topology and algebra. These are followed by eleven research papers concerned with various topics of current interest in algebra and topology. The articles are contributed by some of the many mathematicians with whom he has worked at one time or another. This book will be of interest to both topologists and algebraists, particularly those concerned with homotopy theory.

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196

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Cambridge University Press

Published Date

ISBN 10

0521275814

ISBN 13

9780521275811

Equivariant Stable Homotopy Theory

By: L. Gaunce Jr. Lewis,J. Peter May,Mark Steinberger

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Equivariant Stable Homotopy Theory

By: L. Gaunce Jr. Lewis,J. Peter May,Mark Steinberger

This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.

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548

Publisher

Springer

Published Date

ISBN 10

3540470778

ISBN 13

9783540470779

Directional Statistics

By: Kanti V. Mardia,Peter E. Jupp

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Directional Statistics

By: Kanti V. Mardia,Peter E. Jupp

Presents new and up-dated material on both the underlying theory and the practical methodology of directional statistics, helping the reader to utilise and develop the techniques appropriate to their work. The book is divided into three parts. The first part concentrates on statistics on the circle. Topics covered include tests of uniformity, tests of good-of-fit, inference on von Mises distributions and non-parametric methods. The second part considers statistics on spheres of arbitrary dimension, and includes a detailed account of inference on the main distributions on spheres. Recent material on correlation, regression time series, robust techniques, bootstrap methods, density estimation and curve fitting is presented. The third part considers statistics on more general sample spaces, in particular rotation groups, Stiefel manifolds, Grassmann manifolds and complex projective spaces. Shape analysis is considered from the perspective of directional statistics. Written by leading authors in the field, this text will be invaluable not only to researchers in probability and statistics interested in the latest developments in directional statistics, but also to practitioners and researchers in many scientific fields, including astronomy, biology, computer vision, earth sciences and image analysis.

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460

Publisher

John Wiley & Sons

Published Date

ISBN 10

0470317817

ISBN 13

9780470317815

Collective Excitations in Unconventional Superconductors and Superfluids

By: Peter Brusov,Pavel Brusov

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Collective Excitations in Unconventional Superconductors and Superfluids

By: Peter Brusov,Pavel Brusov

This title gives a complete and detailed description of collective modes (CMs) in unconventional superfluids and superconductors (USC).

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859

Publisher

World Scientific

Published Date

ISBN 10

9812771239

ISBN 13

9789812771230

Zero to Infinity

The Foundations of Physics

By: Peter Rowlands

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Zero to Infinity

The Foundations of Physics

By: Peter Rowlands

Unique in its field, this book uses a methodology that is entirely new, creating the simplest and most abstract foundations for physics to date. The author proposes a fundamental description of process in a universal computational rewrite system, leading to an irreducible form of relativistic quantum mechanics from a single operator. This is not only simpler, and more fundamental, but also seemingly more powerful than any other quantum mechanics formalism available. The methodology finds immediate applications in particle physics, theoretical physics and theoretical computing. In addition, taking the rewrite structure more generally as a description of process, the book shows how it can be applied to large-scale structures beyond the realm of fundamental physics. Sample Chapter(s). Chapter 1: Zero (228 KB). Contents: Zero; Why Does Physics Work?; The Emergence of Physics; Groups and Representations; Breaking the Dirac Code; The Dirac Nilpotent; Nonrelativistic Quantum Mechanics and the Classical Transition; The Classical and Special Relativistic Approximations; The Resolution of Paradoxes; Electric, Strong and Weak Interactions; QED and Its Analogues; Vacuum; Fermion and Boson Structures; A Representation of Strong and Weak Interactions; Grand Unification and Particle Masses; The Factor 2 and Duality; Gravity and Inertia; Dimensionality, Strings and Quantum Gravity; Nature''s Code; Nature''s Rule; Infinity. Readership: Researchers in quantum, theoretical and high energy physics.

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738

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World Scientific

Published Date

ISBN 10

9812709150

ISBN 13

9789812709158

Integral Geometry, Radon Transforms and Complex Analysis

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996

By: Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov

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Integral Geometry, Radon Transforms and Complex Analysis

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Venice, Italy, June 3-12, 1996

By: Carlos A. Berenstein,Peter F. Ebenfelt,Simon Gindikin,Sigurdur Helgason,Alexander Tumanov

This book contains the notes of five short courses delivered at the "Centro Internazionale Matematico Estivo" session "Integral Geometry, Radon Transforms and Complex Analysis" held in Venice (Italy) in June 1996: three of them deal with various aspects of integral geometry, with a common emphasis on several kinds of Radon transforms, their properties and applications, the other two share a stress on CR manifolds and related problems. All lectures are accessible to a wide audience, and provide self-contained introductions and short surveys on the subjects, as well as detailed expositions of selected results.

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166

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Springer

Published Date

ISBN 10

3540697020

ISBN 13

9783540697022

Applications of Lie Groups to Differential Equations

By: Peter J. Olver

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Applications of Lie Groups to Differential Equations

By: Peter J. Olver

This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

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524

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Springer Science & Business Media

Published Date

ISBN 10

1468402749

ISBN 13

9781468402742

The Optimal Version of Hua's Fundamental Theorem of Geometry of Rectangular Matrices

By: Peter Šemrl

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The Optimal Version of Hua's Fundamental Theorem of Geometry of Rectangular Matrices

By: Peter Šemrl

Hua's fundamental theorem of geometry of matrices describes the general form of bijective maps on the space of all m\times n matrices over a division ring \mathbb{D} which preserve adjacency in both directions. Motivated by several applications the author studies a long standing open problem of possible improvements. There are three natural questions. Can we replace the assumption of preserving adjacency in both directions by the weaker assumption of preserving adjacency in one direction only and still get the same conclusion? Can we relax the bijectivity assumption? Can we obtain an analogous result for maps acting between the spaces of rectangular matrices of different sizes? A division ring is said to be EAS if it is not isomorphic to any proper subring. For matrices over EAS division rings the author solves all three problems simultaneously, thus obtaining the optimal version of Hua's theorem. In the case of general division rings he gets such an optimal result only for square matrices and gives examples showing that it cannot be extended to the non-square case.

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American Mathematical Soc.

Published Date

ISBN 10

0821898450

ISBN 13

9780821898451

Lie Algebras, Cohomology, and New Applications to Quantum Mechanics

AMS Special Session on Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, March 20-21, 1992, Southern Missouri State University

By: Niky Kamran,Peter J. Olver

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Lie Algebras, Cohomology, and New Applications to Quantum Mechanics

AMS Special Session on Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, March 20-21, 1992, Southern Missouri State University

By: Niky Kamran,Peter J. Olver

This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.

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322

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American Mathematical Soc.

Published Date

ISBN 10

0821851691

ISBN 13

9780821851692

Aspects of Differential Geometry II

By: Peter Gilkey,JeongHyeong Park,Ramón Vázquez-Lorenzo

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Aspects of Differential Geometry II

By: Peter Gilkey,JeongHyeong Park,Ramón Vázquez-Lorenzo

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.

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Page Count

143

Publisher

Springer Nature

Published Date

ISBN 10

3031024087

ISBN 13

9783031024085

5000 Years of Geometry

Mathematics in History and Culture

By: Christoph J. Scriba,Peter Schreiber

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5000 Years of Geometry

Mathematics in History and Culture

By: Christoph J. Scriba,Peter Schreiber

The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German book “5000 Jahre Geometrie,” in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first “Golden Age” in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. Grattan-Guinness (Middlesex University London) "Five Thousand Years of Geometry" - I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)

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638

Publisher

Birkhäuser

Published Date

ISBN 10

3034808984

ISBN 13

9783034808989

Beyond Geometry

Classic Papers from Riemann to Einstein

By: Peter Pesic

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Beyond Geometry

Classic Papers from Riemann to Einstein

By: Peter Pesic

Eight essays trace seminal ideas about the foundations of geometry that led to the development of Einstein's general theory of relativity. This is the only English-language collection of these important papers, some of which are extremely hard to find. Contributors include Helmholtz, Klein, Clifford, Poincaré, and Cartan.

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226

Publisher

Courier Corporation

Published Date

ISBN 10

0486453502

ISBN 13

9780486453507

Lagrangian and Hamiltonian Dynamics

By: Peter Mann

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Lagrangian and Hamiltonian Dynamics

By: Peter Mann

The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.

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553

Publisher

Oxford University Press

Published Date

ISBN 10

0198822375

ISBN 13

9780198822370

Introduction to Supersymmetry and Supergravity

By: Peter C. West

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Introduction to Supersymmetry and Supergravity

By: Peter C. West

To the 1st edition of this monograph (addressed to advanced graduate students and researchers ) the author, responding to developments within superstring theory, has added 51/2 chapters dealing with two- dimensional supersymmetry. Authoritative, as lucid as the subject matter allows (yet demanding nonetheless!), attractively produced and priced. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

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448

Publisher

World Scientific

Published Date

ISBN 10

9810200994

ISBN 13

9789810200992

Natural Operations in Differential Geometry

By: Ivan Kolar,Peter W. Michor,Jan Slovak

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Natural Operations in Differential Geometry

By: Ivan Kolar,Peter W. Michor,Jan Slovak

The literature on natural bundles and natural operators in differential geometry, was until now, scattered in the mathematical journal literature. This book is the first monograph on the subject, collecting this material in a unified presentation. The book begins with an introduction to differential geometry stressing naturality and functionality, and the general theory of connections on arbitrary fibered manifolds. The functional approach to classical natural bundles is extended to a large class of geometrically interesting categories. Several methods of finding all natural operators are given and these are identified for many concrete geometric problems. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces, and the basic structures from the theory of jets are therefore described here too in a self-contained manner. The relations of these geometric problems to corresponding questions in mathematical physics are brought out in several places in the book, and it closes with a very comprehensive bibliography of over 300 items. This book is a timely addition to literature filling the gap that existed here and will be a standard reference on natural operators for the next few years.

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450

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Springer Science & Business Media

Published Date

ISBN 10

3540562354

ISBN 13

9783540562351

Cosmology and Gravitation

Spin, Torsion, Rotation, and Supergravity

By: Peter G. Bergmann,Venzo De Sabbata

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Cosmology and Gravitation

Spin, Torsion, Rotation, and Supergravity

By: Peter G. Bergmann,Venzo De Sabbata

For the Sixth Course of the International School of Cosmology and Gravitation of the "Ettore Maj orana" Centre for Scientific Cul ture we choose as the principal topics torsion and supergravity, because in our opinion it is one of the principal tasks of today's theoretical physics to attempt to link together the theory of ele mentary particles and general relativity. Our aim was to delineate the present status of the principal efforts directed toward this end, and to explore possible directions of work in the near future. Efforts to incorporate spin as a dynamic variable into the foundations of the theory of gravitation were poineered by E. Cartan, whose contributions to this problem go back half a century. Accord ing to A. Trautman this so-called Einstein-Cartan theory is the sim plest and most natural modification of Einstein's 1916 theory. F. Hehl has contributed a very detailed and comprehensive analysis of this topic, original view of non-Riemannian space-time. Characteristic of Einstein-Cartan theories is the enrichment of Riemannian geometry by torsion, the non-symmetric part of the otherwise metric-compatible affine connection. Torsion has a impact on the theory of elementary particles. According to V. de Sabbata, weak interactions can be based on the Einstein-Cartan geometry, in that the Lagrangian describing weak interactions and torsion inter- action possess analogous structures, leading to a unification of weak and gravitational forces.

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508

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Springer Science & Business Media

Published Date

ISBN 10

1461331234

ISBN 13

9781461331230

Robotics, Vision and Control

Fundamental Algorithms In MATLAB® Second, Completely Revised, Extended And Updated Edition

By: Peter Corke

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Robotics, Vision and Control

Fundamental Algorithms In MATLAB® Second, Completely Revised, Extended And Updated Edition

By: Peter Corke

Robotic vision, the combination of robotics and computer vision, involves the application of computer algorithms to data acquired from sensors. The research community has developed a large body of such algorithms but for a newcomer to the field this can be quite daunting. For over 20 years the author has maintained two open-source MATLAB® Toolboxes, one for robotics and one for vision. They provide implementations of many important algorithms and allow users to work with real problems, not just trivial examples. This book makes the fundamental algorithms of robotics, vision and control accessible to all. It weaves together theory, algorithms and examples in a narrative that covers robotics and computer vision separately and together. Using the latest versions of the Toolboxes the author shows how complex problems can be decomposed and solved using just a few simple lines of code. The topics covered are guided by real problems observed by the author over many years as a practitioner of both robotics and computer vision. It is written in an accessible but informative style, easy to read and absorb, and includes over 1000 MATLAB and Simulink® examples and over 400 figures. The book is a real walk through the fundamentals of mobile robots, arm robots. then camera models, image processing, feature extraction and multi-view geometry and finally bringing it all together with an extensive discussion of visual servo systems. This second edition is completely revised, updated and extended with coverage of Lie groups, matrix exponentials and twists; inertial navigation; differential drive robots; lattice planners; pose-graph SLAM and map making; restructured material on arm-robot kinematics and dynamics; series-elastic actuators and operational-space control; Lab color spaces; light field cameras; structured light, bundle adjustment and visual odometry; and photometric visual servoing. “An authoritative book, reaching across fields, thoughtfully conceived and brilliantly accomplished!” OUSSAMA KHATIB, Stanford

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697

Publisher

Springer

Published Date

ISBN 10

3319544136

ISBN 13

9783319544137

Topics in Differential Geometry

By: Peter W. Michor

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Topics in Differential Geometry

By: Peter W. Michor

This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.

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Page Count

510

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820036

ISBN 13

9780821820032

Book's by Peter Grassmann

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