This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws.
Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
Numerous enhancements and revision are incorporated into this new edition. For example, fiber bundle techniques are used to introduce differential geometry. This more elegant and intuitive approach naturally connects differential geometry with not only the general theory of relativity, but also gauge theories of fundamental forces.
Some praise for the previous edition:
PAGEOPH Pure and Applied Geophysics]
Review by Daniel Wojcik, University of Maryland
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
..". Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics studen
Автор: Jeffrey Hoffstein and Jill Pipher Название: Introduction to Mathematical Cryptography ISBN: 1493917102 ISBN-13(EAN): 9781493917105 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: An Introduction to Mathematical Cryptography
Описание: This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given.
Описание: This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms.
Описание: In this volume are papers written by students and co-authors of Stanley Reiter. Stan has had a strong and important direct effect on many students at Purdue University and Northwestern University. Stan`s students include department chairmen, business executives, Deans, a Secretary of the Air Force, and a College President.
Автор: Hoffstein, Jeffrey Pipher, Jill Silverman, J. H. Название: Introduction to mathematical cryptography ISBN: 1441926747 ISBN-13(EAN): 9781441926746 Издательство: Springer Рейтинг: Цена: 5723.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics. It includes exercises and examples at the end of each section.
Автор: Davis Mark H A Название: Mathematical Finance: A Very Short Introduction ISBN: 0198787944 ISBN-13(EAN): 9780198787945 Издательство: Oxford Academ Рейтинг: Цена: 1582.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Now a vital part of modern economies, the rapid growth of the finance industry in recent decades is largely due to the development of mathematical methods such as the theory of arbitrage. Asset valuation, credit trading, and fund management, now depend on these mathematical tools. Mark Davis explains the theories and their applications.
Автор: Nastase Horatiu Название: Introduction to Quantum Field Theory ISBN: 1108493998 ISBN-13(EAN): 9781108493994 Издательство: Cambridge Academ Рейтинг: Цена: 9821.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This graduate level textbook provides a comprehensive introduction to quantum field theory. Equal emphasis is given to operator and path integral formalisms, and modern research, advanced topics and numerous quantum fields are covered in detail. This is an invaluable resource for students and researchers of quantum field theory.
Автор: Ablowitz, Mark J. (university Of Colorado Boulder) Fokas, Athanassios S. (university Of Cambridge) Название: Introduction to complex variables and applications ISBN: 1108959725 ISBN-13(EAN): 9781108959728 Издательство: Cambridge Academ Рейтинг: Цена: 7286.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. It contains the essential topics along with advanced topics for use in challenging projects. Many worked examples, applications, and exercises are included.
Автор: Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerh Название: A Course in Mathematical Cryptography ISBN: 3110372762 ISBN-13(EAN): 9783110372762 Издательство: Walter de Gruyter Цена: 9288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Cryptography has become essential as bank transactions, credit card infor-mation, contracts, and sensitive medical information are sent through inse-cure channels. This book is concerned with the mathematical, especially algebraic, aspects of cryptography. It grew out of many courses presented by the authors over the past twenty years at various universities and covers a wide range of topics in mathematical cryptography. It is primarily geared towards graduate students and advanced undergraduates in mathematics and computer science, but may also be of interest to researchers in the area. Besides the classical methods of symmetric and private key encryption, the book treats the mathematics of cryptographic protocols and several unique topics such as Group-Based Cryptography Grobner Basis Methods in Cryptography Lattice-Based Cryptography
Автор: Taras Gerya Название: Introduction to Numerical Geodynamic Modelling ISBN: 1107143144 ISBN-13(EAN): 9781107143142 Издательство: Cambridge Academ Рейтинг: Цена: 10611.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The second edition of this popular introduction to numerical geodynamic modelling theory and applications features four new chapters. Based on the author`s experience of teaching the material, and including practical exercises and MATLAB (R) examples, this user-friendly resource encourages students and researchers to experiment with geodynamic models.
Автор: Vladimir S. Lerner Название: Variation Principle in Informational Macrodynamics ISBN: 1461350581 ISBN-13(EAN): 9781461350583 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Information Macrodynamics (IMD) belong to an interdisciplinary science that represents a new theoretical and computer-based methodology for a system informational descriptionand improvement, including various activities in such areas as thinking, intelligent processes, communications, management, and other nonphysical subjects with their mutual interactions, informational superimposition, and theinformation transferredbetweeninteractions. The IMD is based on the implementation of a single concept by a unique mathematical principle and formalism, rather than on an artificial combination of many arbitrary, auxiliary concepts and/or postulates and different mathematical subjects, such as the game, automata, catastrophe, logical operations theories, etc. This concept is explored mathematically using classical mathematics as calculus of variation and the probability theory, which are potent enough, without needing to developnew, specifiedmathematical systemicmethods. The formal IMD model automatically includes the related results from other fields, such as linear, nonlinear, collective and chaotic dynamics, stability theory, theory of information, physical analogies of classical and quantum mechanics, irreversible thermodynamics, andkinetics. The main IMD goal is to reveal the information regularities, mathematically expressed by the considered variation principle (VP), as a mathematical tool to extractthe regularities and define the model, whichdescribes theregularities. The IMD regularities and mechanisms are the results of the analytical solutions and are not retained by logical argumentation, rational introduction, and a reasonable discussion. The IMD's information computer modeling formalism includes a human being (as an observer, carrier and producer ofinformation), with a restoration of the model during the objectobservation
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