Modern Cryptography Volume 1: A Classical Introduction to Informational and Mathematical Principle, Zheng Zhiyong
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
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: Ingemar Bengtsson, Karol Zyczkowski Название: Geometry of Quantum States : An Introduction to Quantum Entanglement ISBN: 1107656141 ISBN-13(EAN): 9781107656147 Издательство: Cambridge Academ Рейтинг: Цена: 8554.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The second edition of a book that has become a standard reference for researchers working on geometric aspects of quantum entanglement and quantum theory of information. Its comprehensive style makes it suitable for students of physics, information science, and mathematics wishing to learn more about quantum mechanics and quantum entanglement.
Описание: There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.
Автор: Shonkwiler Ronald W. Название: Mathematical Biology ISBN: 1489982817 ISBN-13(EAN): 9781489982810 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text presents mathematical biology as a field with a unity of its own, rather than only the intrusion of one science into another. The book focuses on problems of contemporary interest, such as cancer, genetics, and the rapidly growing field of genomics.
Автор: Foucart Simon Название: Mathematical Introduction to Compressive Sensing ISBN: 0817649476 ISBN-13(EAN): 9780817649470 Издательство: Springer Рейтинг: Цена: 9781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.
Автор: Kielh?fer Название: Bifurcation Theory ISBN: 1461405017 ISBN-13(EAN): 9781461405016 Издательство: Springer Рейтинг: Цена: 10480.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a two-dimensional kernel with applications, the buckling of the Euler rod, the appearance of Taylor vortices, the singular limit process of the Cahn-Hilliard model, and an application of this method to more complicated nonconvex variational problems.
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.
Автор: Zheng, Zhiyong Tian, Kun Liu, Fengxia Название: Modern cryptography volume 2 ISBN: 9811976465 ISBN-13(EAN): 9789811976469 Издательство: Springer Рейтинг: Цена: 5589.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of "ambiguity" in both definition and algorithm. The greatest feature of this book is to use probability distribution to carry out rigorous mathematical definition and mathematical demonstration for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattice, ideal lattice and generalized NTRU cryptography. This book is used as a professional book for graduate students majoring in mathematics and cryptography, as well as a reference book for scientific and technological personnel engaged in cryptography research.
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
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.
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.
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