Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven
- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780691175423
- eISBN:
- 9781400885411
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175423.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a ...
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Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton–Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.Less
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton–Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Keith Martin
- Published in print:
- 2017
- Published Online:
- July 2017
- ISBN:
- 9780198788003
- eISBN:
- 9780191829956
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788003.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization, Logic / Computer Science / Mathematical Philosophy
Cryptography is a vital technology that underpins the security of information in computer networks. This book presents a comprehensive introduction to the role that cryptography plays in providing ...
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Cryptography is a vital technology that underpins the security of information in computer networks. This book presents a comprehensive introduction to the role that cryptography plays in providing information security for technologies such as the Internet, mobile phones, payment cards, and wireless local area networks. Focusing on the fundamental principles that ground modern cryptography as they arise in modern applications, it avoids both an over-reliance on transient technologies and overwhelming theoretical research. The first part of the book provides essential background, identifying the core security services provided by cryptography. The next part introduces the main cryptographic mechanisms that deliver these security services such as encryption, hash functions, and digital signatures, discussing why they work and how to deploy them, without delving into any significant mathematical detail. In the third part, the important practical aspects of key management are introduced, which is essential for making cryptography work in real systems. The last part considers the application of cryptography. A range of application case studies is presented, alongside a discussion of the wider societal issues arising from use of cryptography to support contemporary cyber security.Less
Cryptography is a vital technology that underpins the security of information in computer networks. This book presents a comprehensive introduction to the role that cryptography plays in providing information security for technologies such as the Internet, mobile phones, payment cards, and wireless local area networks. Focusing on the fundamental principles that ground modern cryptography as they arise in modern applications, it avoids both an over-reliance on transient technologies and overwhelming theoretical research. The first part of the book provides essential background, identifying the core security services provided by cryptography. The next part introduces the main cryptographic mechanisms that deliver these security services such as encryption, hash functions, and digital signatures, discussing why they work and how to deploy them, without delving into any significant mathematical detail. In the third part, the important practical aspects of key management are introduced, which is essential for making cryptography work in real systems. The last part considers the application of cryptography. A range of application case studies is presented, alongside a discussion of the wider societal issues arising from use of cryptography to support contemporary cyber security.
Howard Elman, David Silvester, and Andy Wathen
- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780199678792
- eISBN:
- 9780191780745
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199678792.001.0001
- Subject:
- Mathematics, Numerical Analysis, Computational Mathematics / Optimization
The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The first part (Chapters 1 through 5) covers the ...
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The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The first part (Chapters 1 through 5) covers the Poisson equation and the Stokes equations. For each PDE, there is a chapter concerned with finite element discretization and a companion chapter concerned with efficient iterative solution of the algebraic equations obtained from discretization. Chapter 5 describes the basics of PDE-constrained optimization. The second part of the book (Chapters 6 to 11) is a more advanced introduction to the numerical analysis of incompressible flows. It starts with four chapters on the convection–diffusion equation and the steady Navier–Stokes equations, organized by equation with a chapter describing discretization coupled with a companion concerned with iterative solution algorithms. The book concludes with two chapters describing discretization and solution methods for models of unsteady flow and buoyancy-driven flow.Less
The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The first part (Chapters 1 through 5) covers the Poisson equation and the Stokes equations. For each PDE, there is a chapter concerned with finite element discretization and a companion chapter concerned with efficient iterative solution of the algebraic equations obtained from discretization. Chapter 5 describes the basics of PDE-constrained optimization. The second part of the book (Chapters 6 to 11) is a more advanced introduction to the numerical analysis of incompressible flows. It starts with four chapters on the convection–diffusion equation and the steady Navier–Stokes equations, organized by equation with a chapter describing discretization coupled with a companion concerned with iterative solution algorithms. The book concludes with two chapters describing discretization and solution methods for models of unsteady flow and buoyancy-driven flow.
Anders Drachen, Pejman Mirza-Babaei, and Lennart Nacke (eds)
- Published in print:
- 2018
- Published Online:
- March 2018
- ISBN:
- 9780198794844
- eISBN:
- 9780191836336
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198794844.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy, Computational Mathematics / Optimization
Today, Games User Research forms an integral component of the development of any kind of interactive entertainment. User research stands as the primary source of business intelligence in the ...
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Today, Games User Research forms an integral component of the development of any kind of interactive entertainment. User research stands as the primary source of business intelligence in the incredibly competitive game industry. This book aims to provide the foundational, accessible, go-to resource for people interested in GUR. It is a community-driven effort—it is written by passionate professionals and researchers in the GUR community as a handbook and guide for everyone interested in user research and games. The book bridges the current gaps of knowledge in Game User Research, building the go-to volume for everyone working with games, with an emphasis on those new to the field.Less
Today, Games User Research forms an integral component of the development of any kind of interactive entertainment. User research stands as the primary source of business intelligence in the incredibly competitive game industry. This book aims to provide the foundational, accessible, go-to resource for people interested in GUR. It is a community-driven effort—it is written by passionate professionals and researchers in the GUR community as a handbook and guide for everyone interested in user research and games. The book bridges the current gaps of knowledge in Game User Research, building the go-to volume for everyone working with games, with an emphasis on those new to the field.
Philip Isett
- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780691174822
- eISBN:
- 9781400885428
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691174822.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization
Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if ...
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Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. This book uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful “Main Lemma”—used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem—has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture.Less
Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. This book uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful “Main Lemma”—used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem—has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture.
Mihály Bakonyi and Hugo J. Woerdeman
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691128894
- eISBN:
- 9781400840595
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691128894.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization
Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly ...
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Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.Less
Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.
Volker Wulf, Volkmar Pipek, David Randall, Markus Rohde, Kjeld Schmidt, and Gunnar Stevens (eds)
- Published in print:
- 2018
- Published Online:
- April 2018
- ISBN:
- 9780198733249
- eISBN:
- 9780191797736
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198733249.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization
The last 25 years have seen a small revolution in our approach to the understanding of new technology and information systems. It has become a founding assumption of computer-supported cooperative ...
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The last 25 years have seen a small revolution in our approach to the understanding of new technology and information systems. It has become a founding assumption of computer-supported cooperative work and human–computer interaction that in the future, if not already, most computer applications will be socially embedded in the sense that they will become infrastructures (in some sense) for the development of the social practices which they are designed to support. Assuming that IT artifacts have to be understood in this sociotechnical way, traditional criteria for good design in computer science, such as performance, reliability, stability or usability, arguably need to be supplemented by methods and perspectives which illuminate the way in which technology and social practice are mutually elaborating. This book concerns the philosophy, conceptual apparatus, and methodological concerns which will inform the development of a systematic and long-term human-centered approach to the IT-product life cycle, addressing issues concerned with appropriation and infrastructuring. This entails an orientation to “practice-based computing.” The book contains a number of chapters which examine both the conceptual foundations of such an approach, and a number of empirical case studies that exemplify it.Less
The last 25 years have seen a small revolution in our approach to the understanding of new technology and information systems. It has become a founding assumption of computer-supported cooperative work and human–computer interaction that in the future, if not already, most computer applications will be socially embedded in the sense that they will become infrastructures (in some sense) for the development of the social practices which they are designed to support. Assuming that IT artifacts have to be understood in this sociotechnical way, traditional criteria for good design in computer science, such as performance, reliability, stability or usability, arguably need to be supplemented by methods and perspectives which illuminate the way in which technology and social practice are mutually elaborating. This book concerns the philosophy, conceptual apparatus, and methodological concerns which will inform the development of a systematic and long-term human-centered approach to the IT-product life cycle, addressing issues concerned with appropriation and infrastructuring. This entails an orientation to “practice-based computing.” The book contains a number of chapters which examine both the conceptual foundations of such an approach, and a number of empirical case studies that exemplify it.
