Mathematics of Discrete Structures for Computer Science

Part of a new series of books for engineers and scientists who are taking advanced mathematics courses, this work presents differential equations from an applied point of view. Like the other volumes

The aim of this series of meetings is to provide a context for exchanging ideas among researchers of different fields in Differential Geometry, Applied Mathematics and Physics; in general, among all p

Calantai (mathematics, U. of Miskolc, Hungary) offers a broad survey of projectors, a type of matrix and operator, for readers who are familiar with linear algebra and mathematical analysis at an unde

Presents an enlarged version of notes for participants at a November 1994 workshop in mathematics held at the Indian Institute of Technology Bombay. Offers a self-contained and detailed account of the

Mandelbrot is world famous for his creation of the new mathematics of fractal geometry. Yet few people know that his original field of applied research was in econometrics and financial models, applyi

Multiple comparisons are the comparisons of two or more treatments. These may be treatments of a disease, groups of subjects, or computer systems, for example. Statistical multiple comparison methods

Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experien

Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experien

Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously

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

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

Almost 50 years have passed since the famous papers of Hugo Rietveld from the late sixties where he describes a method for the refinement of crystal structures from neutron powder diffraction data. So

Within stringent structures, Charles Pictet develops an exciting interplay of free forms, be it in conversions, extensions or in a number of spacious villas in the Greater Geneva area. He has for year

This book discusses the theory that alternative relationship and family structures challenge the privileged status of the nuclear family as the preferable mode of family life for all, and the one to b

Ten years after publication of the popular first edition of this volume, the index theorem continues to stand as a central result of modern mathematics-one of the most important foci for the interacti

This second edition of eCommerce Economics addresses the economic issues associated with using computer-mediated electronic networks, such as the Internet, as mechanisms for transferring ownership of

This second edition of eCommerce Economics addresses the economic issues associated with using computer-mediated electronic networks, such as the Internet, as mechanisms for transferring ownership of

This book is a complete account of the predicate transformation calculus semantics of sequential programs, including repetitions, recursive procedures, computational induction and unbounded nondeterminacy. Predicate transformation semantics are the best specification method for the development of correct and well-structured computer programs. The author develops this theory to a greater depth than has been achieved before, and describes it in a way that makes it readily compatible with programming rules for partial and total correctness of repetitions and recursive procedures, supplies new rules for proving incorrectness, and a stronger rule for proving that two programs satisfy the same specifications. Finally, the semantics are extended so that non-terminating programs can be specified as well. This will be essential reading for all computer scientists working in specification and verification of programs.

Microlocal analysis is a field of mathematics that was invented in the mid-20th century for the detailed investigation of problems from partial differential equations, which incorporated and made rigo

This text addresses a number of technical skills in mathematics, physics, and specific areas of nuclear engineering that will prepare the student for optimum performance in any nuclear engineering or

Groceries, Stamps, nd Measuring Strips: Early Multiplication is one of five units in the Contexts for Learning Mathematics' Investigating Multiplication and Division (3 - 5) The focus of this unit is

Excellent text for upper-level undergraduate and graduate students shows how geometric and algebraic ideas met and grew together into an important branch of mathematics. Lucid coverage of vector field

Statistics is a subject of many uses and surprisingly few effective practitioners. The traditional road to statistical knowledge is blocked, for most, by a formidable wall of mathematics. The approach

An up-to-date text designed for undergraduate courses in control systems engineering and principles of automatic controls. Focuses on design and implementation rather than just the mathematics of cont

This book explores Virginia Woolf's engagement with the professions in her life and writing. Woolf underscored the significance of the professions to society, such as the opportunity they provided for a decent income and the usefulness of professional accreditation. However, she also resisted their hierarchical structures and their role in creating an overspecialised and fragmented modernity, which prevented its members from leading whole, fulfilling lives. This book shows how Woolf's writing reshaped the professions so that they could better serve the individual and society, and argues that her search for alternatives to existing professional structures deeply influenced her literary methods and experimentation.

This book explores Virginia Woolf's engagement with the professions in her life and writing. Woolf underscored the significance of the professions to society, such as the opportunity they provided for a decent income and the usefulness of professional accreditation. However, she also resisted their hierarchical structures and their role in creating an overspecialised and fragmented modernity, which prevented its members from leading whole, fulfilling lives. This book shows how Woolf's writing reshaped the professions so that they could better serve the individual and society, and argues that her search for alternatives to existing professional structures deeply influenced her literary methods and experimentation.

Brown (computer music, Queensland U. of technology, Brisbane, Australia) provides an overview of the use of computers in music education for educators teaching all ages of students. It focuses on the

Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of th

Origami, the art of paper folding, has a rich mathematical theory. Early investigations go back to at least the 1930s, but the twenty-first century has seen a remarkable blossoming of the mathematics of folding. Besides its use in describing origami and designing new models, it is also finding real-world applications from building nano-scale robots to deploying large solar arrays in space. Written by a world expert on the subject, Origametry is the first complete reference on the mathematics of origami. It brings together historical results, modern developments, and future directions into a cohesive whole. Over 180 figures illustrate the constructions described while numerous 'diversions' provide jumping-off points for readers to deepen their understanding. This book is an essential reference for researchers of origami mathematics and its applications in physics, engineering, and design. Educators, students, and enthusiasts will also find much to enjoy in this fascinating account of th

Loved by students for the visual and flexible way to build computer skills, the Illustrated Course Guides are ideal for learning Microsoft Excel 2013 regardless of your experience level. Each two-page

Loved by students for the visual and flexible way to build computer skills, the Illustrated Course Guides are ideal for learning Microsoft Excel 2013 regardless of your experience level. Each two-page

Loved by students for the visual and flexible way to build computer skills, the Illustrated Course Guides are ideal for learning Microsoft Excel 2013 regardless of your experience level. Each two-page

Learning to Program with Alice, 3e is appropriate for all one-semester pre-CS1 and computer literacy courses, and for integration into the first weeks of many introductory CS1 courses. ? Alice was

Loved by students for the visual and flexible way to build computer skills, the Illustrated Course Guides are ideal for learning Microsoft Access 2010 regardless of your experience level. Each two-pa

Loved by students for the visual and flexible way to build computer skills, the Illustrated Course Guides are ideal for learning Microsoft Word 2010 regardless of your experience level. Each two-page

Loved by students for the visual and flexible way to build computer skills, the Illustrated Course Guides are ideal for learning Microsoft Access 2010 regardless of your experience level. Each two-pag

Loved by students for the visual and flexible way to build computer skills, the Illustrated Course Guides are ideal for learning Microsoft Access 2010 regardless of your experience level. Each two-pa

Loved by students for the visual and flexible way to build computer skills, the Illustrated Course Guides are ideal for learning Microsoft Excel 2010 regardless of your experience level. Each two-pag

A textbook for a graduate course on solving differential equations for students in a wide range of scientific disciplines who have completed an elementary course in computer methods and have been expo