Mathematics of Discrete Structures for Computer Science

Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems, including the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalise mathematics. The only prerequisite is a basic knowledge of undergraduate mathematics. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarise themselves with the mat

"Network science is an emerging field of study that encompasses mathematics, computer science, physics, and engineering. An important issue in the study of complex networks is to understand the collec

In the structural design of airframes and buildings, probability-based procedures are used to mitigate the risk of failure as well as produce cost-effective designs. This book introduces the subject of probabilistic analysis to structural and fire protection engineers and can also be used as a reference to guide those applying this technology. In addition to providing an understanding of how fire affects structures and how to optimize the performance of structural framing systems, Probability-Based Structural Fire Load provides guidance for design professionals and is a resource for educators. The goal of this book is to bridge the gap between prescriptive and probability-based performance design methods and to simplify very complex and comprehensive computer analyses to the point that stochastic structural fire loads have a simple, approximate analytical expression that can be used in structural analysis and design on a day-to-day basis. Numerous practical examples are presented in st

Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.

Optimization is an essential technique for solving problems in areas as diverse as accounting, computer science and engineering. Assuming only basic linear algebra and with a clear focus on the fundamental concepts, this textbook is the perfect starting point for first- and second-year undergraduate students from a wide range of backgrounds and with varying levels of ability. Modern, real-world examples motivate the theory throughout. The authors keep the text as concise and focused as possible, with more advanced material treated separately or in starred exercises. Chapters are self-contained so that instructors and students can adapt the material to suit their own needs and a wide selection of over 140 exercises gives readers the opportunity to try out the skills they gain in each section. Solutions are available for instructors. The book also provides suggestions for further reading to help students take the next step to more advanced material.

Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes

Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes

Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes

More scientists now use C than any other programming language. This book contains practical, computer-ready algorithms for many standard methods of numerical mathematics. It describes the principles o

Mathematical psychology is an interdisciplinary area of research in which methods of mathematics, operations research, and computer science in psychology are used. Now more than thirty years old, the

Healthcare practices have been enhanced through the use of information technologies and analytical methods. A cross between computer science, healthcare, and information science is needed for the opti

The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimensio

Written by world-leading experts, this book focusses on the role of biomaterials in stem cell research and regenerative medicine. Emphasising basic principles and methodology, it covers stem cell interactions, fabrication technologies, design principles, physical characterisation and biological evaluation, across a broad variety of systems and biomaterials. Topics include: stem cell biology, including embryonic stem cells, IPS, HSC and progenitor cells; modern scaffold structures, including biopolymer, bioceramic, micro- and nanofiber, ECM and biohydrogel; advanced fabrication technologies, including computer-aided tissue engineering and organ printing; cutting-edge drug delivery systems and gene therapy techniques; and medical applications spanning hard and soft tissues, the cardiovascular system and organ regeneration. With a contribution by Nobel laureate Shinya Yamanaka, this is a must-have reference for anyone in the field of biomaterials, stem cell biology and engineering, tissue

Mathematics is the fundamental knowledge for every scientist. As an academic at the University of Science and Technology of China, Professor Sheng Gong takes his passion for mathematics teaching even

By having its origin in analytical and continuum mechanics, as well as in computer science and applied mathematics, multibody dynamics provides a basis for analysis and virtual prototyping of innovati

Advanced composite materials for bridge structures are recognized as a promising alternative to conventional construction materials such as steel. After an introductory overview and an assessment of

Ultrasonic guided waves in solid media have become a critically important subject in nondestructive testing and structural health monitoring, as new faster, more sensitive, and more economical ways of looking at materials and structures have become possible. This book will lead to fresh creative ideas for use in new inspection procedures. Although the mathematics is sometimes sophisticated, the book can also be read by managers without detailed understanding of the concepts as it can be read from a 'black box' point of view. Overall, the material presented on wave mechanics - in particular, guided wave mechanics - establishes a framework for the creative data collection and signal processing needed to solve many problems using ultrasonic nondestructive evaluation and structural health monitoring. The book can be used as a reference in ultrasonic nondestructive evaluation by professionals and as a textbook for seniors and graduate students. This work extends the coverage of Rose's earli

The theme of HumanCom and EMC is focused on the various aspects of human-centric computing for advances in computer science and its applications, embedded and multimedia computing and provides an oppo

The demands of modeling and computation in engineering are rapidly growing as a multidisciplinary area with connections to engineering, mathematics and computer science. Modeling and Computation in En

This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.

Advances in the growth of novel-engineered structures such as sophisticated semiconductor superlattices and heterostructures, as well as new nonlinear optical materials, have opened exciting possibilities for infrared sources, detectors, modulators and novel devices. Brought to maturity, such discrete devices could likely see widespread use in applications as diverse as infrared imaging, chemical sensing, surveillance, short-link and high-bandwidth communications. This book published by MRS, brings together a group of internationally recognized experts in the field to discuss progress in materials, physics, processing and device design and performance. Developments in materials for cooled and uncooled infrared systems based on pyroelectric, micro-bolometric, photovoltaic and photoconductive detectors are emphasized. Progress in compact infrared sources is also highlighted. Topics include: antimonide-related materials - growth, characterization and analysis; antimonide-related devices;

Over the last 20 years, developments in climatology have provided an amazing array of explanations for the pattern of world climates. This textbook, first published in 2006, examines the earth's climate systems in light of this incredible growth in data availability, data retrieval systems, and satellite and computer applications. It considers regional climate anomalies, developments in teleconnections, unusual sequences of recent climate change, and human impacts upon the climate system. The physical climate forms the main part of the book, but it also considers social and economic aspects of the global climate system. This textbook has been derived from the authors' extensive experience of teaching climatology and atmospheric science. Each chapter contains an essay by a specialist in the field to enhance the understanding of selected topics. An extensive bibliography is included and lists of websites for further study. This textbook will be invaluable to advanced students of climatol

This book presents a unique, interdisciplinary approach to disaster risk research, combining cutting-edge natural science and social science methodologies. Bringing together leading scientists, policy makers and practitioners from around the world, it presents the risks of global hazards such as volcanoes, seismic events, landslides, hurricanes, precipitation floods and space weather, and provides real-world hazard case studies from Latin America, the Caribbean, Africa, the Middle East, Asia and the Pacific region. Avoiding complex mathematics, the authors provide insight into topics such as the vulnerability of society, disaster risk reduction policy, relations between disaster policy and climate change, adaptation to hazards, and (re)insurance approaches to extreme events. This is a key resource for academic researchers and graduate students in a wide range of disciplines linked to hazard and risk studies, including geophysics, volcanology, hydrology, atmospheric science, geomorpholo

Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich–Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mat

This is a comprehensive, authoritative and innovative account of Pythagoras and Pythagoreanism, one of the most enigmatic and influential philosophies in the West. In twenty-one chapters covering a timespan from the sixth century BC to the seventeenth century AD, leading scholars construct a number of different images of Pythagoras and his community, assessing current scholarship and offering new answers to central problems. Chapters are devoted to the early Pythagoreans, and the full breadth of Pythagorean thought is explored including politics, religion, music theory, science, mathematics and magic. Separate chapters consider Pythagoreanism in Plato, Aristotle, the Peripatetics and the later Academic tradition, while others describe Pythagoreanism in the historical tradition, in Rome and in the pseudo-Pythagorean writings. The three great lives of Pythagoras by Diogenes Laertius, Porphyry and Iamblichus are also discussed in detail, as is the significance of Pythagoras for the Middle

Machine learning is one of the fastest growing areas of computer science, with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way. The book provides a theoretical account of the fundamentals underlying machine learning and the mathematical derivations that transform these principles into practical algorithms. Following a presentation of the basics, the book covers a wide array of central topics unaddressed by previous textbooks. These include a discussion of the computational complexity of learning and the concepts of convexity and stability; important algorithmic paradigms including stochastic gradient descent, neural networks, and structured output learning; and emerging theoretical concepts such as the PAC-Bayes approach and compression-based bounds. Designed for advanced undergraduates or beginning graduates, the text makes the fundamentals and algorithms of machine learning accessible t

Mathematics is the fundamental knowledge for every scientist. As an academic at the University of Science and Technology of China, Professor Sheng Gong takes his passion for mathematics teaching even

Automated machinery, such as computer numerical control machines (CNM), require constant monitoring for accuracy and precision. Thus, a correct understanding of 'metrology'--the science of measurement

"This book compiles prestigious research and provides a well-rounded composite of role of human enhancement technologies in emerging areas for those involved in computer science and the humanities, as

Offering a comprehensive treatment of adhesive particle flows, this book adopts a particle-level approach oriented toward directly simulating the various fluid, electric field, collision, and adhesion forces and torques acting on the particles, within the framework of a discrete-element model. It is ideal for professionals and graduate students working in engineering and atmospheric and condensed matter physics, materials science, environmental science, and other disciplines where particulate flows have a significant role. The presentation is applicable to a wide range of flow fields, including aerosols, colloids, fluidized beds, and granular flows. It describes both physical models of the various forces and torques on the particles as well as practical aspects necessary for efficient implementation of these models in a computational framework.

Over the past thirty years, a new systemic conception of life has emerged at the forefront of science. New emphasis has been given to complexity, networks, and patterns of organisation, leading to a novel kind of 'systemic' thinking. This volume integrates the ideas, models, and theories underlying the systems view of life into a single coherent framework. Taking a broad sweep through history and across scientific disciplines, the authors examine the appearance of key concepts such as autopoiesis, dissipative structures, social networks, and a systemic understanding of evolution. The implications of the systems view of life for health care, management, and our global ecological and economic crises are also discussed. Written primarily for undergraduates, it is also essential reading for graduate students and researchers interested in understanding the new systemic conception of life and its implications for a broad range of professions - from economics and politics to medicine, psychol

Today's pervasive computing and communications networks have created an intense need for secure and reliable cryptographic systems. Bringing together a fascinating mixture of topics in engineering, mathematics, computer science, and informatics, this book presents the timeless mathematical theory underpinning cryptosystems both old and new. Major branches of classical and modern cryptography are discussed in detail, from basic block and stream cyphers through to systems based on elliptic and hyperelliptic curves, accompanied by concise summaries of the necessary mathematical background. Practical aspects such as implementation, authentication and protocol-sharing are also covered, as are the possible pitfalls surrounding various cryptographic methods. Written specifically with engineers in mind, and providing a solid grounding in the relevant algorithms, protocols and techniques, this insightful introduction to the foundations of modern cryptography is ideal for graduate students and r

Written in a unique style, this book is a valuable resource for faculty, graduate students, and researchers in the communications and networking area whose work interfaces with optimization. It teaches you how various optimization methods can be applied to solve complex problems in wireless networks. Each chapter reviews a specific optimization method and then demonstrates how to apply the theory in practice through a detailed case study taken from state-of-the-art research. You will learn various tips and step-by-step instructions for developing optimization models, reformulations, and transformations, particularly in the context of cross-layer optimization problems in wireless networks involving flow routing (network layer), scheduling (link layer), and power control (physical layer). Throughout, a combination of techniques from both operations research and computer science disciplines provides a holistic treatment of optimization methods and their applications. Each chapter includes

Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate st

Strength of Materials, 3rd Edition is ideal for students pursuing degrees in civil and mechanical engineering, as well as computer science, electronics, and instrumentation. Topics include combined st

This textbook is ideal for a course in engineering systems dynamics and controls. The work is a comprehensive treatment of the analysis of lumped parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input/output and state space models, computer simulation and modeling methods and techniques in mechanical, electrical, thermal and fluid domains. Frequency domain methods, transfer functions and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lead-lag, root locus) and an introduction to discrete time systems. This new edition features many new and expanded sections on such topics as: solving stiff systems, operational amplifiers, electrohydraulic servovalves, using Matlab with transfer functions, using Matlab with frequency response, Matlab tutorial and an expanded Simulink tutorial. The work has 40% more end-of-chapter exercises and 3

The skills, knowledge and understanding of the subjects involved in STEM (science, technology, engineering and mathematics) are vital for all young people in an increasingly science and technology dri

The skills, knowledge and understanding of the subjects involved in STEM (science, technology, engineering and mathematics) are vital for all young people in an increasingly science and technology dri

In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behin

Classical computer science textbooks tell us that some problems are 'hard'. Yet many areas, from machine learning and computer vision to theorem proving and software verification, have defined their own set of tools for effectively solving complex problems. Tractability provides an overview of these different techniques, and of the fundamental concepts and properties used to tame intractability. This book will help you understand what to do when facing a hard computational problem. Can the problem be modelled by convex, or submodular functions? Will the instances arising in practice be of low treewidth, or exhibit another specific graph structure that makes them easy? Is it acceptable to use scalable, but approximate algorithms? A wide range of approaches is presented through self-contained chapters written by authoritative researchers on each topic. As a reference on a core problem in computer science, this book will appeal to theoreticians and practitioners alike.