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Topics in Computational Number Theory Inspired by Peter L. Montgomery
by Joppe W. BosPeter L. Montgomery has made significant contributions to computational number theory, introducing many basic tools such as Montgomery multiplication, Montgomery simultaneous inversion, Montgomery curves, and the Montgomery ladder. This book features state-of-the-art research in computational number theory related to Montgomery's work and its impact on computational efficiency and cryptography. Topics cover a wide range of topics such as Montgomery multiplication for both hardware and software implementations; Montgomery curves and twisted Edwards curves as proposed in the latest standards for elliptic curve cryptography; and cryptographic pairings. This book provides a comprehensive overview of integer factorization techniques, including dedicated chapters on polynomial selection, the block Lanczos method, and the FFT extension for algebraic-group factorization algorithms. Graduate students and researchers in applied number theory and cryptography will benefit from this survey of Montgomery's work.
Topics in Commutative Ring Theory
by John J. WatkinsTopics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.
Topics in Combinatorics and Graph Theory
by R. RamaThe book covers all the basics of both the topics. The topics are sequenced in such a manner that there is a flow in understanding the advances. The first and second chapters cover all the basic methods and tools for counting. Chapter 3 is on binomial theorem and binomial identities. Topics such as partitions, permutations on multisets, generating functions, recurrence relation, principle of inclusion exclusion, repeated counting, partially ordered sets and Mobius inversion, Polya's counting are covered in different chapters. Some basic chapters have some worked-out exercise. Information on Catalan numbers, Eulerian Numbers, Narayana Numbers, and Schroder Number are given in a chapter. The topic on "discrete probability" covers the connection between counting techniques and probability theory. There second part of the book covers topics in graph theory such as basics of graphs, trees,bipartite graphs, matching , planar graphs, Euler and Hamilton graphs, graph coloring, Ramsey theory, spectral properties, and some graph algorithms.Adequate exercise and examples are provided so as to enhance the reader's interest and understanding. Some interesting concepts like high hamiltonicity, power of graphs, domination, and matrix tree theorem are introduced.
Topics in Cognitive Rehabilitation in the TBI Post-Hospital Phase
by Renato Anghinah Wellingson Paiva Linamara Rizzo Battistella Robson AmorimTraumatic brain injury (TBI) refers to nondegenerative, noncongenital damage to the brain from an external mechanical force, which can lead to permanent or temporary impairment of cognitive, physical, and psychosocial functions, with an associated diminished or altered state of consciousness. Despite this broad definition, it is estimated that more than 1.500.000 people suffer TBI annually in US, with 20% afflicted with moderate or severe forms. Additionally, a high percentage of these patients are unable to return to their daily routine (approximately 50%). In this context, both motor and cognitive rehabilitation are extremely important for these individuals. The aim of cognitive and motor rehabilitation is to recover an individual’s ability to process, interpret and respond to environmental inputs, as well as to create strategies and procedures to compensate for lost functions that are necessary in familial, social, educational and occupational settings. The purpose of this book is to review the basic concepts related to TBI, including mechanisms of injury, acute and post-acute care, severity levels, the most common findings in mild, moderate and severe TBI survivors, and the most frequent cognitive and motor impairments following TBI, as well as to discuss the strategies used to support post-TBI patients. The most important rehabilitation techniques, both from cognitive and motor perspectives, are addressed. Finally, information regarding work and community re-entry and familial and psychological support are discussed in detail.Topics in Cognitive Rehabilitation in the TBI Post-Hospital Phase is intended as a reference guide for all professionals who have contact with or are related to patients suffering from TBI. Any professionals who work with or are related to patients suffering from TBI will find here a broad and comprehensive overview of TBI, addressing all essential issues, from acute care to rehabilitation strategies, follow up and re-socialization.
Topics in Clifford Analysis: Special Volume in Honor of Wolfgang Sprößig (Trends in Mathematics)
by Swanhild BernsteinQuaternionic and Clifford analysis are an extension of complex analysis into higher dimensions. The unique starting point of Wolfgang Sprößig’s work was the application of quaternionic analysis to elliptic differential equations and boundary value problems. Over the years, Clifford analysis has become a broad-based theory with a variety of applications both inside and outside of mathematics, such as higher-dimensional function theory, algebraic structures, generalized polynomials, applications of elliptic boundary value problems, wavelets, image processing, numerical and discrete analysis. The aim of this volume is to provide an essential overview of modern topics in Clifford analysis, presented by specialists in the field, and to honor the valued contributions to Clifford analysis made by Wolfgang Sprößig throughout his career.
Topics in Classical and Modern Analysis: In Memory of Yingkang Hu (Applied and Numerical Harmonic Analysis)
by Sharon Taylor Sergey Tikhonov Martha Abell Emil Iacob Alex Stokolos Jiehua ZhuDifferent aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.
Topics in Classical Micro- and Macroeconomics
by Peter FlaschelThis book demonstrates that classical micro- and macroeconomics, in particular in the tradition of Smith, Ricardo and Marx, can be synthesized into a coherent whole from the perspective of formal model building as well as applied Leontief-Stone systems of national accounts and the input-output approaches built on them. This reformulation of classical economics differs significantly from the static Neoricardian formalization of the classical approach to economics. The book presents a collection of revised versions of papers that were written between 1983 and 2000, some jointly with coauthors, and supplements them in a coherent way with recent unpublished work on the subject.
Topics in Chromatic Graph Theory
by Lowell W. Beineke Robin J. Wilson Bjarne ToftChromatic graph theory is a thriving area that uses various ideas of 'colouring' (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks, where colouring algorithms form an important feature. While other books cover portions of the material, no other title has such a wide scope as this one, in which acknowledged international experts in the field provide a broad survey of the subject. All fifteen chapters have been carefully edited, with uniform notation and terminology applied throughout. Bjarne Toft (Odense, Denmark), widely recognized for his substantial contributions to the area, acted as academic consultant. The book serves as a valuable reference for researchers and graduate students in graph theory and combinatorics and as a useful introduction to the topic for mathematicians in related fields.
Topics in Biostatistics
by Walter T. AmbrosiusThis book presents a multidisciplinary survey of biostatics methods, each illustrated with hands-on examples. It introduces advanced methods in statistics, including how to choose and work with statistical packages. Specific topics of interest include microarray analysis, missing data techniques, power and sample size, statistical methods in genetics. The book is an essential resource for researchers at every level of their career.
Topics in Biomedical Gerontology
by Pramod C. Rath Ramesh Sharma S. PrasadThis book presents a collection of articles on various aspects of current research on aging. These include model systems, cellular, biochemical and molecular aspects of experimental aging research, as well as selected intervention studies on age-related diseases. Aging is a global challenge to human society. Children are always in a hurry to become adults, while adults produce offspring and add to the gene pool. However, after adulthood or the attainment of reproductive maturity, all physiological parameters of the living organism start to undergo the aging process. Old age sets in slowly but surely, and usually continues for a prolonged period. If vigor and vitality are the main advantages of adulthood, old age offers the rewards of experience and maturity. Biologists ask questions such as: Why do we age? How do we become old? Is it possible to slow down, postpone or even prevent aging? In turn, medical experts ask: What are the diseases associated with old age? Are there medicines that can help affected elderly patients? In fact both groups are asking themselves how can we add more health to old age. Healthy aging is the dream of every individual. But to achieve this, it is fundamental that we first understand the cellular, biochemical and molecular basis of the aging process in mammalian cells, tissues and intact living organisms, which can serve as experimental model systems in Biomedical Gerontology. Once the biology of aging is understood at the genetic and molecular levels, interventional approaches to aging and its associated diseases may be easier to plan and implement at the preclinical level.
Topics in Banach Space Theory
by Nigel J. Kalton Fernando AlbiacThis text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book. . . succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly. . . It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments. . . I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book. . . " --Gilles Godefroy, Mathematical Reviews
Topics in Artificial Intelligence Applied to Industry 4.0
by Amit Kumar Tyagi Swetta Kukreja Mahmoud Ragab AL-Refaey Abdullah Saad AL-MalaiseTopics in Artificial Intelligence Applied to Industry 4.0 Forward thinking resource discussing emerging AI and IoT technologies and how they are applied to Industry 4.0 Topics in Artificial Intelligence Applied to Industry 4.0 discusses the design principles, technologies, and applications of emerging AI and IoT solutions on Industry 4.0, explaining how to make improvements in infrastructure through emerging technologies. Providing a clear connection with different technologies such as IoT, Big Data, AR and VR, and Blockchain, this book presents security, privacy, trust, and other issues whilst delving into real-world problems and case studies. The text takes a highly practical approach, with a clear insight on how readers can increase productivity by drastically shortening the time period between the development of a new product and its delivery to customers in the market by 50%. This book also discusses how to save energy across systems to ensure competitiveness in a global market, and become more responsive in how they produce products and services for their consumers, such as by investing in flexible production lines. Written by highly qualified authors, Topics in Artificial Intelligence Applied to Industry 4.0 explores sample topics such as: Quantum machine learning, neural network implementation, and cloud and data analytics for effective analysis of industrial data Computer vision, emerging networking technologies, industrial data spaces, and an industry vision for 2030 in both developing and developed nations Novel or improved nature-inspired optimization algorithms in enhancing Industry 5.0 and the connectivity of any components for smart environment Future professions in agriculture, medicine, education, fitness, R&D, and transport and communication as a result of new technologies Aimed at researchers and students in the interdisciplinary fields of Smart Manufacturing and Smart Applications, Topics in Artificial Intelligence Applied to Industry 4.0 provides the perfect overview of technology from the perspective of modern society and operational environment.
Topics in Applied Statistics
by Yi Liu Mingxiu Hu Jianchang LinThis volume presents 27 selected papers in topics that range from statistical applications in business and finance to applications in clinical trials and biomarker analysis. All papers feature original, peer-reviewed content. The editors intentionally selected papers that cover many topics so that the volume will serve the whole statistical community and a variety of research interests. The papers represent select contributions to the 21st ICSA Applied Statistics Symposium. The International Chinese Statistical Association (ICSA) Symposium took place between the 23rd and 26th of June, 2012 in Boston, Massachusetts. It was co-sponsored by the International Society for Biopharmaceutical Statistics (ISBS) and American Statistical Association (ASA). This is the inaugural proceedings volume to share research from the ICSA Applied Statistics Symposium.
Topics in Algorithmic Graph Theory (Encyclopedia of Mathematics and its Applications #178)
by Lowell W. Beineke Robin J. Wilson Martin Charles GolumbicAlgorithmic graph theory has been expanding at an extremely rapid rate since the middle of the twentieth century, in parallel with the growth of computer science and the accompanying utilization of computers, where efficient algorithms have been a prime goal. This book presents material on developments on graph algorithms and related concepts that will be of value to both mathematicians and computer scientists, at a level suitable for graduate students, researchers and instructors. The fifteen expository chapters, written by acknowledged international experts on their subjects, focus on the application of algorithms to solve particular problems. All chapters were carefully edited to enhance readability and standardize the chapter structure as well as the terminology and notation. The editors provide basic background material in graph theory, and a chapter written by the book's Academic Consultant, Martin Charles Golumbic (University of Haifa, Israel), provides background material on algorithms as connected with graph theory.
Topics in Algebraic Graph Theory
by Lowell W. Beineke Robin J. WilsonThe rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references.
Topics in Advanced Quantum Mechanics (Dover Books on Physics)
by Barry R. HolsteinThis graduate-level text is based on a course in advanced quantum mechanics, taught many times at the University of Massachusetts, Amherst. Topics include propagator methods, scattering theory, charged particle interactions, alternate approximate methods, and Klein-Gordon and Dirac equations. Problems appear in the flow of the discussion, rather than at the end of chapters. 1992 edition.
Topics from the 8th Annual UNCG Regional Mathematics and Statistics Conference
by Jan Rychtář Sat Gupta Ratnasingham Shivaji Maya ChhetriThe Annual University of North Carolina Greensboro Regional Mathematics and Statistics Conference (UNCG RMSC) has provided a venue for student researchers to share their work since 2005. The 8th Conference took place on November 3, 2012. The UNCG-RMSC conference established a tradition of attracting active researchers and their faculty mentors from NC and surrounding states. The conference is specifically tailored for students to present the results of their research and to allow participants to interact with and learn from each other. This type of engagement is truly unique. The broad scope of UNCG-RMSC includes topics in applied mathematics, number theory, biology, statistics, biostatistics and computer sciences.
Topics from Australian Conferences on Teaching Statistics
by Michael A. Martin Helen Macgillivray Brian PhillipsThe first OZCOTS conference in 1998 was inspired by papers contributed by Australians to the 5th International Conference on Teaching Statistics. In 2008, as part of the program of one of the first National Senior Teaching Fellowships, the 6th OZCOTS was held in conjunction with the Australian Statistical Conference, with Fellowship keynotes and contributed papers, optional refereeing and proceedings. This venture was so successful that the 7th and 8th OZCOTS were similarly run, conjoined with Australian Statistical Conferences in 2010 and 2012. Authors of papers from these OZCOTS conferences were invited to develop chapters for refereeing and inclusion in this volume. There are sections on keynote topics, undergraduate curriculum and learning, professional development, postgraduate learning, and papers from OZCOTS 2012. Because OZCOTS aim to unite statisticians and statistics educators, the approaches this volume takes are immediately relevant to all who have a vested interest in good teaching practices. Globally, statistics as a discipline, statistical pedagogy and statistics in academia and industry are all critically important to the modern information society. This volume addresses these roles within the wider society as well as questions that are specific to the discipline itself. Other chapters share research on learning and teaching statistics in interdisciplinary work and student preparation for futures in academia, government and industry
Topics and Trends in Current Statistics Education Research: International Perspectives (ICME-13 Monographs)
by Gail Burrill Dani Ben-ZviThis book focuses on international research in statistics education, providing a solid understanding of the challenges in learning statistics. It presents the teaching and learning of statistics in various contexts, including designed settings for young children, students in formal schooling, tertiary level students, and teacher professional development. The book describes research on what to teach and platforms for delivering content (curriculum), strategies on how to teach for deep understanding, and includes several chapters on developing conceptual understanding (pedagogy and technology), teacher knowledge and beliefs, and the challenges teachers and students face when they solve statistical problems (reasoning and thinking). This new research in the field offers critical insights for college instructors, classroom teachers, curriculum designers, researchers in mathematics and statistics education as well as policy makers and newcomers to the field of statistics education. Statistics has become one of the key areas of study in the modern world of information and big data. The dramatic increase in demand for learning statistics in all disciplines is accompanied by tremendous growth in research in statistics education. Increasingly, countries are teaching more quantitative reasoning and statistics at lower and lower grade levels within mathematics, science and across many content areas. Research has revealed the many challenges in helping learners develop statistical literacy, reasoning, and thinking, and new curricula and technology tools show promise in facilitating the achievement of these desired outcomes.
Topics and Trends in Current Science Education
by Andrée Tiberghien Catherine Bruguière Pierre ClémentThis book features 35 of best papers from the 9th European Science Education Research Association Conference, ESERA 2011, held in Lyon, France, September 5th-9th 2011. The ESERA international conference featured some 1,200 participants from Africa, Asia, Australia, Europe as well as North and South America offering insight into the field at the end of the first decade of the 21st century. This book presents studies that represent the current orientations of research in science education and includes studies in different educational traditions from around the world. It is organized into six parts around the three poles (content, students, teachers) and their interrelations of science education: after a general presentation of the volume (first part), the second part concerns SSI (Socio-Scientific Issues) dealing with new types of content, the third the teachers, the fourth the students, the fifth the relationships between teaching and learning, and the sixth the teaching resources and the curricula.
Topics and Solved Exercises at the Boundary of Classical and Modern Physics (Undergraduate Lecture Notes in Physics)
by Samir KheneThis book provides a simple and well-structured course followed by an innovative collection of exercises and solutions that will enrich a wide range of courses as part of the undergraduate physics curriculum. It will also be useful for first-year graduate students who are preparing for their qualifying exams. The book is divided into four main themes at the boundary of classical and modern physics: atomic physics, matter-radiation interaction, blackbody radiation, and thermodynamics. Each chapter starts with a thorough and well-illustrated review of the core material, followed by plenty of original exercises that progress in difficulty, replete with clear, step-by-step solutions. This book will be invaluable for undergraduate course instructors who are looking for a source of original exercises to enhance their classes, while students that want to hone their skills will encounter challenging and stimulating problems.
Topics and Methods for Urban and Landscape Design
by Roberta Ingaramo Angioletta VogheraThis book combines urban planning and architectural tools in an attempt to overcome the limitations of sectoral measures. In this perspective, it offers a forum for the debate of different approaches used by schools of planning and architecture. It explores strategies by drawing from the potential contributions of cognitive models for decisions, the role of utopian thinking and retrofitting actions and their interconnectedness, the role of cultural legacy for urban and landscape design, the design perspectives about public spaces, and the role of architecture design and urban and regional planning for landscape quality. The book also discusses on design as a process of decision-making that operates as an act of empathy that aligns with human and ecological values - emotional, physical and socio-cultural. Each planning and design act has different possible effects able to help making clear strategic and local actions, contributing to community empowerment and to landscape and local governance. Design activity along the river and multiple experiences (design processes, urban fringe design, agri-urban models, river parks, UNESCO sites, River Contracts, greenbelts and ecological networks), through reflection on design roles, helping to understand the design process and its results at different scales. Roberta Ingaramo, architect, PhD, is Assistant Professor in Architectural and Urban Design, Department of Architecture and Design (DAD), Polytechnic University of Turin (Italy), Master in Conservation of Historic Towns and Buildings, Katholieke Universiteit (Belgium). roberta. ingaramo@polito. it Angioletta Voghera, architect, PhD, is Associate Professor of Urban and Regional Planning, Inter-university Department of Urban and Regional Studies and Planning (DIST), Polytechnic University of Turin (Italy). angioletta. voghera@polito. it
Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II: Tripods and Combinatorial Cuspidalization (Lecture Notes in Mathematics #2299)
by Yuichiro Hoshi Shinichi MochizukiThe present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero.The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space.We then turn to the study of tripod synchronization, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve induces the same outer automorphism on certain subquotients of such a fundamental group determined by tripods [i.e., copies of the projective line minus three points]. The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists.In the final portion of the monograph, we develop a theory of localizability, on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space. This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the étale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
Topicalization in Asian Englishes: Forms, Functions, and Frequencies of a Fronting Construction (Routledge Studies in World Englishes)
by Sven LeuckertThis monograph is the first comprehensive study of topicalization in Asian second-language varieties of English and provides an in-depth analysis of the forms, functions, and frequencies of topicalization in four Asian Englishes. Topicalization, that is, the sentence-initial placement of constituents other than the subject, has been found to occur frequently in the English spoken by many Asians, but so far the possible reasons for this have never been scrutinized. This book closes this research gap by taking into account the structures of the major contact languages, the roles of second-language acquisition and politeness as well as other factors in order to explain why topicalization is highly frequent in some varieties such as Indian English and much less frequent in other varieties such as Hong Kong English. In addition to exploring major and minor forces involved in explaining the frequency of topicalization, the forms and functions of the feature are assessed. Central questions addressed in this regard are the following: Which syntactic constituents tend to be topicalized the most and the least frequently? Which discourse effects does topicalization achieve? How can we approach topicalization methodologically? And, lastly, which influence do language processing and production have on topicalization?
Topical and Transdermal Drug Delivery
by Adam C. Watkinson Heather A. BensonPractical drug development approaches presented by leading expertsDesigned to support the development of new, effective therapeutics, Topical and Transdermal Drug Delivery: Principles and Practice explains the principles underlying the field and then demonstrates how these principles are put into practice in the design and development of new drug products. Drawing together and reviewing the latest research findings, the book focuses on practical, tested, and proven approaches that are backed by industry case studies and the authors' firsthand experience. Moreover, the book emphasizes the mechanistic information that is essential for successful drug product development.Topical and Transdermal Drug Delivery: Principles and Practice is divided into two parts:Part One, Current Science, Skin Permeation, and Enhancement Approaches, offers readers a fundamental understanding of the underlying science in the field. It describes the principles and techniques needed to successfully perform experimental approaches, covering such issues as skin permeation, enhancement, and assessment.Part Two, Topical and Transdermal Product Development, guides readers through the complete product development process from concept to approval, offering practical tips and cautions from experts in the field. This part also discusses regulations that are specific to the development of dermal drug products. The final chapter explores current and future trends, forecasting new development techniques and therapeutics.Throughout the book, the authors clearly set forth the basic science and experimental procedures, making it possible for researchers to design their own experimental approaches and accurately interpret their results.With contributions from experienced drug researchers, this text is highly recommended for all researchers involved in topical and transdermal product development who need to know both the state of the science and the standards of practice.