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An Invitation to Knot Theory: Virtual and Classical
by Heather A. DyeThe Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.
Invitation to Linear Algebra (Textbooks in Mathematics)
by David C. MelloUnlike most books of this type, the book has been organized into “lessons” rather than chapters. This has been done to limit the size of the mathematical morsels that students must digest during each class, and to make it easier for instructors to budget class time. The book contains considerably more material than normally appears in a first course. For example, several advanced topics such as the Jordan canonical form and matrix power series have been included. This was done to make the book more flexible than most books presently available, and to allow instructors to choose enrichment material which may reflect their interests, and those of their students.
Invitation to Linear Programming and Game Theory
by David C. VellaWritten in a conversational tone, this classroom-tested text introduces the fundamentals of linear programming and game theory, showing readers how to apply serious mathematics to practical real-life questions by modelling linear optimization problems and strategic games. The treatment of linear programming includes two distinct graphical methods. The game theory chapters include a novel proof of the minimax theorem for 2x2 zero-sum games. In addition to zero-sum games, the text presents variable-sum games, ordinal games, and n-player games as the natural result of relaxing or modifying the assumptions of zero-sum games. All concepts and techniques are derived from motivating examples, building in complexity, which encourages students to think creatively and leads them to understand how the mathematics is applied. With no prerequisite besides high school algebra, the text will be useful to motivated high school students and undergraduates studying business, economics, mathematics, and the social sciences.
An Invitation to Mathematical Biology
by David G Costa Paul J SchulteThe textbook is designed to provide a "non-intimidating" entry to the field of mathematical biology. It is also useful for those wishing to teach an introductory course. Although there are many good mathematical biology texts available, most books are too advanced mathematically for most biology majors. Unlike undergraduate math majors, most biology major students possess a limited math background. Given that computational biology is a rapidly expanding field, more students should be encouraged to familiarize themselves with this powerful approach to understand complex biological phenomena. Ultimately, our goal with this undergraduate textbook is to provide an introduction to the interdisciplinary field of mathematical biology in a way that does not overly terrify an undergraduate biology major, thereby fostering a greater appreciation for the role of mathematics in biology
An Invitation to Mathematical Logic (Graduate Texts in Mathematics #301)
by David MarkerIn addition to covering the essentials, the author’s intention in writing this text is to entice the reader to further study mathematical logic. There is no current “standard text” for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks’ worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading. New definitions, formalism, and syntax have been streamlined to engage thereader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.
An Invitation to Mathematical Physics and Its History
by Jont AllenThis state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.
An Invitation to Model Theory
by Jonathan KirbyModel theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
An Invitation to Morse Theory (Universitext)
by Liviu NicolaescuThis self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
An Invitation to Statistics in Wasserstein Space (SpringerBriefs in Probability and Mathematical Statistics)
by Victor M. Panaretos Yoav ZemelThis open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.
An Invitation to the Rogers-Ramanujan Identities (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Andrew V. SillsThe Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.
An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method: Projections, Estimates, Tools (SpringerBriefs in Mathematics)
by Shukai Du Francisco-Javier SayasThis monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.
An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space (Graduate Texts in Mathematics #285)
by Konrad SchmüdgenThis textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules.Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.
An Invitation to Web Geometry (IMPA Monographs #2)
by Jorge Vitório Pereira Luc PirioThis book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focuses of the book include how many abelian relations can a web carry and which webs are carrying the maximal possible number of abelian relations. The book offers complete proofs of both Chern's bound and Trépreau's algebraization theorem, including all the necessary prerequisites that go beyond elementary complex analysis or basic algebraic geometry. Most of the examples known up to date of non-algebraizable planar webs of maximal rank are discussed in detail. A historical account of the algebraization problem for maximal rank webs of codimension one is also presented.
Invited Lectures from the 13th International Congress on Mathematical Education
by Gabriele Kaiser Helen Forgasz Mellony Graven Alain Kuzniak Elaine Simmt Binyan XuThe book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.
Involutive Category Theory (Lecture Notes in Mathematics #2279)
by Donald YauThis monograph introduces involutive categories and involutive operads, featuring applications to the GNS construction and algebraic quantum field theory. The author adopts an accessible approach for readers seeking an overview of involutive category theory, from the basics to cutting-edge applications. Additionally, the author’s own recent advances in the area are featured, never having appeared previously in the literature. The opening chapters offer an introduction to basic category theory, ideal for readers new to the area. Chapters three through five feature previously unpublished results on coherence and strictification of involutive categories and involutive monoidal categories, showcasing the author’s state-of-the-art research. Chapters on coherence of involutive symmetric monoidal categories, and categorical GNS construction follow. The last chapter covers involutive operads and lays important coherence foundations for applications to algebraic quantum field theory. With detailed explanations and exercises throughout, Involutive Category Theory is suitable for graduate seminars and independent study. Mathematicians and mathematical physicists who use involutive objects will also find this a valuable reference.
Ion Correlations at Electrified Soft Matter Interfaces
by Nouamane LaanaitIon Correlations at Electrified Soft Matter Interfaces presents an investigation that combines experiments, theory, and computer simulations to demonstrate that the interdependency between ion correlations and other ion interactions in solution can explain the distribution of ions near an electrified liquid/liquid interface. The properties of this interface are exploited to vary the coupling strength of ion-ion correlations from weak to strong while monitoring their influence on ion distributions at the nanometer scale with X-ray reflectivity and on the macroscopic scale with interfacial tension measurements. This thesis demonstrates that a parameter-free density functional theory that includes ion-ion correlations and ion-solvent interactions is in agreement with the data over the entire range of experimentally tunable correlation coupling strengths. The reported findings represent a significant advance towards understanding the nature and role of ion correlations in charged soft-matter. Ion distributions underlie many scientific phenomena and technological applications, including electrostatic interactions between charged biomolecules and the efficiency of energy storage devices. These distributions are determined by interactions dictated by the chemical properties of the ions and their environment, as well as the long-range nature of the electrostatic force. The presence of strong correlations between ions is responsible for counterintuitive effects such as like-charge attraction.
IoT/AI Control of VRF Distributed Building Air-Conditioners
by Chuzo NinagawaThis book describes new energy service controls of VRF (Variable Refrigerant Flow) air-conditioners, i.e., distributed-type air-conditioners for commercial buildings in the near future, in the context of the energy savings for CO2 reduction and the reform of the electric power system. In other words, this book introduces the state-of-the-art technology of the next-generation distributed building air-conditioning energy service system, from IoT cloud control to AI optimal control, as well as standards for the smart grid supply and demand adjustment market. Rather than simple saving energy by On Off operations or shifting set- temperatures, the author proposes technology that sends numerical commands for the air-conditioner inverters directly from the cloud. By using this innovative IoT method, this book describes how to realizes the AI optimal cloud control as a cluster of air-conditioners while machine-learning of each air conditioner's situation.
IoT and AI in Agriculture: Smart Automation Systems for increasing Agricultural Productivity to Achieve SDGs and Society 5.0
by Tofael AhamedThis book covers smart agricultural space and its further development with an emphasis on ultra-saving labor shortages using AI-based technologies. A transboundary approach, as well as artificial intelligence (AI) and big data for bioinformatics, are required to increase timeliness and supplement the labor shortages, ensure the safety of intangible labor migration system to achieve one of the sustainable development goals (SDG) to secure food security (Society 5.0, SDG 1 and 2). With this in mind, the book focuses on the solution through smart Internet of Things (IoT) and AI-based agriculture, such as automation navigation, insect infestation, and decreasing agricultural inputs such as water and fertilizer, to maintain food security while ensuring environmental sustainability. Readers will gain a solid foundation for developing new knowledge through the in-depth research and education orientation of the book on how the deployment of outdoor and indoor sensors, AI/machine learning (ML), and IoT setups for sensing, tracking, collection, processing, and storing information over cloud platforms is nurturing and driving the pace of smart agriculture outdoor and indoors at this current time. Furthermore, the book introduces the smart system for automation challenges that are important for an unmanned system for considering safety and security points. The book is designed for researchers, graduates, and undergraduate students working in any area of machine learning, deep learning in agricultural engineering, smart agriculture, and environmental science. The greatest care has been made to deliver a diverse range of resource areas, as well as enormous insights into the significance and scope of IoT, AI, and ML in the development of intelligent digital farming and smart agriculture, providing comprehensive information to the intended readers.
IoT and ML for Information Management: A Smart Healthcare Perspective (Studies in Computational Intelligence #1169)
by Suyel NamasudraThis book discusses the roles of the Internet of Things (IoT) and machine learning (ML) in smart health care, including the integration of cloud computing with IoT and ML for managing healthcare data. It presents the fundamentals and many applications of IoT and ML in different areas of smart health care. It deliberates upon security and privacy issues, including trust concerns about smart healthcare systems based on IoT and ML algorithms. This book is concluded by discussing challenges and future work directions in smart health care using IoT and ML, and it serves as a reference resource for researchers and practitioners in academia and industry.
The IoT Architect's Guide to Attainable Security and Privacy
by Damilare D. Fagbemi David M Wheeler JC WheelerThis book describes how to architect and design Internet of Things (loT) solutions that provide end-to-end security and privacy at scale. It is unique in its detailed coverage of threat analysis, protocol analysis, secure design principles, intelligent loT's impact on privacy, and the effect of usability on security. The book also unveils the impact of digital currency and the dark web on the loT-security economy. It's both informative and entertaining. "Filled with practical and relevant examples based on years of experience ... with lively discussions and storytelling related to loT security design flaws and architectural issues."— Dr. James F. Ransome, Senior Director of Security Development Lifecycle (SOL) Engineering, Intel 'There is an absolute treasure trove of information within this book that will benefit anyone, not just the engineering community. This book has earned a permanent spot on my office bookshelf."— Erv Comer, Fellow of Engineering, Office of Chief Architect Zebra Technologies 'The importance of this work goes well beyond the engineer and architect. The IoT Architect's Guide to Attainable Security & Privacy is a crucial resource for every executive who delivers connected products to the market or uses connected products to run their business."— Kurt Lee, VP Sales and Strategic Alliances at PWNIE Express "If we collectively fail to follow the advice described here regarding loT security and Privacy, we will continue to add to our mounting pile of exploitable computing devices. The attackers are having a field day. Read this book, now."— Brook S.E. Schoenfield, Director of Advisory Services at IOActive, previously Master Security Architect at McAfee, and author of Securing Systems
IoT as a Service: 4th EAI International Conference, IoTaaS 2018, Xi’an, China, November 17–18, 2018, Proceedings (Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering #271)
by Bo Li Mao Yang Hui Yuan Zhongjiang YanThis book constitutes the refereed post-conference proceedings of the Fourth International Conference on IoT as a Service, IoTaaS 2018, which took place in Xi’an, China, in November 2018. The 50 revised full papers were carefully reviewed and selected from 83 submissions. The technical track present IoT-based services in various applications. In addition, there are three workshops: international workshop on edge computing for 5G/IoT, international workshop on green communications for internet of things, and international workshop on space-based internet of things.
IP Routing Protocols: Link-State and Path-Vector Routing Protocols
by James AweyaThis book discusses link-state routing protocols (OSPF and IS-IS), and the path-vector routing protocol (BGP). It covers their most identifying characteristics, operations, and the databases they maintain. Material is presented from a practicing engineer’s perspective, linking theory and fundamental concepts to common practices and real-world examples. Every aspect of the book is written to reflect current best practices using real-world examples. The book begins with a detailed description of the OSPF area types and hierarchical routing, and the different types of routers used in an OSPF autonomous system. The author goes on to describe in detail the different OSPF packet types, and inbound and outbound processing of OSPF link-state advertisements (LSAs). Next, the book gives an overview of the main features of IS-IS. The author then discusses the two-level routing hierarchy for controlling the distribution of intra-domain (Level 1) and inter-domain (Level 2) routing information within an IS-IS routing domain. He then describes in detail IS-IS network address formats, IS-IS routing metrics, IS-IS packet types, IS-IS network types and adjacency formation, IS-IS LSDB and synchronization, and IS-IS authentication. The book then reviews the main concepts of path-vector routing protocols, and describes BGP packet types, BGP session states and Finite State Machine, BGP path attributes types, and BGP Autonomous System Numbers (ASNs). Focuses solely on link-state routing protocols (OSPF and IS-IS), and the only path-vector routing protocol in use today (BGP). Reviews the basic concepts underlying the design of IS-IS and provides a detailed description of IS-IS area types and hierarchical routing, and the different types of routers used by IS-IS. Discusses the two-level routing hierarchy for controlling the distribution of intra-domain (Level 1) and inter-domain (Level 2) routing information within an IS-IS routing domain. Describes in detail BGP packet types, BGP session states and Finite State Machine, BGP path attributes types, and BGP ASNs, includes a high-level view of the typical BGP router and its components, and inbound and outbound message processing. James Aweya, PhD, is a chief research scientist at the Etisalat British Telecom Innovation Center (EBTIC), Khalifa University, Abu Dhabi, UAE. He has authored four books including this book and is a senior member of the Institute of Electrical and Electronics Engineers (IEEE).
IPython Interactive Computing and Visualization Cookbook
by Cyrille RossantIntended to anyone interested in numerical computing and data science: students, researchers, teachers, engineers, analysts, hobbyists... Basic knowledge of Python/NumPy is recommended. Some skills in mathematics will help you understand the theory behind the computational methods.
IPython Notebook Essentials
by L. Felipe MartinsIf you are a professional, student, or educator who wants to learn to use IPython Notebook as a tool for technical and scientific computing, visualization, and data analysis, this is the book for you. This book will prove valuable for anyone that needs to do computations in an agile environment.
IRobot - uMan
by Ulrich Furbach Ulrike BarthelmeßWarum werden Roboter oft als bedrohlich empfunden? Können künstliche Systeme Emotionen und Bewusstsein haben? Die Autoren gehen von der These aus, dass die Literatur- und Geistesgeschichte uns helfen kann, aktuelle Entwicklungen der Robotik unvoreingenommen zu betrachten. Denn ob es um mittelalterliche Mythen, androide Roboter der Romantik, die Aufklärung oder die Entwicklung der künstlichen Intelligenz geht, stets stellt sich die Frage nach dem, was der Mensch ist, was sein Bewusstsein ausmacht und was ihn von anderen Wesen unterscheidet.