Carve out your niche in the exploding world of blockchain technology Cryptocurrency, NFTs, smart contracts, and ever-more-important business and finance functions--they all run on blockchain. Blockchain For Dummies is the must-have guide to the basics of blockchain. This clear reference breaks down exactly what blockchain technology is, how it's used across industries, and what it all means for you and your investment portfolio. Learn the latest token standards, emerging tools and platforms, and opportunities that you'll want to hop aboard. This book demystifies all of it, so you can understand and profit from this major disruptor in the world of finance. Evaluate new ideas and trends, make smarter decisions, and establish your presence on your blockchains of choice. Peek under the hood of the new tech that's changing finance (and everything else) Learn how blockchain powers cryptocurrency and smart contracts Launch your own blockchain apps on stable platforms Understand and take advantage of blockchain investment opportunities Investors, financial pros, and technologists who need Blockchain 101 will love Blockchain For Dummies. Exploring blockchain to build your personal portfolio? This book has your essentials.

Since the 1960s, many researchers have extended topological degree theory to various non-compact type nonlinear mappings, and it has become a valuable tool in nonlinear analysis. Presenting a survey of advances made in generalizations of degree theory during the past decade, this book focuses on topological degree theory in normed spaces and its applications. The authors begin by introducing the Brouwer degree theory in Rn, then consider the Leray-Schauder degree for compact mappings in normed spaces. Next, they explore the degree theory for condensing mappings, including applications to ODEs in Banach spaces. This is followed by a study of degree theory for A-proper mappings and its applications to semilinear operator equations with Fredholm mappings and periodic boundary value problems. The focus then turns to construction of Mawhin's coincidence degree for L-compact mappings, followed by a presentation of a degree theory for mappings of class (S+) and its perturbations with other monotone-type mappings. The final chapter studies the fixed point index theory in a cone of a Banach space and presents a notable new fixed point index for countably condensing maps. Examples and exercises complement each chapter. With its blend of old and new techniques, Topological Degree Theory and Applications forms an outstanding text for self-study or special topics courses and a valuable reference for anyone working in differential equations, analysis, or topology.

Developed by Jean-Paul Benzerci more than 30 years ago, correspondence analysis as a framework for analyzing data quickly found widespread popularity in Europe. The topicality and importance of correspondence analysis continue, and with the tremendous computing power now available and new fields of application emerging, its significance is greater than ever. Correspondence Analysis and Data Coding with Java and R clearly demonstrates why this technique remains important and in the eyes of many, unsurpassed as an analysis framework. After presenting some historical background, the author presents a theoretical overview of the mathematics and underlying algorithms of correspondence analysis and hierarchical clustering. The focus then shifts to data coding, with a survey of the widely varied possibilities correspondence analysis offers and introduction of the Java software for correspondence analysis, clustering, and interpretation tools. A chapter of case studies follows, wherein the author explores applications to areas such as shape analysis and time-evolving data. The final chapter reviews the wealth of studies on textual content as well as textual form, carried out by Benzecri and his research lab. These discussions show the importance of correspondence analysis to artificial intelligence as well as to stylometry and other fields. This book not only shows why correspondence analysis is important, but with a clear presentation replete with advice and guidance, also shows how to put this technique into practice. Downloadable software and data sets allow quick, hands-on exploration of innovative correspondence analysis applications.

As the theories and methods have evolved over the years, the mechanics of solid bodies has become unduly fragmented. Most books focus on specific aspects, such as the theories of elasticity or plasticity, the theories of shells, or the mechanics of materials. While a narrow focus serves immediate purposes, much is achieved by establishing the common foundations and providing a unified perspective of the discipline as a whole. Mechanics of Solids and Shells accomplishes these objectives. By emphasizing the underlying assumptions and the approximations that lead to the mathematical formulations, it offers a practical, unified presentation of the foundations of the mechanics of solids, the behavior of deformable bodies and thin shells, and the properties of finite elements. The initial chapters present the fundamental kinematics, dynamics, energetics, and behavior of materials that build the foundation for all of the subsequent developments. These are presented in full generality without the usual restrictions on the deformation. The general principles of work and energy form the basis for the consistent theories of shells and the approximations by finite elements. The final chapter views the latter as a means of approximation and builds a bridge between the mechanics of the continuum and the discrete assembly. Expressly written for engineers, Mechanics of Solids and Shells forms a reliable source for the tools of analysis and approximation. Its constructive presentation clearly reveals the origins, assumptions, and limitations of the methods described and provides a firm, practical basis for the use of those methods.

This text offers an overview of the basic theories and techniques of functional analysis and its applications. It contains topics such as the fixed point theory starting from Ky Fan's KKM covering and quasi-Schwartz operators. It also includes over 200 exercises to reinforce important concepts.;The author explores three fundamental results on Banach spaces, together with Grothendieck's structure theorem for compact sets in Banach spaces (including new proofs for some standard theorems) and Helley's selection theorem. Vector topologies and vector bornologies are examined in parallel, and their internal and external relationships are studied. This volume also presents recent developments on compact and weakly compact operators and operator ideals; and discusses some applications to the important class of Schwartz spaces.;This text is designed for a two-term course on functional analysis for upper-level undergraduate and graduate students in mathematics, mathematical physics, economics and engineering. It may also be used as a self-study guide by researchers in these disciplines.

"A collection of proofs of fundamental theorems, this volume utilizes a format that is exhaustive and consistent. Every result covered in ``Econometrics''is proved as well as stated. One notation system is used throughout the volume. The topics included in the book cover such areas as estimations and testing in linear regression models under various sets of assumptions, and estimation and testing in simultaneous equations models. The latter subject is treated more extensively than in most econometrics books, and the entire volume is characterized by its rigorous level of examination. "

Welcome to Singapore Math--the leading math program in the world This workbook features math practice and activities for sixth grade students based on the Singapore Math method. Level A is designed for the first semester and Level B is for the second. An introduction at the front of each book explains Singapore Math and its common problem types. Each unit has learning objectives, which clearly define the skills to be learned in that section, and an answer key with step-by-step worked out solutions that help students see how to work the problems. This book is perfect for students familiar with Singapore Math and for those who just need extra math practice --Directly correlated to Singapore Math textbooks, this comprehensive practice series allows learners to practice various types of math problems while developing their thinking and analytical skills. Learning objectives and unit assessments are included to ensure that students obtain a thorough understanding of each concept. Perfect as a supplement to classroom work or as a homeschool resource, these workbooks will boost confidence in problem-solving and critical-thinking skills.

Understand How to Use and Develop Meshfree Techniques An Update of a Groundbreaking Work Reflecting the significant advances made in the field since the publication of its predecessor, Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition systematically covers the most widely used meshfree methods. With 70% new material, this edition addresses important new developments, especially on essential theoretical issues. New to the Second Edition Much more details on fundamental concepts and important theories for numerical methods Discussions on special properties of meshfree methods, including stability, convergence, accurate, efficiency, and bound property More detailed discussion on error estimation and adaptive analysis using meshfree methods Developments on combined meshfree/finite element method (FEM) models Comparison studies using meshfree and FEM Drawing on the author's own research, this book provides a single-source guide to meshfree techniques and theories that can effectively handle a variety of complex engineering problems. It analyzes how the methods work, explains how to use and develop the methods, and explores the problems associated with meshfree methods. To access MFree2D (copyright, G. R. Liu), which accompanies MESHFREE METHODS: MOVING BEYOND THE FINITE ELEMENT METHOD, Second Edition (978-1-4200-8209-8) by Dr. G. R. Liu, please go to the website: www.ase.uc.edu/~liugr An access code is needed to use program - to receive it please email Dr. Liu directly at: [email protected] Dr. Liu will reply to you directly with the code, and you can then proceed to use the software.

D.W. Winnicott - one of this centuries most important theorists - is the focus of the new edition of this extraordinary volume. Drawing extensively upon Winnicott's own papers and lectures, the main themes of his theory and personal development are revealed. His vast contributions to the understandings of the profound significance of infancy in the

MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools. This third edition of MATLAB Guide completely revises and updates the best-selling second edition and is more than 25 per cent longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox. Key features are:* A tutorial in Chapter 1 that gives a hands-on overview of MATLAB.* A thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers.* A web page provides example program files, updates, and links to MATLAB resources. The new edition:* Contains colour figures throughout. * Includes pithy discussions of related topics in new "Asides" boxes that augment the text. * Has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets.* Covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables.* Contains more on MATLAB workflow, including the Live Editor and unit tests.* Fully reflects major updates to the MATLAB graphics system. Features a tutorial in Chapter 1 that gives a hands-on overview of MATLAB, a thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers, and a web page that provides example program files, updates, and links to MATLAB resources. The new edition contains color figures throughout, includes pithy discussions of related topics in new "Asides" boxes that augment the text, has new chapters on the Parallel Computing Toolbox, object-oriented programming, graphs, and large data sets, covers important new MATLAB data types such as categorical arrays, string arrays, tall arrays, tables, and timetables, contains more on MATLAB workflow, including the Live Editor and unit tests, and fully reflects major updates to the MATLAB graphics system.

In the early 1970s, fuzzy systems and fuzzy control theories added a new dimension to control systems engineering. From its beginnings as mostly heuristic and somewhat ad hoc, more recent and rigorous approaches to fuzzy control theory have helped make it an integral part of modern control theory and produced many exciting results. Yesterday's "art" of building a working fuzzy controller has turned into today's "science" of systematic design. To keep pace with and further advance the rapidly developing field of applied control technologies, engineers, both present and future, need some systematic training in the analytic theory and rigorous design of fuzzy control systems. Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems provides that training by introducing a rigorous and complete fundamental theory of fuzzy sets and fuzzy logic, and then building a practical theory for automatic control of uncertain and ill-modeled systems encountered in many engineering applications. The authors proceed through basic fuzzy mathematics and fuzzy systems theory and conclude with an exploration of some industrial application examples. Almost entirely self-contained, Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems establishes a strong foundation for designing and analyzing fuzzy control systems under uncertain and irregular conditions. Mastering its contents gives students a clear understanding of fuzzy control systems theory that prepares them for deeper and broader studies and for many practical challenges faced in modern industry.

As the amount of information recorded and stored electronically grows ever larger, it becomes increasingly useful, if not essential, to develop better and more efficient ways to summarize and extract information from these large, multivariate data sets. The field of classification does just that-investigates sets of "objects" to see if they can be summarized into a small number of classes comprising similar objects. Researchers have made great strides in the field over the last twenty years, and classification is no longer perceived as being concerned solely with exploratory analyses. The second edition of Classification incorporates many of the new and powerful methodologies developed since its first edition. Like its predecessor, this edition describes both clustering and graphical methods of representing data, and offers advice on how to decide which methods of analysis best apply to a particular data set. It goes even further, however, by providing critical overviews of recent developments not widely known, including efficient clustering algorithms, cluster validation, consensus classifications, and the classification of symbolic data. The author has taken an approach accessible to researchers in the wide variety of disciplines that can benefit from classification analysis and methods. He illustrates the methodologies by applying them to data sets-smaller sets given in the text, larger ones available through a Web site. Large multivariate data sets can be difficult to comprehend-the sheer volume and complexity can prove overwhelming. Classification methods provide efficient, accurate ways to make them less unwieldy and extract more information. Classification, Second Edition offers the ideal vehicle for gaining the background and learning the methodologies-and begin putting these techniques to use.

The financial industry is swamped by credit products whose economic performance is linked to the performance of some underlying portfolio of credit-risky instruments, like loans, bonds, swaps, or asset-backed securities. Financial institutions continuously use these products for tailor-made long and short positions in credit risks. Based on a steadily growing market, there is a high demand for concepts and techniques applicable to the evaluation of structured credit products. Written from the perspective of practitioners who apply mathematical concepts to structured credit products, Structured Credit Portfolio Analysis, Baskets & CDOs starts with a brief wrap-up on basic concepts of credit risk modeling and then quickly moves on to more advanced topics such as the modeling and evaluation of basket products, credit-linked notes referenced to credit portfolios, collateralized debt obligations, and index tranches. The text is written in a self-contained style so readers with a basic understanding of probability will have no difficulties following it. In addition, many examples and calculations have been included to keep the discussion close to business applications. Practitioners as well as academics will find ideas and tools in the book that they can use for their daily work.

The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. Hundreds of examples of past and prevalent tone systems are featured. Topics include Fuzziness and Sonance, Wavelets and Nonspecificity, Pitch Granulation and Ambiguity, Equal Temperaments, Mean Tone Systems. Well Tempered Systems, Ptolemy Systems, and more. Appendices include extended lists of tone systems and a catalogue of historical organs with subsemitones.

Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory and their relative generalizations. Thus, this book makes computations of higher K-theory of group rings more accessible and provides novel techniques for the computations of higher K-theory of finite and some infinite groups. Authored by a premier authority in the field, the book begins with a careful review of classical K-theory, including clear definitions, examples, and important classical results. Emphasizing the practical value of the usually abstract topological constructions, the author systematically discusses higher algebraic K-theory of exact, symmetric monoidal, and Waldhausen categories with applications to orders and group rings and proves numerous results. He also defines profinite higher K- and G-theory of exact categories, orders, and group rings. Providing new insights into classical results and opening avenues for further applications, the book then uses representation-theoretic techniques-especially induction theory-to examine equivariant higher algebraic K-theory, their relative generalizations, and equivariant homology theories for discrete group actions. The final chapter unifies Farrell and Baum-Connes isomorphism conjectures through Davis-Luck assembly maps.

Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one. Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras. This treatment provides a clear account of historically important results, exposes the principal methods of attack, and includes some results that are more recent and some that are lesser known. Unique in its focus, this book will prove useful for experts as well as beginners in the field and for those who simply want to acquaint themselves with this area of Banach space theory.

This study guide for Varsity Maths Preparation has been compiled by Emeritus Professor John Webb in response to the dire challenges experienced by first year university students, in Mathematics as well as in courses in Science, Engineering and Business Science, all heavily dependent on mathematical thinking. By working through the problem sets in this self-study book, learners should develop and test their skills, on their own, in areas such as algebraic expertise, trigonometry skills, word problems, geometric insight, numerical facility, logical reasoning and flexible thinking. This cannot be taught and is best achieved without assistance and timeously, i.e. prior to students entering university. The problem-solving techniques which learners could acquire from dedicated, independent use of this outstanding booklet will contribute significantly to their success in the National Benchmark tests (NBTs). Varsity Maths Prep is a gem for learners who are serious about an academic future.

This book is designed for a first course in numerical analysis. It differs considerably from other such texts in its choice of topics.

Here is a short, well-written book that covers the material essential for learning LaTeX. It includes incisive examples that teach LaTeX in a powerful yet abbreviated fashion. This is the handbook to have if you don't want to wade through extraneous material. It includes the following crucial features: numerous examples of widely used mathematical expressions; complete documents illustrating the creation of articles, reports, presentations, and posters; troubleshooting tips to help you pinpoint an error; details of how to set up an index and a bibliography; and information about online LaTeX resources. Why do you need to learn LaTeX? LaTeX has become an extremely popular typesetting system and is widely used throughout the sciences. As a student, you may need to typeset reports and theses in LaTeX (particularly if you are a graduate student in any mathematics or computer science discipline). Or you may be someone who had planned to "eventually" get around to learning LaTeX, but you are still using older or less appropriate methods of typesetting. Procrastinate no more! This second edition of the well-regarded and highly successful book includes additional material on the American Mathematical Society packages for typesetting additional mathematical symbols and multi-line displays; the BiBTeX program for creating bibliographies; the Beamer package for creating presentations; and the a0poster class for creating posters.

This book aims to provide theoretical discussions of assessment development and implementation in mathematics education contexts, as well as to offer readers discussions of assessment related to instruction and affective areas, such as attitudes and beliefs. By providing readers with theoretical implications of assessment creation and implementation, this volume demonstrates how validation studies have the potential to advance the field of mathematics education. Including chapters addressing a variety of established and budding areas within assessment and evaluation in mathematics education contexts, this book brings fundamental issues together with new areas of application.

This book is based on a series of lectures on mathematical biology, the essential dynamics of complex and crucially important social systems, and the unifying power of mathematics and nonlinear dynamical systems theory.

A readable introduction to the subject of calculus on arbitrary surfaces or manifolds. Accessible to readers with knowledge of basic calculus and linear algebra. Sections include series of problems to reinforce concepts.