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Introduction to Classical Mathematics I
6Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the human mce. It has put common sense back je n'y serais point alle.' Jules Verne where it belongs, on the topmost shelf nCllt to the dusty canister labelled 'discarded non- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
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Cambridge Introduction to Performance Theory
What does 'performance theory' really mean and why has it become so important across such a large number of disciplines, from art history to religious studies and architecture to geography? In this introduction Simon Shepherd explains the origins of performance theory, defines the terms and practices within the field and provides new insights into performance's wide range of definitions and uses. Offering an overview of the key figures, their theories and their impact, Shepherd provides a fresh approach to figures including Erving Goffman and Richard Schechner and ideas such as radical art practice, performance studies, radical scenarism and performativity. Essential reading for students, scholars and enthusiasts, this engaging account travels from universities into the streets and back again to examine performance in the context of political activists and teachers, countercultural experiments and feminist challenges, and ceremonies and demonstrations.
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Introduction to Linear and Matrix Algebra
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra. Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, “Extra Topic” sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software.Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author’s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.
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Introduction to the Theory of Point Processes
This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.
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Introduction to SNG and ENG Microwave
An excellent primer on the subject, this book gives beginning professionals in satellite newsgathering an introduction to the technologies and processes involved. It will also suit journalists, editors and producers needing to understand this important element of the newsgathering chain. Written for the complete beginner, the book shows how typical transmission chains work and their communication with the studio. It also offers a brief introduction to analogue and digital theory before going onto to explain Electronic Newsgathering (ENG) systems: from basic principles: transmission and reception chains, frequencies used and why, through to audio channel, subcarriers and digital modulation, as well as applications: radio cameras, window links, infra-red & laser links.A brief chapter on satellite theory gives an overview of satellite communication and orbits, basic satellite communication theory, transportables (`flyaways') and trucks, as well as analogue vs digital issues, digital compression and MPEG. Systems regulations and operations are also introduced as well as safety and logistics issues.If you're looking for a quick and easy introduction to the subject, this book will act as an essential on the job reference guide.
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Analysis On Fock Spaces And Mathematical Theory Of Quantum Fields: An Introduction To Mathematical Analysis Of Quantum Fields
This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation relations and canonical anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and a short description to each model is given.To graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory, this book is a good introductory text. It is also well suited for self-study and will provide readers a firm foundation of knowledge and mathematical techniques for reading more advanced books and current research articles in the field of mathematical analysis on quantum fields. Also, numerous problems are added to aid readers to develop a deeper understanding of the field.
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Introduction to Probability
An essential guide to the concepts of probability theory that puts the focus on models and applications Introduction to Probability offers an authoritative text that presents the main ideas and concepts, as well as the theoretical background, models, and applications of probability. The authors—noted experts in the field—include a review of problems where probabilistic models naturally arise, and discuss the methodology to tackle these problems.A wide-range of topics are covered that include the concepts of probability and conditional probability, univariate discrete distributions, univariate continuous distributions, along with a detailed presentation of the most important probability distributions used in practice, with their main properties and applications. Designed as a useful guide, the text contains theory of probability, de finitions, charts, examples with solutions, illustrations, self-assessment exercises, computational exercises, problems and a glossary. This important text:• Includes classroom-tested problems and solutions to probability exercises • Highlights real-world exercises designed to make clear the concepts presented • Uses Mathematica software to illustrate the text’s computer exercises • Features applications representing worldwide situations and processes • Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress. Written for students majoring in statistics, engineering, operations research, computer science, physics, and mathematics, Introduction to Probability: Models and Applications is an accessible text that explores the basic concepts of probability and includes detailed information on models and applications.
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Introduction to Probability and Statistics
A well-balanced introduction to probability theory and mathematical statistics Featuring updated material, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided intothree parts, the Third Edition begins by presenting the fundamentals and foundationsof probability. The second part addresses statistical inference, and the remainingchapters focus on special topics. An Introduction to Probability and Statistics, Third Edition includes: A new section on regression analysis to include multiple regression, logistic regression, and Poisson regressionA reorganized chapter on large sample theory to emphasize the growing role of asymptotic statisticsAdditional topical coverage on bootstrapping, estimation procedures, and resamplingDiscussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervalsOver 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarksNumerous figures to further illustrate examples and proofs throughout An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.
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Introduction to Wavelets Through Linear Algebra
Wavelet theory is on the boundary between mathematics and engineering, making it ideal for demonstrating to students that mathematics research is thriving in the modern day. Students can see non-trivial mathematics ideas leading to natural and important applications, such as video compression and the numerical solution of differential equations. The only prerequisites assumed are a basic linear algebra background and a bit of analysis background. Intended to be as elementary an introduction to wavelet theory as possible, the text does not claim to be a thorough or authoritative reference on wavelet theory.
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Introduction to Analysis
The third edition of this widely popular textbook is authored by a master teacher. This book provides a mathematically rigorous introduction to analysis of realvalued functions of one variable. This intuitive, student-friendly text is written in a manner that will help to ease the transition from primarily computational to primarily theoretical mathematics. The material is presented clearly and as intuitive as possible while maintaining mathematical integrity. The author supplies the ideas of the proof and leaves the write-up as an exercise. The text also states why a step in a proof is the reasonable thing to do and which techniques are recurrent.Examples, while no substitute for a proof, are a valuable tool in helping to develop intuition and are an important feature of this text. Examples can also provide a vivid reminder that what one hopes might be true is not always true. Features of the Third Edition: Begins with a discussion of the axioms of the real number system. The limit is introduced via sequences. Examples motivate what is to come, highlight the need for hypothesis in a theorem, and make abstract ideas more concrete. A new section on the Cantor set and the Cantor function. Additional material on connectedness. Exercises range in difficulty from the routine "getting your feet wet" types of problems to the moderately challenging problems. Topology of the real number system is developed to obtain the familiar properties of continuous functions. Some exercises are devoted to the construction of counterexamples. The author presents the material to make the subject understandable and perhaps exciting to those who are beginning their study of abstract mathematics.Table of ContentsPrefaceIntroduction The Real Number System Sequences of Real Numbers Topology of the Real Numbers Continuous Functions Differentiation Integration Series of Real Numbers Sequences and Series of Functions Fourier SeriesBibliographyHints and Answers to Selected ExercisesIndexBiographyJames R. Kirkwood holds a Ph.D. from University of Virginia. He has authored fifteen, published mathematics textbooks on various topics including calculus, real analysis, mathematical biology and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer, he teaches real analysis to entering graduate students at the University of Virginia. He has been awarded several National Science Foundation grants. His texts, Elementary Linear Algebra, Linear Algebra, and Markov Processes, are also published by CRC Press.
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Introduction To Modern Physics: Theoretical Foundations
Our understanding of the physical world was revolutionized in the twentieth century — the era of “modern physics''. This book, aimed at the very best students, presents the foundations and frontiers of today's physics. It focuses on the following topics: quantum mechanics; applications in atomic, nuclear, particle, and condensed-matter physics; special relativity; relativistic quantum mechanics, including the Dirac equation and Feynman diagrams; quantum fields; and general relativity. The aim is to cover these topics in sufficient depth such that things “make sense'' to students and they can achieve an elementary working knowledge of them. Many problems are included, a great number of which take dedicated readers just as far as they want to go in modern physics. Although the book is designed so that one can, in principle, read and follow the text without doing any of the problems, the reader is urged to attempt as many of them as possible. Several appendices help bring the reader up to speed on any additional required mathematics. With very few exceptions, the reader should then find the text, together with the appendices and problems, to be self-contained.
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Introduction to Hamiltonian Fluid Dynamics and Stability Theory
Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and Stability Theory does just that-offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism.The author uses the example of the nonlinear pendulum-giving a thorough linear and nonlinear stability analysis of its equilibrium solutions-to introduce many of the ideas associated with the mathematical argument required in infinite dimensional Hamiltonian theory needed for fluid mechanics. He examines Andrews' Theorem, derives and develops the Charney-Hasegawa-Mima (CMH) equation, presents an account of the Hamiltonian structure of the Korteweg-de Vries (KdV) equation, and discusses the stability theory associated with the KdV soliton.The book's tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book.
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Introduction to Socio-Finance
This introductory text is devoted to exposing the underlying nature of price formation in financial markets as a predominantly sociological phenomenon that relates individual decision-making to emergent and co-evolving social and financial structures.Two different levels of this sociological influence are considered: First, we examine how price formation results from the social dynamics of interacting individuals, where interaction occurs either through the price or by direct communication. Then the same processes are revisited and examined at the level of larger groups of individuals.In this book, models of both levels of socio-finance are presented, and it is shown, in particular, how complexity theory provides the conceptual and methodological tools needed to understand and describe such phenomena. Accordingly, readers are first given a broad introduction to the standard economic theory of rational financial markets and will come to understand its shortcomings with the help of concrete examples. Complexity theory is then introduced in order to properly account for behavioral decision-making and match the observed market dynamics.This book is conceived as a primer for newcomers to the field, as well as for practitioners seeking new insights into the field of complexity science applied to socio-economic systems in general, and financial markets and price formation in particular.
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Introduction to the Confinement Problem
This book addresses the confinement problem, which concerns the behavior of non-abelian gauge theories, and the force which is mediated by gauge fields, at large distances. The word “confinement” in the context of hadronic physics originally referred to the fact that quarks and gluons appear to be trapped inside mesons and baryons, from which they cannot escape. There are other, and possibly deeper meanings that can be attached to the term, and these will be explored in this book. Although the confinement problem is far from solved, much is now known about the general features of the confining force, and there are a number of very well motivated theories of confinement which are under active investigation. This volume gives a both pedagogical and concise introduction and overview of the main ideas in this field, their attractive features, and, as appropriate, their shortcomings. This second edition summarizes some of the developments in this area which have occurred since the first edition of this book appeared in 2011. These include new results in the caloron/dyon picture of confinement, in functional approaches, and in studies of the Yang-Mills vacuum wave functional. Special attention, in two new chapters, is given to recent numerical investigations of the center vortex theory, and to the varieties of confinement which may exist in gauge-Higgs theories.Reviews of the first edition:“This is indeed a very good book. I enjoyed reading it and… I learned a lot from it.… It is definitely a research book that provides readers with a guide to the most updated confinement models.” (Giuseppe Nardelli, Mathematical Reviews, Issue 2012 d)“The book is beautifully produced with special emphasis on the relevance of center symmetry and lattice formulation as well as an introduction to current research on confinement.” (Paninjukunnath Achuthan, Zentralblatt MATH, Vol. 1217, 2011)
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Introduction to Theory-Driven Program Evaluation
Introduction to Theory-Driven Program Evaluation provides a clear guide for practicing evaluation science, and numerous examples of how these evaluations actually unfold in contemporary practice. A special emphasis is placed how to conduct theory-driven program evaluations that are culturally responsive and strengths-focused.In this thoroughly revised new edition, author Stewart I. Donaldson provides a state-of-the art treatment of the basics of conducting theory-driven program evaluations. Each case follows a three-step model: developing program impact theory; formulating and prioritizing evaluation questions; and answering evaluation questions. The initial chapters discuss the evolution and popularity of theory-driven program evaluation, as well as step-by-step guide for culturally responsive and strengths-focused applications. Succeeding chapters provide actual cases and discuss the practical implications of theory-driven evaluation science. Reflections, challenges, and lessons learned across numerous cases from practices are discussed.The volume is of significant value to practicing evaluators, professors of introductory evaluation courses and their students, advanced undergraduate and graduate students, and serves as a text or a supplementary text for a wide range of evaluation and applied research courses. It is also of great interest to those interested in the connections between work and health, well-being, career development, human service organizations, and organizational improvement and effectiveness.
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Introduction to Complex Analysis
Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. "Introduction to Complex Analysis" was first published in 1985, and for this second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter.
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Introduction to Architecture
A survey of the built environment distills the work of legendary author and illustrator Francis D. K. Ching into a single volume Introduction to Architecture presents the essential texts and drawings of Francis D. K. Ching for those new to architecture and design. With his typical highly graphic approach, this is the first introductory text from Ching that surveys the design of spaces, buildings, and cities. In an easy to understand format, readers will explore the histories and theories of architecture, design elements and process, and the technical aspects of the contemporary profession of architecture. The book explains the experience and practice of architecture and allied disciplines for future professionals, while those who love the beauty of architecture drawing will delight in the gorgeous illustrations included. Overview of the issues and practices of architecture in an all-in-one introductory textIncludes new chapters and introductory essays by James Eckler, and features more than 1,000 drawings throughoutProfessor Ching is the bestselling author of numerous books on architecture and design, all published by Wiley; his works have been translated into 16 languages and are regarded as classics for their renowned graphical presentation For those pursuing a career in architecture or anyone who loves architectural design and drawing, Introduction to Architecture presents a beautifully illustrated and comprehensive guide to the subject.
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Radical Approach to Lebesgue's Theory of Integration
Meant for advanced undergraduate and graduate students in mathematics, this lively introduction to measure theory and Lebesgue integration is rooted in and motivated by the historical questions that led to its development. The author stresses the original purpose of the definitions and theorems and highlights some of the difficulties that were encountered as these ideas were refined. The story begins with Riemann's definition of the integral, a definition created so that he could understand how broadly one could define a function and yet have it be integrable. The reader then follows the efforts of many mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work in the late 19th and early 20th centuries of Jordan, Borel, and Lebesgue, who finally broke with Riemann's definition. Ushering in a new way of understanding integration, they opened the door to fresh and productive approaches to many of the previously intractable problems of analysis.
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Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems
Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems. The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.
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Introduction to Ontology
In this engaging and wide-ranging new book, Nikk Effingham provides an introduction to contemporary ontology - the study of what exists - and its importance for philosophy today. He covers the key topics in the field, from the ontology of holes, numbers and possible worlds, to space, time and the ontology of material objects - for instance, whether there are composite objects such as tables, chairs or even you and me. While starting from the basics, every chapter is up-to-date with the most recent developments in the field, introducing both longstanding theories and cutting-edge advances. As well as discussing the latest issues in ontology, Effingham also helpfully deals in-depth with different methodological principles (including theory choice, Quinean ontological commitment and Meinongianism) and introduces them alongside an example ontological theory that puts them into practice. This accessible and comprehensive introduction will be essential reading for upper-level undergraduate and post-graduate students, as well as any reader interested in the present state of the subject.
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Gentle Introduction To Knots, Links And Braids, A
The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
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Introduction to Multimodal Analysis
Introduction to Multimodal Analysis is a unique and accessible textbook that critically explains this ground-breaking approach to visual analysis. Now thoroughly revised and updated, the second edition reflects the most recent developments in theory and shifts in communication, outlining the tools for analysis and providing a clear model that students can follow. Chapters on colour, typography, framing and composition contain fresh, contemporary examples, ranging from product packaging and website layouts to film adverts and public spaces, showing how design elements make up a visual language that is used to communicate with the viewer. The book also includes two new chapters on texture and diagrams, as well as a helpful image index so students can clearly understand how images and multimodal texts can be analysed from different perspectives.Featuring chapter summaries, student activities and a companion website hosting all images in full colour, this new edition remains an essential guide for students studying multimodality within visual communication in linguistics, media and cultural studies, critical discourse analysis or journalism studies.
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Introduction to Holomorphic Functions of Several Variables, Volume I
Introduction to Holomorphlc Functions of SeveralVariables, Volumes 1-111 provide an extensiveintroduction to the Oka-Cartan theory of holomorphicfunctions of several variables and holomorphicvarieties. Each volume covers a different aspect andcan be read independently.
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Introduction To Evolutionary Informatics
Science has made great strides in modeling space, time, mass and energy. Yet little attention has been paid to the precise representation of the information ubiquitous in nature.Introduction to Evolutionary Informatics fuses results from complexity modeling and information theory that allow both meaning and design difficulty in nature to be measured in bits. Built on the foundation of a series of peer-reviewed papers published by the authors, the book is written at a level easily understandable to readers with knowledge of rudimentary high school math. Those seeking a quick first read or those not interested in mathematical detail can skip marked sections in the monograph and still experience the impact of this new and exciting model of nature's information.This book is written for enthusiasts in science, engineering and mathematics interested in understanding the essential role of information in closely examined evolution theory.
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Introduction to Statistical Mechanics and Thermodynamics
This text presents the two complementary aspects of thermal physics as an integrated theory of the properties of matter. Conceptual understanding is promoted by thorough development of basic concepts. In contrast to many texts, statistical mechanics, including discussion of the required probability theory, is presented first. This provides a statistical foundation for the concept of entropy, which is central to thermal physics. A unique feature of the book is thedevelopment of entropy based on Boltzmann's 1877 definition; this avoids contradictions or ad hoc corrections found in other texts. Detailed fundamentals provide a natural grounding for advanced topics, such as black-body radiation and quantum gases. An extensive set of problems (solutions areavailable for lecturers through the OUP website), many including explicit computations, advance the core content by probing essential concepts. The text is designed for a two-semester undergraduate course but can be adapted for one-semester courses emphasizing either aspect of thermal physics. It is also suitable for graduate study.
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Introduction to Electromagnetic Theory and the Physics of Conducting Solids
This book consists of two parts. Part A (Chapters 1-3) is an introduction to the physics of conducting solids, while Part B (Chapters 4-10) is an introduction to the theory of electromagnetic fields and waves. The book is intended to introduce the student to classical electrodynamics and, at the same time, to explain in simple terms the quantum theory of conducting substances – in particular, the solid ones. Excessive mathematical proof is avoided as much as possible, in favor of pedagogical efficiency at an introductory level. The theory of vector fields is briefly discussed in a separate chapter, helping the student cope with the mathematical challenges of Maxwell's theory. The book serves as a primary source for a sophomore-level electromagnetics course in an electronics-oriented engineering program, but it can also be used as a secondary (tutorial) source for an intermediate-level course in electrodynamics for physicists and engineers. The content is based on the author’s lecture notes for his sophomore-level Physics course at the Hellenic Naval Academy.
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Introduction to the Theory of Games
Game theory, defined in the broadest sense, is a collection of mathematical models designed for the analysis of strategic aspects of situations of conflict and cooperation in a broad spectrum of fields including economics, politics, biology, engineering, and operations research. This book, besides covering the classical results of game theory, places special emphasis on methods of determining `solutions' of various game models. Generalizations reaching beyond the `convexity paradigm' and leading to nonconvex optimization problems are enhanced and discussed in more detail than in standard texts on this subject. The development is theoretical-mathematical interspersed with elucidating interpretations and examples. Audience: The material in the book is accessible to PhD and graduate students and will also be of interest to researchers. Solid knowledge of standard undergraduate mathematics is required to read the book.
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Introduction to the Semantics of Law
This book offers an introduction to the language of law from the perspective of logical semantics. As a logical tool, Boguslaw Wolniewicz’s formal ontology of situations is adapted. The central issue addressed is the meaning of normative statements, primarily legal norms. The main outcome of the book consists in explications of several legal notions (including legal events, legal acts and legal rules) in terms of the formal ontology of situations. In addition, the book concludes that legal norms are sentences in a logical sense, so some are true, while others are false, and that their logical value does not depend on whether or not they were adopted in the law-making process. Lastly, the book contends that there are semantic relations between orders that are similar to entailment, contradiction, opposition, and sub-opposition, despite the fact that orders are not sentences in a logical sense, i.e., they are neither true nor false.The book also presents some original Wittgenstein-style deontic logics built on the first order logic. The formal results are applied to selected problems in the theory of law, including the problem of the possibility of algorithmic application of legal norms.
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Introduction to Cognitive Behaviour Therapy
This bestselling guide to the basic theory, skills and applications of cognitive behaviour therapy is fully updated to reflect recent developments in CBT theory. It includes in-depth material on working with diversity, and new case studies and exercises to help you reflect and explore how theory can be used to develop effective practice. The Companion Website features over 40 videos illustrating the CBT skills and strategies discussed in the book, including: Measuring CBT’s effectivenessSocratic method and applicationsPhysical techniques and behavioural experimentsApplications of CBT to specific client disordersUsing supervision in CBT.
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Introduction to Mathematical Finance
The purpose of this book is to provide a rigorous yet accessible introduction to the modern financial theory of security markets. The main subjects are derivatives and portfolio management. The book is intended to be used as a text by advanced undergraduates and beginning graduate students. It is also likely to be useful to practicing financial engineers, portfolio manager, and actuaries who wish to acquire a fundamental understanding of financial theory. The book makes heavy use of mathematics, but not at an advanced level. Various mathematical concepts are developed as needed, and computational examples are emphasized.
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Introduction to Homological Algebra, 85
An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author’s attempt to make it lovable. This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and ?; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences. This book will be of interest to practitioners in the field of pure and applied mathematics.
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L2-Invariants: Theory and Applications to Geometry and K-Theory
In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.
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Introduction to Stochastic Calculus for Finance
Although there are many textbooks on stochastic calculus applied to finance, this volume earns its place with a pedagogical approach. The text presents a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader should be familiar with elementary real analysis and basic probability theory.
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Introduction To Stochastic Processes
The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.
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