Математика
Различные книги в жанре МатематикаBeginning Partial Differential Equations
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible, combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger’s equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is organized around four themes: methods of solution for initial-boundary value problems; applications of partial differential equations; existence and properties of solutions; and the use of software to experiment with graphics and carry out computations. With a primary focus on wave and diffusion processes, Beginning Partial Differential Equations, Third Edition also includes: Proofs of theorems incorporated within the topical presentation, such as the existence of a solution for the Dirichlet problem The incorporation of Maple™ to perform computations and experiments Unusual applications, such as Poe’s pendulum Advanced topical coverage of special functions, such as Bessel, Legendre polynomials, and spherical harmonics Fourier and Laplace transform techniques to solve important problems Beginning of Partial Differential Equations, Third Edition is an ideal textbook for upper-undergraduate and first-year graduate-level courses in analysis and applied mathematics, science, and engineering.
Fundamentals of Actuarial Mathematics
Provides a comprehensive coverage of both the deterministic and stochastic models of life contingencies, risk theory, credibility theory, multi-state models, and an introduction to modern mathematical finance. New edition restructures the material to fit into modern computational methods and provides several spreadsheet examples throughout. Covers the syllabus for the Institute of Actuaries subject CT5, Contingencies Includes new chapters covering stochastic investments returns, universal life insurance. Elements of option pricing and the Black-Scholes formula will be introduced.
Probability and Stochastic Processes
A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book’s primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes. Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes: Multiple examples from disciplines such as business, mathematical finance, and engineering Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material A rigorous treatment of all probability and stochastic processes concepts An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.
The Intelligent Enterprise in the Era of Big Data
“ … the enterprise of today has changed … wherever you sit in this new corporation … Srinivasan gives us a practical and provocative guide for rethinking our business process … calling us all to action around rapid development of our old, hierarchical structures into flexible customer centric competitive force …. A must read for today’s business leader.” Mark Nunnelly, Executive Director, MassIT, Commonwealth of Massachusetts and Managing Director, Bain Capital “’Efficiency,’ ‘agile,’ and ‘analytics’ used to be the rage. Venkat Srinivasan explains in this provocative book why organizations can no longer afford to stop there. They need to move beyond – to be ‘intelligent.’ It isn’t just theory. He’s done it.” Bharat Anand, Henry R. Byers Professor of Business Administration, Harvard Business School In the era of big data and automation, the book presents a cutting-edge approach to how enterprises should organize and function. Striking a practical balance between theory and practice, The Intelligent Enterprise in the Era of Big Data presents the enterprise architecture that identifies the power of the emerging technology environment. Beginning with an introduction to the key challenges that enterprises face, the book systematically outlines modern enterprise architecture through a detailed discussion of the inseparable elements of such architecture: efficiency, flexibility, and intelligence. This architecture enables rapid responses to market needs by sensing important developments in internal and external environments in real time. Illustrating all of these elements in an integrated fashion, The Intelligent Enterprise in the Era of Big Data also features: • A detailed discussion on issues of time-to-market and flexibility with respect to enterprise application technology • Novel analyses illustrated through extensive real-world case studies to help readers better understand the applicability of the architecture and concepts • Various applications of natural language processing to real-world business transactions • Practical approaches for designing and building intelligent enterprises The Intelligent Enterprise in the Era of Big Data is an appropriate reference for business executives, information technology professionals, data scientists, and management consultants. The book is also an excellent supplementary textbook for upper-undergraduate and graduate-level courses in business intelligence, data mining, big data, and business process automation. “a compelling vision of the next generation of organization—the intelligent enterprise—which will leverage not just big data but also unstructured text and artificial intelligence to optimize internal processes in real time … a must-read book for CEOs and CTOs in all industries.” Ravi Ramamurti, D”Amore-McKim Distinguished Professor of International Business and Strategy, and Director, Center for Emerging Markets, Northeastern University “It is about the brave new world that narrows the gap between technology and business …. The book has practical advice from a thoughtful practitioner. Intelligent automation will be a competitive strength in the future. Will your company be ready?” Victor J. Menezes, Retired Senior Vice Chairman, Citigroup Venkat Srinivasan, PhD, is Chairman and Chief Executive Officer of RAGE Frameworks, Inc., which supports the creation of intelligent business process automation solutions and cognitive intelligence solutions for global corporations. He is an entrepreneur and holds several patents in the area of knowledge-based technology architectures. He is t
Matrix Algebra for Linear Models
A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data. Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.
Computational Approaches to Studying the Co-evolution of Networks and Behavior in Social Dilemmas
Computational Approaches to Studying the Co-evolution of Networks and Behaviour in Social Dilemmas shows students, researchers, and professionals how to use computation methods, rather than mathematical analysis, to answer research questions for an easier, more productive method of testing their models. Illustrations of general methodology are provided and explore how computer simulation is used to bridge the gap between formal theoretical models and empirical applications.
Introduction to Stochastic Processes with R
An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: More than 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion web site that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.
Basic Data Analysis for Time Series with R
Written at a readily accessible level, Basic Data Analysis for Time Series with R emphasizes the mathematical importance of collaborative analysis of data used to collect increments of time or space. Balancing a theoretical and practical approach to analyzing data within the context of serial correlation, the book presents a coherent and systematic regression-based approach to model selection. The book illustrates these principles of model selection and model building through the use of information criteria, cross validation, hypothesis tests, and confidence intervals. Focusing on frequency- and time-domain and trigonometric regression as the primary themes, the book also includes modern topical coverage on Fourier series and Akaike's Information Criterion (AIC). In addition, Basic Data Analysis for Time Series with R also features: Real-world examples to provide readers with practical hands-on experience Multiple R software subroutines employed with graphical displays Numerous exercise sets intended to support readers understanding of the core concepts Specific chapters devoted to the analysis of the Wolf sunspot number data and the Vostok ice core data sets
A First Course in Mathematical Logic and Set Theory
A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Multivariate Nonparametric Regression and Visualization. With R and Applications to Finance
A modern approach to statistical learning and its applications through visualization methods With a unique and innovative presentation, Multivariate Nonparametric Regression and Visualization provides readers with the core statistical concepts to obtain complete and accurate predictions when given a set of data. Focusing on nonparametric methods to adapt to the multiple types of data generating mechanisms, the book begins with an overview of classification and regression. The book then introduces and examines various tested and proven visualization techniques for learning samples and functions. Multivariate Nonparametric Regression and Visualization identifies risk management, portfolio selection, and option pricing as the main areas in which statistical methods may be implemented in quantitative finance. The book provides coverage of key statistical areas including linear methods, kernel methods, additive models and trees, boosting, support vector machines, and nearest neighbor methods. Exploring the additional applications of nonparametric and semiparametric methods, Multivariate Nonparametric Regression and Visualization features: An extensive appendix with R-package training material to encourage duplication and modification of the presented computations and research Multiple examples to demonstrate the applications in the field of finance Sections with formal definitions of the various applied methods for readers to utilize throughout the book Multivariate Nonparametric Regression and Visualization is an ideal textbook for upper-undergraduate and graduate-level courses on nonparametric function estimation, advanced topics in statistics, and quantitative finance. The book is also an excellent reference for practitioners who apply statistical methods in quantitative finance.