Introduction to the Theory of Distributions

Author: Friedrich Gerard Friedlander,Mark Suresh Joshi

Publisher: Cambridge University Press

ISBN: 9780521649711

Category: Mathematics

Page: 175

View: 9244

The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book, first published in 1999, adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces.


Theory and Applications

Author: J.J. Duistermaat,Johan A.C. Kolk

Publisher: Springer Science & Business Media

ISBN: 9780817646752

Category: Mathematics

Page: 445

View: 661

This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.

An Introduction to Heavy-Tailed and Subexponential Distributions

Author: Sergey Foss,Dmitry Korshunov,Stan Zachary

Publisher: Springer Science & Business Media

ISBN: 146147101X

Category: Mathematics

Page: 157

View: 6314

Heavy-tailed probability distributions are an important component in the modeling of many stochastic systems. They are frequently used to accurately model inputs and outputs of computer and data networks and service facilities such as call centers. They are an essential for describing risk processes in finance and also for insurance premia pricing, and such distributions occur naturally in models of epidemiological spread. The class includes distributions with power law tails such as the Pareto, as well as the lognormal and certain Weibull distributions. One of the highlights of this new edition is that it includes problems at the end of each chapter. Chapter 5 is also updated to include interesting applications to queueing theory, risk, and branching processes. New results are presented in a simple, coherent and systematic way. Graduate students as well as modelers in the fields of finance, insurance, network science and environmental studies will find this book to be an essential reference.

Theory of Distributions

Author: Svetlin G. Georgiev

Publisher: Springer

ISBN: 3319195271

Category: Mathematics

Page: 218

View: 9031

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

A First Look at Rigorous Probability Theory

Second Edition

Author: Jeffrey S Rosenthal

Publisher: World Scientific Publishing Company

ISBN: 9813101652

Category: Mathematics

Page: 236

View: 7458

Solutions Manual for Free Download This textbook is an introduction to probability theory using measure theory. It is designed for graduate students in a variety of fields (mathematics, statistics, economics, management, finance, computer science, and engineering) who require a working knowledge of probability theory that is mathematically precise, but without excessive technicalities. The text provides complete proofs of all the essential introductory results. Nevertheless, the treatment is focused and accessible, with the measure theory and mathematical details presented in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects. In this new edition, many exercises and small additional topics have been added and existing ones expanded. The text strikes an appropriate balance, rigorously developing probability theory while avoiding unnecessary detail.

Probability-Based Structural Fire Load

Author: Leo Razdolsky

Publisher: Cambridge University Press

ISBN: 110703874X

Category: Mathematics

Page: 375

View: 2737

This book introduces the subject of probabilistic analysis to engineers and can be used as a reference in applying this technology.

An Introduction to Probability and Mathematical Statistics

Author: Howard G. Tucker

Publisher: Academic Press

ISBN: 1483225143

Category: Mathematics

Page: 240

View: 4979

An Introduction to Probability and Mathematical Statistics provides information pertinent to the fundamental aspects of probability and mathematical statistics. This book covers a variety of topics, including random variables, probability distributions, discrete distributions, and point estimation. Organized into 13 chapters, this book begins with an overview of the definition of function. This text then examines the notion of conditional or relative probability. Other chapters consider Cochran's theorem, which is of extreme importance in that part of statistical inference known as analysis of variance. This book discusses as well the fundamental principles of testing statistical hypotheses by providing the reader with an idea of the basic problem and its relation to practice. The final chapter deals with the problem of estimation and the Neyman theory of confidence intervals. This book is a valuable resource for undergraduate university students who are majoring in mathematics. Students who are majoring in physics and who are inclined toward abstract mathematics will also find this book useful.

Introduction to the Theory of Computation

Author: Michael Sipser

Publisher: Cengage Learning

ISBN: 1285401069

Category: Computers

Page: 504

View: 2105

Now you can clearly present even the most complex computational theory topics to your students with Sipser's distinct, market-leading INTRODUCTION TO THE THEORY OF COMPUTATION, 3E. The number one choice for today's computational theory course, this highly anticipated revision retains the unmatched clarity and thorough coverage that make it a leading text for upper-level undergraduate and introductory graduate students. This edition continues author Michael Sipser's well-known, approachable style with timely revisions, additional exercises, and more memorable examples in key areas. A new first-of-its-kind theoretical treatment of deterministic context-free languages is ideal for a better understanding of parsing and LR(k) grammars. This edition's refined presentation ensures a trusted accuracy and clarity that make the challenging study of computational theory accessible and intuitive to students while maintaining the subject's rigor and formalism. Readers gain a solid understanding of the fundamental mathematical properties of computer hardware, software, and applications with a blend of practical and philosophical coverage and mathematical treatments, including advanced theorems and proofs. INTRODUCTION TO THE THEORY OF COMPUTATION, 3E's comprehensive coverage makes this an ideal ongoing reference tool for those studying theoretical computing. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

The Theory of Algebraic Numbers

Author: Harry Pollard,Harold G. Diamond

Publisher: Courier Corporation

ISBN: 0486154378

Category: Mathematics

Page: 192

View: 2433

Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 edition.


Author: Willliam Feller

Publisher: John Wiley & Sons

ISBN: 9788126518067


Page: 700

View: 7426

· The Exponential and the Uniform Densities· Special Densities. Randomization· Densities in Higher Dimensions. Normal Densities and Processes· Probability Measures and Spaces· Probability Distributions in Rr· A Survey of Some Important Distributions and Processes· Laws of Large Numbers. Applications in Analysis· The Basic Limit Theorems· Infinitely Divisible Distributions and Semi-Groups· Markov Processes and Semi-Groups· Renewal Theory· Random Walks in R1· Laplace Transforms. Tauberian Theorems. Resolvents· Applications of Laplace Transforms· Characteristic Functions· Expansions Related to the Central Limit Theorem,· Infinitely Divisible Distributions· Applications of Fourier Methods to Random Walks· Harmonic Analysis
Language Arts & Disciplines

The History and Theory of Rhetoric

An Introduction

Author: James A. Herrick

Publisher: Routledge

ISBN: 1315404125

Category: Language Arts & Disciplines

Page: 330

View: 2364

By tracing the traditional progression of rhetoric from the Greek Sophists to contemporary theorists, The History and Theory of Rhetoric illustrates how persuasive public discourse performs essential social functions and shapes our daily worlds. Students gain a conceptual framework for evaluating and practicing persuasive writing and speaking in a wide range of settings and in both written and visual media. This new 6th edition includes greater attention to non-Western studies, as well as contemporary developments such as the rhetoric of science, feminist rhetoric, the rhetoric of display, and comparative rhetoric. Known for its clear writing style and contemporary examples throughout, The History and Theory of Rhetoric emphasizes the relevance of rhetoric to today’s students.

Molecular Electronics

An Introduction to Theory and Experiment

Author: Juan Carlos Cuevas,Elke Scheer

Publisher: World Scientific

ISBN: 9814282588

Category: Science

Page: 703

View: 1006

This book provides a comprehensive overview of the rapidly developing field of molecular electronics. It focuses on our present understanding of the electrical conduction in single-molecule circuits and provides a thorough introduction to the experimental techniques and theoretical concepts. It will also constitute as the first textbook-like introduction to both the experiment and theory of electronic transport through single atoms and molecules. In this sense, this publication will prove invaluable to both researchers and students interested in the field of nanoelectronics and nanoscience in general. Molecular Electronics is self-contained and unified in its presentation. It may be used as a textbook on nanoelectronics by graduate students and advanced undergraduates studying physics and chemistry. In addition, included are previously unpublished material that will help researchers gain a deeper understanding into the basic concepts involved in the field of molecular electronics.

An Introduction to Probability and Statistics

Author: Vijay K. Rohatgi,A.K. Md. Ehsanes Saleh

Publisher: John Wiley & Sons

ISBN: 1118799658

Category: Mathematics

Page: 728

View: 8375

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 regression A reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics Additional topical coverage on bootstrapping, estimation procedures, and resampling Discussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals Over 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarks Numerous 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.

Introduction to Seismology

Author: Peter M. Shearer

Publisher: Cambridge University Press

ISBN: 1139478753

Category: Science

Page: N.A

View: 2744

This book provides an approachable and concise introduction to seismic theory, designed as a first course for undergraduate students. It clearly explains the fundamental concepts, emphasizing intuitive understanding over lengthy derivations. Incorporating over 30% new material, this second edition includes all the topics needed for a one-semester course in seismology. Additional material has been added throughout including numerical methods, 3-D ray tracing, earthquake location, attenuation, normal modes, and receiver functions. The chapter on earthquakes and source theory has been extensively revised and enlarged, and now includes details on non-double-couple sources, earthquake scaling, radiated energy, and finite slip inversions. Each chapter includes worked problems and detailed exercises that give students the opportunity to apply the techniques they have learned to compute results of interest and to illustrate the Earth's seismic properties. Computer subroutines and datasets for use in the exercises are available at
Political Science

Theories of Violent Conflict

An Introduction

Author: Jolle Demmers

Publisher: Routledge

ISBN: 1317502752

Category: Political Science

Page: 166

View: 9858

This revised and updated second edition introduces students of violent conflict to a variety of prominent theoretical approaches, and examines the ontological stances and epistemological traditions underlying these approaches. Theories of Violent Conflict takes the centrality of the ‘group’ as an actor in contemporary conflict as a point of departure, leaving us with three main questions: • What makes a group? • Why and how does a group resort to violence? • Why and how do or don’t they stop? The book examines and compares the ways by which these questions are addressed from a number of perspectives: primordialism/constructivism, social identity theory, critical political economy, human needs theory, relative deprivation theory, collective action theory and rational choice theory. The final chapter aims to synthesize structure and agency-based theories by proposing a critical discourse analysis of violent conflict. With new material on violence, religion, extremism and military urbanism, this book will be essential reading for students of war and conflict studies, peace studies, conflict analysis and conflict resolution, and ethnic conflict, as well as security studies and IR in general.
Technology & Engineering

Theory of Vibration

An Introduction

Author: A.A. Shabana

Publisher: Springer Science & Business Media

ISBN: 9780387945248

Category: Technology & Engineering

Page: 350

View: 8628

The aim of this book is to impart a sound understanding, both physical and mathematical, of the fundamental theory of vibration and its applications. The book presents in a simple and systematic manner techniques that can easily be applied to the analysis of vibration of mechanical and structural systems. Unlike other texts on vibrations, the approach is general, based on the conservation of energy and Lagrangian dynamics, and develops specific techniques from these foundations in clearly understandable stages. Suitable for a one-semester course on vibrations, the book presents new concepts in simple terms and explains procedures for solving problems in considerable detail.

Introduction to Coding Theory, Second Edition

Author: Jurgen Bierbrauer

Publisher: CRC Press

ISBN: 148229981X

Category: Computers

Page: 538

View: 3945

This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.

Security Engineering

A Guide to Building Dependable Distributed Systems

Author: Ross J. Anderson

Publisher: John Wiley & Sons

ISBN: 1118008367

Category: Computers

Page: 1080

View: 7050

The world has changed radically since the first edition of this book was published in 2001. Spammers, virus writers, phishermen, money launderers, and spies now trade busily with each other in a lively online criminal economy and as they specialize, they get better. In this indispensable, fully updated guide, Ross Anderson reveals how to build systems that stay dependable whether faced with error or malice. Here?s straight talk on critical topics such as technical engineering basics, types of attack, specialized protection mechanisms, security psychology, policy, and more.
Mathematical statistics

Foundations and Applications of Statistics: An Introduction Using R , Second Edition

Author: Randall Pruim

Publisher: American Mathematical Soc.

ISBN: 1470428482

Category: Mathematical statistics

Page: 820

View: 5512

Foundations and Applications of Statistics simultaneously emphasizes both the foundational and the computational aspects of modern statistics. Engaging and accessible, this book is useful to undergraduate students with a wide range of backgrounds and career goals. The exposition immediately begins with statistics, presenting concepts and results from probability along the way. Hypothesis testing is introduced very early, and the motivation for several probability distributions comes from p-value computations. Pruim develops the students' practical statistical reasoning through explicit examples and through numerical and graphical summaries of data that allow intuitive inferences before introducing the formal machinery. The topics have been selected to reflect the current practice in statistics, where computation is an indispensible tool. In this vein, the statistical computing environment R is used throughout the text and is integral to the exposition. Attention is paid to developing students' mathematical and computational skills as well as their statistical reasoning. Linear models, such as regression and ANOVA, are treated with explicit reference to the underlying linear algebra, which is motivated geometrically. Foundations and Applications of Statistics discusses both the mathematical theory underlying statistics and practical applications that make it a powerful tool across disciplines. The book contains ample material for a two-semester course in undergraduate probability and statistics. A one-semester course based on the book will cover hypothesis testing and confidence intervals for the most common situations. In the second edition, the R code has been updated throughout to take advantage of new R packages and to illustrate better coding style. New sections have been added covering bootstrap methods, multinomial and multivariate normal distributions, the delta method, numerical methods for Bayesian inference, and nonlinear least squares. Also, the use of matrix algebra has been expanded, but remains optional, providing instructors with more options regarding the amount of linear algebra required.

Probability and Statistics for Computer Scientists, Second Edition

Author: Michael Baron

Publisher: CRC Press

ISBN: 1498760600

Category: Mathematics

Page: 449

View: 9417

Student-Friendly Coverage of Probability, Statistical Methods, Simulation, and Modeling Tools Incorporating feedback from instructors and researchers who used the previous edition, Probability and Statistics for Computer Scientists, Second Edition helps students understand general methods of stochastic modeling, simulation, and data analysis; make optimal decisions under uncertainty; model and evaluate computer systems and networks; and prepare for advanced probability-based courses. Written in a lively style with simple language, this classroom-tested book can now be used in both one- and two-semester courses. New to the Second Edition Axiomatic introduction of probability Expanded coverage of statistical inference, including standard errors of estimates and their estimation, inference about variances, chi-square tests for independence and goodness of fit, nonparametric statistics, and bootstrap More exercises at the end of each chapter Additional MATLAB® codes, particularly new commands of the Statistics Toolbox In-Depth yet Accessible Treatment of Computer Science-Related Topics Starting with the fundamentals of probability, the text takes students through topics heavily featured in modern computer science, computer engineering, software engineering, and associated fields, such as computer simulations, Monte Carlo methods, stochastic processes, Markov chains, queuing theory, statistical inference, and regression. It also meets the requirements of the Accreditation Board for Engineering and Technology (ABET). Encourages Practical Implementation of Skills Using simple MATLAB commands (easily translatable to other computer languages), the book provides short programs for implementing the methods of probability and statistics as well as for visualizing randomness, the behavior of random variables and stochastic processes, convergence results, and Monte Carlo simulations. Preliminary knowledge of MATLAB is not required. Along with numerous computer science applications and worked examples, the text presents interesting facts and paradoxical statements. Each chapter concludes with a short summary and many exercises.