Download or read book Introduction to Probability written by Joseph K. Blitzstein and published by CRC Press. This book was released on 2014-07-24 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2016-08-16 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions.

Download or read book Notes on Introductory Combinatorics written by George Polya and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.

Download or read book Mathematical Models in Biology written by Elizabeth Spencer Allman and published by Cambridge University Press. This book was released on 2004 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.

Download or read book Polymer Solutions written by Iwao Teraoka and published by John Wiley & Sons. This book was released on 2004-04-07 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymer Solutions: An Introduction to Physical Properties offers a fresh, inclusive approach to teaching the fundamentals of physical polymer science. Students, instructors, and professionals in polymer chemistry, analytical chemistry, organic chemistry, engineering, materials, and textiles will find Iwao Teraoka’s text at once accessible and highly detailed in its treatment of the properties of polymers in the solution phase. Teraoka’s purpose in writing Polymer Solutions is twofold: to familiarize the advanced undergraduate and beginning graduate student with basic concepts, theories, models, and experimental techniques for polymer solutions; and to provide a reference for researchers working in the area of polymer solutions as well as those in charge of chromatographic characterization of polymers. The author’s incorporation of recent advances in the instrumentation of size-exclusion chromatography, the method by which polymers are analyzed, renders the text particularly topical. Subjects discussed include: Real, ideal, Gaussian, semirigid, and branched polymer chains Polymer solutions and thermodynamics Static light scattering of a polymer solution Dynamic light scattering and diffusion of polymers Dynamics of dilute and semidilute polymer solutions Study questions at the end of each chapter not only provide students with the opportunity to test their understanding, but also introduce topics relevant to polymer solutions not included in the main text. With over 250 geometrical model diagrams, Polymer Solutions is a necessary reference for students and for scientists pursuing a broader understanding of polymers.

Download or read book Femtosecond Optical Frequency Comb Principle Operation and Applications written by Jun Ye and published by Springer Science & Business Media. This book was released on 2006-06-15 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few years, there has been a convergence between the fields of ultrafast science, nonlinear optics, optical frequency metrology, and precision laser spectroscopy. These fields have been developing largely independently since the birth of the laser, reaching remarkable levels of performance. On the ultrafast frontier, pulses of only a few cycles long have been produced, while in optical spectroscopy, the precision and resolution have reached one part in Although these two achievements appear to be completely disconnected, advances in nonlinear optics provided the essential link between them. The resulting convergence has enabled unprecedented advances in the control of the electric field of the pulses produced by femtosecond mode-locked lasers. The corresponding spectrum consists of a comb of sharp spectral lines with well-defined frequencies. These new techniques and capabilities are generally known as “femtosecond comb technology. ” They have had dramatic impact on the diverse fields of precision measurement and extreme nonlinear optical physics. The historical background for these developments is provided in the Foreword by two of the pioneers of laser spectroscopy, John Hall and Theodor Hänsch. Indeed the developments described in this book were foreshadowed by Hänsch’s early work in the 1970s when he used picosecond pulses to demonstrate the connection between the time and frequency domains in laser spectroscopy. This work complemented the advances in precision laser stabilization developed by Hall.

Download or read book QCA with R written by Adrian Duşa and published by Springer. This book was released on 2018-06-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive guide to qualitative comparative analysis (QCA) using R. Using Boolean algebra to implement principles of comparison used by scholars engaged in the qualitative study of macro social phenomena, QCA acts as a bridge between the quantitative and the qualitative traditions. The QCA package for R, created by the author, facilitates QCA within a graphical user interface. This book provides the most current information on the latest version of the QCA package, which combines written commands with a cross-platform interface. Beginning with a brief introduction to the concept of QCA, this book moves from theory to calibration, from analysis to factorization, and hits on all the key areas of QCA in between. Chapters one through three are introductory, familiarizing the reader with R, the QCA package, and elementary set theory. The next few chapters introduce important applications of the package beginning with calibration, analysis of necessity, analysis of sufficiency, parameters of fit, negation and factorization, and the construction of Venn diagrams. The book concludes with extensions to the classical package, including temporal applications and panel data. Providing a practical introduction to an increasingly important research tool for the social sciences, this book will be indispensable for students, scholars, and practitioners interested in conducting qualitative research in political science, sociology, business and management, and evaluation studies.

Download or read book An Introduction to Ray Tracing written by Andrew S. Glassner and published by Elsevier. This book was released on 1989-06-01 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: The creation of ever more realistic 3-D images is central to the development of computer graphics. The ray tracing technique has become one of the most popular and powerful means by which photo-realistic images can now be created. The simplicity, elegance and ease of implementation makes ray tracing an essential part of understanding and exploiting state-of-the-art computer graphics.An Introduction to Ray Tracing develops from fundamental principles to advanced applications, providing "how-to" procedures as well as a detailed understanding of the scientific foundations of ray tracing. It is also richly illustrated with four-color and black-and-white plates. This is a book which will be welcomed by all concerned with modern computer graphics, image processing, and computer-aided design. - Provides practical "how-to" information - Contains high quality color plates of images created using ray tracing techniques - Progresses from a basic understanding to the advanced science and application of ray tracing

Download or read book Sampling written by Sharon L. Lohr and published by CRC Press. This book was released on 2019-04-08 with total page 923 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition is a reprint of the second edition published by Cengage Learning, Inc. Reprinted with permission. What is the unemployment rate? How many adults have high blood pressure? What is the total area of land planted with soybeans? Sampling: Design and Analysis tells you how to design and analyze surveys to answer these and other questions. This authoritative text, used as a standard reference by numerous survey organizations, teaches sampling using real data sets from social sciences, public opinion research, medicine, public health, economics, agriculture, ecology, and other fields. The book is accessible to students from a wide range of statistical backgrounds. By appropriate choice of sections, it can be used for a graduate class for statistics students or for a class with students from business, sociology, psychology, or biology. Readers should be familiar with concepts from an introductory statistics class including linear regression; optional sections contain the statistical theory, for readers who have studied mathematical statistics. Distinctive features include: More than 450 exercises. In each chapter, Introductory Exercises develop skills, Working with Data Exercises give practice with data from surveys, Working with Theory Exercises allow students to investigate statistical properties of estimators, and Projects and Activities Exercises integrate concepts. A solutions manual is available. An emphasis on survey design. Coverage of simple random, stratified, and cluster sampling; ratio estimation; constructing survey weights; jackknife and bootstrap; nonresponse; chi-squared tests and regression analysis. Graphing data from surveys. Computer code using SAS® software. Online supplements containing data sets, computer programs, and additional material. Sharon Lohr, the author of Measuring Crime: Behind the Statistics, has published widely about survey sampling and statistical methods for education, public policy, law, and crime. She has been recognized as Fellow of the American Statistical Association, elected member of the International Statistical Institute, and recipient of the Gertrude M. Cox Statistics Award and the Deming Lecturer Award. Formerly Dean’s Distinguished Professor of Statistics at Arizona State University and a Vice President at Westat, she is now a freelance statistical consultant and writer. Visit her website at www.sharonlohr.com.

Download or read book Handbook of Physics written by Walter Benenson and published by Springer Science & Business Media. This book was released on 2006-01-13 with total page 1183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Physics is a veritable toolbox for rapid access to a wealth of physics information for everyday use in problem solving, homework, and examinations. This complete reference includes not only the fundamental formulas of physics but also experimental methods used in practice.

Download or read book Computing the Continuous Discretely written by Matthias Beck and published by Springer. This book was released on 2015-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE

Download or read book Generatingfunctionology written by Herbert S. Wilf and published by Elsevier. This book was released on 2014-05-10 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

Download or read book Algebra Geometry and Software Systems written by Michael Joswig and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

Download or read book Problem Solving Strategies written by Arthur Engel and published by Springer Science & Business Media. This book was released on 2008-01-19 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.