Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.

    Dealing with measure theory and Lebesque integration, this is an introductory graduate text.

    More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you:  Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.

    They are established tools in a wide range of industrial applications, including search engines, DNA sequencing, stock market analysis, and robot locomotion, and their use is spreading rapidly. People who know the methods have their choice of rewarding jobs. This hands-on text opens these opportunities to computer science students with modest mathematical backgrounds. It is designed for final-year undergraduates and master's students with limited background in linear algebra and calculus. Comprehensive and coherent, it develops everything from basic reasoning to advanced techniques within the framework of graphical models. Students learn more than a menu of techniques, they develop analytical and problem-solving skills that equip them for the real world. Numerous examples and exercises, both computer based and theoretical, are included in every chapter. Resources for students and instructors, including a MATLAB toolbox, are available online.

    Reflecting the need for even minor programming in today's model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work.The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation.By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling.Web ResourceThe book is accompanied by an R package (rethinking) that is available on the author's website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

    Changes in the fifth edition include: A new chapter on credit derivatives (Chapter 21). New! Business Snapshots highlight real-world situations and relevant issues. The first six chapters have been -reorganized to better meet the needs of students and .instructors. A new release of the Excel-based software, DerivaGem, is included with each text. A useful Solutions Manual/Study Guide, which includes the worked-out answers to the "Questions and Problems" sections of each chapter, can be purchased separately (ISBN: 0-13-144570-7).

    Increasingly, the decisions that affect our lives--where we go to school, whether we can get a job or a loan, how much we pay for health insurance--are being made not by humans, but by machines. In theory, this should lead to greater fairness: Everyone is judged according to the same rules.But as mathematician and data scientist Cathy O'Neil reveals, the mathematical models being used today are unregulated and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination--propping up the lucky, punishing the downtrodden, and undermining our democracy in the process.

    The new edition includes the most up-to-date research developments and many more examples and problems.

    This text provides a simple and straightforward introduction to econometrics for the beginner. The book is designed to help students understand econometric techniques through extensive examples, careful explanations, and a wide variety of problem material. In each of the editions, I have tried to incorporate major developments in the field in an intuitive and informative way without resort to matrix algebra, calculus, or statistics beyond the introductory level. The fourth edition continues that tradition.

    While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

    With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.Currently available in the Series: Emil ArtinGeometnc Algebra R. W. CarterSimple Groups Of Lie Type Richard CourantDifferential and Integrai Calculus. Volume I Richard CourantDifferential and Integral Calculus. Volume II Richard Courant & D. HilbertMethods of Mathematical Physics, Volume I Richard Courant & D. HilbertMethods of Mathematical Physics. Volume II Harold M. S. CoxeterIntroduction to Modern Geometry. Second Edition Charles W. Curtis, Irving ReinerRepresentation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartzunear Operators. Part One. General Theory Nelson Dunford. Jacob T. SchwartzLinear Operators, Part Two. Spectral Theory--Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. SchwartzLinear Operators. Part Three. Spectral Operators Peter HenriciApplied and Computational Complex Analysis. Volume I--Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang WuA Course in Modern Algebra Harry HochstadtIntegral Equations Erwin KreyszigIntroductory Functional Analysis with Applications P. M. PrenterSplines and Variational Methods C. L. SiegelTopics in Complex Function Theory. Volume I --Elliptic Functions and Uniformizatton Theory C. L. SiegelTopics in Complex Function Theory. Volume II --Automorphic and Abelian Integrals C. L. SiegelTopics In Complex Function Theory. Volume III --Abelian Functions & Modular Functions of Several Variables J. J. StokerDifferential Geometry

    Collected from the series of blog posts starting at: https://bartoszmilewski.com/2014/10/2...Hardcover available at: http://www.blurb.com/b/9008339-catego...

    This overview has enabled students to make sense more easily of what instructors are doing when they produce proofs, theorems and formulas.

    That’s a mistake, Tim Harford says in The Data Detective. We shouldn’t be suspicious of statistics—we need to understand what they mean and how they can improve our lives: they are, at heart, human behavior seen through the prism of numbers and are often “the only way of grasping much of what is going on around us.” If we can toss aside our fears and learn to approach them clearly—understanding how our own preconceptions lead us astray—statistics can point to ways we can live better and work smarter.As “perhaps the best popular economics writer in the world” (New Statesman), Tim Harford is an expert at taking complicated ideas and untangling them for millions of readers. In The Data Detective, he uses new research in science and psychology to set out ten strategies for using statistics to erase our biases and replace them with new ideas that use virtues like patience, curiosity, and good sense to better understand ourselves and the world. As a result, The Data Detective is a big-idea book about statistics and human behavior that is fresh, unexpected, and insightful.

    Fully revised to meet the needs of the wide range of students beginning engineering courses, this edition has an extended Foundation section including new chapters on graphs, trigonometry, binomial series and functions and a CD-ROM