Building on the field of mathematical statistics, probabilistic robotics endows robots with a new level of robustness in real-world situations. This book introduces the reader to a wealth of techniques and algorithms in the field. All algorithms are based on a single overarching mathematical foundation. Each chapter provides example implementations in pseudo code, detailed mathematical derivations, discussions from a practitioner's perspective, and extensive lists of exercises and class projects. The book's Web site, www.probabilistic-robotics.org, has additional material. The book is relevant for anyone involved in robotic software development and scientific research. It will also be of interest to applied statisticians and engineers dealing with real-world sensor data.

    In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.

    His yearly gatherings of short and inventive problems were easily his most anticipated math columns. Loyal readers would savor the wit and elegance of his explorations in physics, probability, topology, and chess, among others. Grouped by subject and arrayed from easiest to hardest, the puzzles gathered here, which complement the lengthier, more involved problems in The Colossal Book of Mathematics, have been selected by Gardner for their illuminating; and often bewildering; solutions. Filled with over 300 illustrations, this new volume even contains nine new mathematical gems that Gardner, now ninety, has been gathering for the last decade. No amateur or expert math lover should be without this indispensable volume; a capstone to Gardner's seventy-year career.

    Topics covered in the book include permutations, combinations, Pascal's Triangle, basic combinatorial identities, expected value, fundamentals of probability, geometric probability, the Binomial Theorem, and much more.As you'll see in the excerpts below, the text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which counting and probability techniques are taught. Important facts and powerful problem solving approaches are highlighted through out the text. In addition to the instructional material, the book contains over 400 problems. The solutions manual contains full solutions to all of the problems, not just answers.This book is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of counting and probability will find this book an instrumental part of their mathematics libraries.

    Starting from basic algebra, it takes the reader to mathematical research. It includes numerical examples, analyzed for patterns and used to make conjectures.

    Book by Michael Spivak, Spivak, Michael

    It includes random sampling, expectations, Markov's and Chevyshev's inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales, entropy, and other topics. The book is designed to accompany a one- or two-semester course for graduate students in computer science and applied mathematics.

    

    Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas.This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical.The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

    Using a refreshingly clear and encouraging reader-friendly approach, this book helps students understand how to choose, carry out, interpret and report the results of complex statistical analyses, critically evaluate the design of experiments and proceed to more advanced material. Taking a straightforward conceptual approach, it is specifically designed to foster understanding, demystify difficult concepts and encourage the unsure. Even complex topics are explained clearly, using a pictorial approach with a minimum of formulae and terminology. Examples of tests included throughout are kept simple by using small data sets. In addition, end-of-chapter exercises, new to this edition, allow self-testing. Handy diagnostic tables help students choose the right test for their work and remain a useful refresher tool for postgraduates.

    This unique textbook covers two entirely different ways of looking at such reasoning. Topics include: the representation of mathematical statements by formulas in a formal language; the interpretation of formulas as true or false in a mathematical structure; logical consequence of one formula from others; formal proof; the soundness and completeness theorems connecting logical consequence and formal proof; the axiomatization of some mathematical theories using a formal language; the compactness theorem and an introduction to model theory.This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught.Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects.Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK.

    It will teach you to see the connections among these part-whole relationships and practice implementing strategic shortcuts.Each chapter builds comprehensive content understanding by providing rules, strategies, and in-depth examples of how the GMAT tests a given topic and how you can respond accurately and quickly. The Guide contains a total of 82 “In-Action” problems of increasing difficulty with detailed answer explanations. The content of the book is aligned to the latest Official Guides from GMAC (12th edition).Purchase of this book includes one year of access to Manhattan GMAT’s online practice exams and Fractions, Decimals, & Percents question bank.

    The author, David A. Freedman, explains the basic ideas of association and regression, and takes you through the current models that link these ideas to causality. The focus is on applications of linear models, including generalized least squares and two-stage least squares, with probits and logits for binary variables. The bootstrap is developed as a technique for estimating bias and computing standard errors. Careful attention is paid to the principles of statistical inference. There is background material on study design, bivariate regression, and matrix algebra. To develop technique, there are computer labs with sample computer programs. The book is rich in exercises, most with answers. Target audiences include advanced undergraduates and beginning graduate students in statistics, as well as students and professionals in the social and health sciences. The discussion in the book is organized around published studies, as are many of the exercises. Relevant journal articles are reprinted at the back of the book. Freedman makes a thorough appraisal of the statistical methods in these papers and in a variety of other examples. He illustrates the principles of modeling, and the pitfalls. The discussion shows you how to think about the critical issues including the connection (or lack of it) between the statistical models and the real phenomena. Features of the book: authoritative guidance from a well-known author with wide experience in teaching, research, and consulting careful analysis of statistical issues in substantive applications no-nonsense, direct style versatile structure, enabling the text to be used as a text in a course, or read on its own text that has been thoroughly class-tested at Berkeley background material on regression and matrix algebra plenty of exercises, most with solutions extra material for instructors, including data sets and code for lab projects (available from Cambridge University Press) many new exercises and examples reorganized, restructured, and revised chapters to aid teaching and understanding"

    The new edition has been revised in line with the new CXC syllabus, and now includes the use of investigations with opportunities for group work. It provides complete coverage of the CXC syllabus for the CSEC examination.

    There are five chapters about women that provide insight into the nineteenth and the mid-twentieth century, the early 1970s, the early 1990s, and 2004. Activists in many fields will take heart at the progress made during that time. The author documents the rudimentary struggles to become professionals, being married without entirely giving up a career, organizing to eliminate flagrant discrimination, improving the daily treatment of women in the professional community, and the widespread efforts toward true equality. The stories of African Americans in mathematics include the efforts of Benjamin Banneker, an eighteenth century American who had three grandparents born in Africa. He helped design Washington, DC, and made the computations for almanacs that succeeded Benjamin Franklin's. There are stories about African American mathematicians who were students and faculty in late nineteenth century colleges and accounts of several efforts to integrate the mathematical community in the mid-twentieth century. These stories indicate that though some efforts were more successful than others, all of them were difficult. The book concludes with a happier chapter about five black mathematicians in the early twenty-first century. The book also includes five interviews with leading Latin American mathematicians, along with the results of a survey of Latino research mathematicians in the Southwest. The author is a skilled story-teller with good stories to tell. This book is a page-turner that all mathematicians--as well as others concerned with equality--should read. It is a work of great interest and an enjoyable read.

    And working for fundamental social change and rectifying injustice are rarely included in any mathematics curriculum. Reading and Writing the World with Mathematics argues that mathematics education should prepare students to investigate and critique injustice, and to challenge, in words and actions, oppressive structures and acts. Based on teacher-research, the book provides a theoretical framework and practical examples for how mathematics educators can connect schooling to a larger sociopolitical context and concretely teach mathematics for social justice.

    It covers such topics as number, ratio and scale, rhythm and harmony, similarity and contrast, and suggests how these may relate to design problems.

    It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website.

    Connections are made between diverse biological examples linked by common mathematical themes, exploring a variety of discrete and continuous ordinary and partial differential equation models. Although great advances have taken place in many of the topics covered, the simple lessons contained in Mathematical Models in Biology are still important and informative. Shortly after the first publication of Mathematical Models in Biology, the genomics revolution turned Mathematical Biology into a prominent area of interdisciplinary research. In this new millennium, biologists have discovered that mathematics is not only useful, but indispensable! As a result, there has been much resurgent interest in, and a huge expansion of, the fields collectively called mathematical biology. This book serves as a basic introduction to concepts in deterministic biological modeling.

    For two millennia, the "right" way was Euclid's way, and it is still good in many respects. But in the 1950s the cry "Down with triangles!" was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new "right" way, or was the "right" way something else again, perhaps transformation groups? In this book, I wish to show that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Euclid-style construction and axiomatics seem the best way to start, but linear algebra smooths the later stages by replacing some tortuous arguments by simple calculations. And how can one avoid projective geometry? It not only explains why objects look the way they do; it also explains why geometry is entangled with algebra. Finally, one needs to know that there is not one geometry, but many, and transformation groups are the best way to distinguish between them. Two chapters are devoted to each approach: The ?rst is concrete and introductory, whereas the second is more abstract. Thus, the ?rst chapter on Euclid is about straightedge and compass constructions; the second is about axioms and theorems. The ?rst chapter on linear algebra is about coordinates; the second is about vector spaces and the inner product.

    This analysis clearly shows that if the world and the physical objects were three-dimensional, none of the kinematic relativistic effects and the experimental evidence supporting them would be possible. The implications of this result for physics, philosophy, and our entire world view are discussed.

    Based on the author's belief that only "hands-on" experience with the material can promote intuitive understanding, the approach is to motivate the need for theory using MATLAB examples, followed by theory and analysis, and finally descriptions of "real-world" examples to acquaint the reader with a wide variety of applications. The latter is intended to answer the usual question "Why do we have to study this?" Other salient features are:*heavy reliance on computer simulation for illustration and student exercises*the incorporation of MATLAB programs and code segments*discussion of discrete random variables followed by continuous random variables to minimize confusion*summary sections at the beginning of each chapter*in-line equation explanations*warnings on common errors and pitfalls*over 750 problems designed to help the reader assimilate and extend the conceptsIntuitive Probability and Random Processes using MATLAB(r) is intended for undergraduate and first-year graduate students in engineering. The practicing engineer as well as others having the appropriate mathematical background will also benefit from this book.About the AuthorSteven M. Kay is a Professor of Electrical Engineering at the University of Rhode Island and a leading expert in signal processing. He has received the Education Award "for outstanding contributions in education and in writing scholarly books and texts..." from the IEEE Signal Processing society and has been listed as among the 250 most cited researchers in the world in engineering.

    The section on general relativity gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes, Penrose processes, and similar topics), and considers the energy-momentum tensor for various solutions. The next section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects. Lastly, the section on cosmology discusses various cosmological models, observational tests, and scenarios for the early universe.

    This is a new English translation of his Rawda-yi taslim--the single most important Ismaili text from the Alamut period. In this work the Persian and English texts are edited and published together for the first time. This is Tusi’s major Ismaili work and the most important primary source on Ismaili doctrines during the Alamut period.

    The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them.

    General non-perturbative methods are also reviewing leading to the development of holomorphy and the Affleck-Dine-Seiberg superpotential as powerful tools for analyzing supersymmetric theories. Seiberg duality is discussed in detail, with many example applications provided, with special attention paid to its use in understanding dynamical supersymmetry breaking. The Seiberg-Witten theory of monopoles is introduced through the analysis of simpler N=1 analogues. Superconformal field theories are described along with the most recent development known as a-maximization. Supergravity theories are examined in 4, 10, and 11 dimensions, allowing for a discussion of anomaly and gaugino mediation, and setting the stage for the anti-de-Sitter/conformal field theory correspondence. This book is unique in containing an overview of the important developments in supersymmetry since the publication of Supersymmetry and Supergravity by Wess and Bagger. It also strives to cover topics that are of interest to both formal and phenomenological theorists.

    It is vital to advancing their careers. Later, some are asked to become editors. However, most mathematicians are trained to do mathematics, not to publish it. But here, finally, for graduate students and researchers interested in publishing their work, Steven G. Krantz, the respected author of several how-to guides in mathematics, shares his experience as an author, editor, editorial board member, and independent publisher. This new volume is an informative, comprehensive guidebook to publishing mathematics. Krantz describes both the general setting of mathematical publishing and the specifics about all the various publishing situations mathematicians may encounter. As with his other books, Krantz's style is engaging and frank. He gives advice on how to get your book published, how to get organized as an editor, what to do when things go wrong, and much more. He describes the people, the language (including a glossary), and the process of publishing both books and journals. Steven G. Krantz is an accomplished mathematician and an award-winning author. as an editor of several book series, research journals, and for the Notices of the AMS. He is also the founder of the Journal of Geometric Analysis. Other titles available from the AMS by Steven G. Krantz are How to Teach Mathematics, A Primer of Mathematical Writing, A Mathematician's Survival Guide, and Techniques of Problem Solving

    There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of this book is to introduce advanced undergraduates and beginning graduate students studying the mathematics of finance to the Black-Scholes formula. The author uses a first-principles approach, developing only the minimum background necessary to justify mathematical concepts and placing mathematical developments in context. The book skillfully draws the reader toward the art of thinking mathematically and then proceeds to lay the foundations in analysis and probability theory underlying modern financial mathematics. It rigorously reveals the mathematical secrets of topics such as abstract measure theory, conditional expectations, martingales, Wiener processes, the Ito calculus, and other ingredients of the Black-Scholes formula. In explaining these topics, the author uses examples drawn from the universe of finance. The book also contains many exercises, some included to clarify simple points of exposition, others to introduce new ideas and techniques, and a few containing relatively deep mathematical results. With the modest prerequisite of a first course in calculus, the book is suitable for undergraduates and graduate students in mathematics, finance, and economics and can be read, using appropriate selections, at a number of levels.

    Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.

    Presents hundreds of extreme value problems, examples, and solutions primarily through Euclidean geometryUnified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinatorial reasoningApplications to physics, engineering, and economicsIdeal for use at the junior and senior undergraduate level, with wide appeal to students, teachers, professional mathematicians, and puzzle enthusiasts

    It is also appropriate for mathematically oriented readers in the physical and social sciences. Prerequisite material consists of basic set theory and a firm foundation in elementary calculus, including infinite series, partial differentiation, and multiple integration. Some exposure to rudimentary linear algebra (e.g., matrices and determinants) is also desirable. This text includes pedagogical techniques not often found in books at this level, in order to make the learning process smooth, efficient, and enjoyable. KEY TOPICS: Fundamentals of Probability: Probability Basics. Mathematical Probability. Combinatorial Probability. Conditional Probability and Independence. Discrete Random Variables: Discrete Random Variables and Their Distributions. Jointly Discrete Random Variables. Expected Value of Discrete Random Variables. Continuous Random Variables: Continuous Random Variables and Their Distributions. Jointly Continuous Random Variables. Expected Value of Continuous Random Variables. Limit Theorems and Advanced Topics: Generating Functions and Limit Theorems. Additional Topics. MARKET: For all readers interested in probability.

    Volume III is mainly concerned with general theories rather than with special problems and special theorems. The investigations deal with the most advanced parts of the theory of numbers. 1919 edition.

    This volume will define new standards for years to come. You will be swept through transcendent realms of light and awareness, even as Buess's solid psychological base and down-to-earth reality keep you centered right here in the present moment. It will be of help in your journey through life and in your search for the meaning of numbers.

    The first part of the book provides easy-to-readinformal discussion of abstract mathematics and computers for generalaudiences. The later parts provide in-depth coverage of the foundations of mathematics, the Metamathlanguage, and the Metamath program. More information can be found atthe Metamath web site.

    Throughout the book, Philosopher pursues his dream of a unified theory of conics, here exceptions are banished. With a helpful teacher and example-hungry student, the trio soon finds that conics reveal much of their beauty when viewed over the complex numbers. In their odyssey, they uncover a goldmine of unsuspected results. They experience a series of "Aha!" moments as they stumble upon living brothers to familiar conics objects like foci and directrices. They also discover a normally-unseen ellipse spanning the gap between the branches of any hyperbola. On the applied side, they learn how two interfering wave sources create systems of hyperbolas; these are used in making astonishingly precise astronomical observations. All these discoveries are profusely illustrated with pictures, worked-out examples, a generous selection of exercises, and a CD containing 36 applets. If you've ever needed a conics formula for area, eccentricity, curvature and the like, look in the formula appendix. Here are dozens of useful formulas-a set for each of eight different ways of looking at a conic: as a cone slice; as the path of a planet moving under the influence of a fixed sun; as a figure constructed using two stakes and string; plus five other sets. Conics is written in an easy, conversational style, and many historical tidbits and other points of interest are scattered throughout the text. Many students self-study the book without outside help. This book is ideal for anyone having a little exposure to linear algebra and complex numbers. System Requirements for running the appletsWindows Pentium 4: Windows NT/2000, or Windows XP128MB of RAMInternet Explorer 6 SP1 or later. Java:  Java Plug-in TM  version 1.42 or later.   MacintoshG4 or G5 processor: Mac OS X v. 10.3.4 or laterSafari browser recommended for the Mac128MB of RAM Java:  Java Plug-in TM  version 1.42 or later.

    

    This introduction includes many simple explanations and examples. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with exercises. Further teaching material is available via the web, including assignable problem sheets with solutions.

    Understanding and Using Advanced Statistics provides the basis for gaining an understanding of what these analytic procedures do, when they should be used, and what the results provided signify. This comprehensive textbook guides students and researchers through the transition from simple statistics to more complex procedures with accessible language and illustration.

    Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistryInterdisciplinary book that will be useful in several fields-with a cross-disciplinary subject area, and contributions from researchers of various disciplines

    (Each of these has been honored by at least one recent book.) Here, in an imaginary dialogue between teacher and student, readers will learn why v2 is an important number in its own right, and how, in puzzling out its special qualities, mathematicians gained insights into the illusive nature of irrational numbers. Using no more than basic high school algebra and geometry, David Flannery manages to convey not just why v2 is fascinating and significant, but how the whole enterprise of mathematical thinking can be played out in a dialogue that is imaginative, intriguing, and engaging. Original and informative, The Square Root of 2 is a one-of-a-kind introduction to the pleasure and playful beauty of mathematical thinking.

    The book is aimed at Masters or PhD level students in statistics, computer science, and engineering. It is also suitable for researchers who want to get up to speed quickly on modern nonparametric methods. It covers a wide range of topics including the bootstrap, the nonparametric delta method, nonparametric regression, density estimation, orthogonal function methods, minimax estimation, nonparametric confidence sets, and wavelets. The book's dual approach includes a mixture of methodology and theory.

    The new book is intended for advanced undergraduate and graduate students of economics whose requirements go beyond the material usually taught in undergraduate mathematics courses for economists. It presents most of the mathematical tools that are required for advanced courses in economic theory - both micro and macro.

    The main thread throughout the book is the idea of ap- proximating "complicated expressions" with "simpler expressions," and how this plays a decisive role in many areas of modern mathematics and its applications. One of the main goals of the presentation is to make it clear to the reader that mathematics is a subject in a state of continuous evolution. This fact is usually difficult to explain to students at or near their second year of uni- versity. Often, teachers do not have adequate elementary material to give to students as motivation and encouragement for their further studies. The present book will be of use in this context because the exposition demon- strates the dynamic nature of mathematics and how classical disciplines influence many areas of modern mathematics and applications. The book may lead readers toward more advanced literature, such as the other pub- lications in the Applied and Numerical Harmonic Analysis series (ANHA), by introducing ideas presented in several of those books in an elementary context. The focus here is on ideas rather than on technical details, and the book is not primarily meant to be a textbook.

    It clearly emphasizes the connection between statistics and probability, and helps students concentrate on statistical strategies without being overwhelmed by calculations.The book provides comprehensive coverage of descriptive statistics; detailed treatment of univariate and bivariate probability distributions; and thorough coverage of probability theory with numerous event classifications.This book is designed for statistics majors who are already familiar with introductory calculus and statistics, and can be used in either a one- or two-semester course. It can also serve as a statistics tutorial or review for working professionals.Students who use this book will be well on their way to thinking like a statistician in terms of problem solving and decision-making. Graduates who pursue careers in statistics will continue to find this book useful, due to numerous statistical test procedures (both parametric and non-parametric) and detailed examples.

    Along with a companion volume Advanced Real Analysis (available separately or together as a Set via the Related Links nearby), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features of Basic Real Analysis: * Early chapters treat the fundamentals of real variables, sequences and series of functions, the theory of Fourier series for the Riemann integral, metric spaces, and the theoretical underpinnings of multivariable calculus and differential equations * Subsequent chapters develop the Lebesgue theory in Euclidean and abstract spaces, Fourier series and the Fourier transform for the Lebesgue integral, point-set topology, measure theory in locally compact Hausdorff spaces, and the basics of Hilbert and Banach spaces * The subjects of Fourier series and harmonic functions are used as recurring motivation for a number of theoretical developments * The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * The text includes many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most of the problems Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Basic Real Analysis make it a welcome addition to the personal library of every mathematician.

    This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations.After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory.Throughout the book, the author presents over 150 problems and exercises - many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory--together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians.Intended for senior undergraduates and first-year graduatesin science and engineering, this is equally useful as a reference and self-study guide.

    Tied to the land and each other in complex ways, the characters are Ohio angels with halos slightly askew. The truth of this story made my heart sing." Phyllis Wilson Moore, Independent Researcher, West Virginia Literature, Clarksburg, WV "A story of two men and a village who find their heart's desire - and their family roots - in their own backyard. The characters are original fiction, but the fight to save the farm is real. And the fight continues, every day, all across the nation." Krista Magaw, Executive Director, Tecumseh Land Trust, Yellow Springs, Ohio

    It also provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students, the self-contained treatment also constitutes a handy reference for researchers. The only mathematical background necessary is a sound knowledge of high school mathematics and a first course in statistics.Consisting of two interrelated parts, this volume begins with the basic structure of vectors and vector spaces. The latter part emphasizes the diverse properties of matrices and their associated linear transformations--and how these, in turn, depend upon results derived from linear vector spaces. An overview of introductory concepts leads to more advanced topics such as latent roots and vectors, generalized inverses, and nonnegative matrices. Each chapter concludes with a section on real-world statistical applications, plus exercises that offer concrete examples of the applications of matrix algebra.

    Of the 240 puzzles, 220 are the popular 9x9 puzzles, 10 are 16 x 16, and 10 are circular puzzles. Within each of these categories there are Easy, Tricky, Tough and Diabolical puzzle ratings; and each puzzle is clearly identified with the rating. More than just a listing of puzzles, Sudoku For Dummies, Volume 3 features a chapter explaining how to solve puzzles and the strategies involved. Additionally, readers receive all puzzle solutions in the back of the book. Finally, Sudoku For Dummies, Volume 3 includes a brief history of Sudoku (or Su Doku) for those interested. Descriptions of the puzzles are listed below.Circular Sudoku (10 included: 3 Easy, 3 Tricky, 2 Tough, and 2 Diabolical) The rules are similar to the normal 9x9 Sudoku but with some important differences. The puzzle is circular for a start, with 8 concentric rings. Each ring must contain the numbers 1-8 and each segment running into the centre of the circle and through to the opposite side of the circle must contain the numbers 1 - 8 and or course there can be no duplicate numbers!16 x 16 Sudoku (10 included: 3 Easy, 3 Tricky, 2 Tough, and 2 Diabolical) The grid is larger at 16 x 16 and solvers must fit the letters A-F into the grid alongside the numbers 0-9. 16 x 16 Sudoku are more difficult, take more time and are more infuriating than the normal puzzles - but just as addictive!

    So this book is designed not only for mathematicians but for all the people who have an interest in the various aspects of culture, both scientific and literary, with a special emphasis on the visual aspects.

    The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. This book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones.

    Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but too small to have room to undo them. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. The first part of the book puts things in context with a survey of higher dimensions and of topological 4-manifolds. The second part investigates the main invariant of a 4-manifold - the intersection form - and its interaction with the topology of the manifold. The third part reviews complex surfaces as an important source of examples. The fourth and final part of the book presents gauge theory. This differential-geometric method has brought to light the unwieldy nature of smooth 4-manifolds; and although the method brings new insights, it has raised more questions than answers.

    Comprehensive tables of standard derivatives and integrals, together with the tables of Laplace, Fourier, and Z transforms are included. A spiral binding that allows the handbook to lay flat for easy reference enhances the user-friendly design.

    Starting with the underlying mathematical ideas, it gradually leads the reader to a sufficient understanding of the detail to be able to implement libraries and programs for 2D and 3D graphics. Using lots of code examples, the reader is encouraged to explore and experiment with data and computer programs (in the C programming language) and to master the related mathematical techniques.A simple but effective set of routines are included, organised as a library, covering both 2D and 3D graphics taking a parallel approach to mathematical theory, and showing the reader how to incorporate it into example programs. This approach both demystifies the mathematics and demonstrates its relevance to 2D and 3D computer graphics."

    

    The data stream agenda now pervades many branches of Computer Science including databases, networking, knowledge discovery and data mining, and hardware systems. Industry is in synch too, with Data Stream Management Systems (DSMSs) and special hardware to deal with data speeds. Even beyond Computer Science, data stream concerns are emerging in physics, atmospheric science and statistics. Data Streams: Algorithms and Applications focuses on the algorithmic foundations of data streaming. In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerged for reasoning about algorithms that work within these constraints on space, time and number of passes. Some of the methods rely on metric embeddings, pseudo-random computations, sparse approximation theory and communication complexity. The applications for this scenario include IP network traffic analysis, mining text message streams and processing massive data sets in general. Data Streams: Algorithms and Applications surveys the emerging area of algorithms for processing data streams and associated applications. An extensive bibliography with over 200 entries points the reader to further resources for exploration.

    By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica(r) notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.

    Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

    It meets the needs of systems designers, installation engineers, electronic engineers and anyone else looking to gain a working knowledge of fiber optics with a minimum of maths. Review questions are included in the text to enable the reader to check their understanding as they work through the book.The new edition of this successful book is now fully up to date with the new standards, latest technological developments and includes a new chapter on specifying optical components.Whether you are looking for a complete self-study course in fiber optics, a concise reference text to dip into, or a readable introduction to this fast moving technology, this book has the solution.

    Includes complex symmetric, antisymmetric, and orthogonal matrices; singular bundles of matrices and matrices with nonnegative elements. Also features linear differential equations and the Routh-Hurwitz problem. 1959 edition.

    This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to G�del.Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This collection, presented as a whole, reveals the underlying unity of Tait's work. The volume includes an introduction in which Tait reflects more generally on the evolution of his point of view, as well as an appendix and added endnotes in which he gives some interesting background to the original essays. This is an important collection of the work of one of the most eminent philosophers of mathematics in this generation.

    For example, C.T.C. Wall [72] has shown that the problem of deciding whether a ?nitely dominated space with fundamental group? is homotopy equivalent to a ?nite CW-complex leads naturally to the study of a certain class in the reduced K-theoryK (Z?) of the group ringZ?. 0 As another example, consider a discrete groupG which acts freely, properly discontinuously, cocompactly and isometrically on a Riemannian manifold. Then, following A. Connes and H. Moscovici [16], the index of an invariant 0th-order elliptic pseudo-di?erential operator is de?ned as an element in the ? ? K -group of the reduced groupC -algebraCG. 0 r Theidempotentconjecture(alsoknownasthegeneralizedKadisonconjec- ? ? ture) asserts that the reduced groupC -algebraCG of a discrete torsion-free r groupG has no idempotents =0,1; this claim is known to be a consequence of a far-reaching conjecture of P. Baum and A. Connes [6]. Alternatively, one mayapproachtheidempotentconjectureasanassertionabouttheconnect- ness of a non-commutative space;ifG is a discrete torsion-free abelian group ? thenCG is the algebra of continuous complex-valued functions on the dual r