An introductory course in complex analysis for incoming graduate students. Created to teach Math 5283 at Oklahoma State University. The book has somewhat more material than could fit in a one-semester course, allowing some choices. There are also appendices on metric spaces and some basic analysis background to make for a longer and more complete course for those that have only had an introduction to basic analysis on the real line.
This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.
A complete guide to carrying out complex survey analysis using R As survey analysis continues to serve as a core component of sociological research, researchers are increasingly relying upon data gathered from complex surveys to carry out traditional analyses. Complex Surveys is a practical guide to the analysis of this kind of data using R, the freely available and downloadable statistical programming language. As creator of the specific survey package for R, the author provides the ultimate presentation of how to successfully use the software for analyzing data from complex surveys while also utilizing the most current data from health and social sciences studies to demonstrate the application of survey research methods in these fields. The book begins with coverage of basic tools and topics within survey analysis such as simple and stratified sampling, cluster sampling, linear regression, and categorical data regression. Subsequent chapters delve into more technical aspects of complex survey analysis, including post-stratification, two-phase sampling, missing data, and causal inference. Throughout the book, an emphasis is placed on graphics, regression modeling, and two-phase designs. In addition, the author supplies a unique discussion of epidemiological two-phase designs as well as probability-weighting for causal inference. All of the book's examples and figures are generated using R, and a related Web site provides the R code that allows readers to reproduce the presented content. Each chapter concludes with exercises that vary in level of complexity, and detailed appendices outline additional mathematical and computational descriptions to assist readers with comparing results from various software systems. Complex Surveys is an excellent book for courses on sampling and complex surveys at the upper-undergraduate and graduate levels. It is also a practical reference guide for applied statisticians and practitioners in the social and health sciences who use statistics in their everyday work.
A single seed is more than just the promise of a plant. In rural south India, seeds represent diverging paths toward a sustainable livelihood. Development programs and global agribusiness promote genetically modified seeds and organic certification as a path toward more sustainable cotton production, but these solutions mask a complex web of economic, social, political, and ecological issues that may have consequences as dire as death. In Cultivating Knowledge anthropologist Andrew Flachs shows how rural farmers come to plant genetically modified or certified organic cotton, sometimes during moments of agrarian crisis. Interweaving ethnographic detail, discussions of ecological knowledge, and deep history, Flachs uncovers the unintended consequences of new technologies, which offer great benefits to some—but at others’ expense. Flachs shows that farmers do not make simple cost-benefit analyses when evaluating new technologies and options. Their evaluation of development is a complex and shifting calculation of social meaning, performance, economics, and personal aspiration. Only by understanding this complicated nexus can we begin to understand sustainable agriculture. By comparing the experiences of farmers engaged with these mutually exclusive visions for the future of agriculture, Cultivating Knowledge investigates the human responses to global agrarian change. It illuminates the local impact of global changes: the slow, persistent dangers of pesticides, inequalities in rural life, the aspirations of people who grow fibers sent around the world, the place of ecological knowledge in modern agriculture, and even the complex threat of suicide. It all begins with a seed.
In the tradition of Octavia Butler, here is radical self-help, society-help, and planet-help to shape the futures we want. Change is constant. The world, our bodies, and our minds are in a constant state of flux. They are a stream of ever-mutating, emergent patterns. Rather than steel ourselves against such change, Emergent Strategy teaches us to map and assess the swirling structures and to read them as they happen, all the better to shape that which ultimately shapes us, personally and politically. A resolutely materialist spirituality based equally on science and science fiction: a wild feminist and afro-futurist ride! adrienne maree brown, co-editor of Octavia’s Brood: Science Fiction from Social Justice Movements, is a social justice facilitator, healer, and doula living in Detroit.
Develops the higher parts of function theory in a unified presentation. Starts with elliptic integrals and functions and uniformization theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular functions in several variables. The last topic originates with the author and appears here for the first time in book form.
Traditional economic theory studies idealized markets in which prices alone can guide efficient allocation, with no need for central organization. Such models build from Adam Smith’s famous concept of an invisible hand, which guides markets and renders regulation or interference largely unnecessary. Yet for many markets, prices alone are not enough to guide feasible and efficient outcomes, and regulation alone is not enough, either. Consider air traffic control at major airports. While prices could encourage airlines to take off and land at less congested times, prices alone do just part of the job; an air traffic control system is still indispensable to avoid disastrous consequences. With just an air traffic controller, however, limited resources can be wasted or poorly used. What’s needed in this and many other real-world cases is an auction system that can effectively reveal prices while still maintaining enough direct control to ensure that complex constraints are satisfied. In Discovering Prices, Paul Milgrom—the world’s most frequently cited academic expert on auction design—describes how auctions can be used to discover prices and guide efficient resource allocations, even when resources are diverse, constraints are critical, and market-clearing prices may not even exist. Economists have long understood that externalities and market power both necessitate market organization. In this book, Milgrom introduces complex constraints as another reason for market design. Both lively and technical, Milgrom roots his new theories in real-world examples (including the ambitious U.S. incentive auction of radio frequencies, whose design he led) and provides economists with crucial new tools for dealing with the world’s growing complex resource-allocation problems.
Large surveys are becoming increasingly available for public use, and researchers are often faced with the need to analyse complex survey data to address key scientific issues. For proper analysis it is also important to be aware of the different aspects of the design of complex surveys. Practical Methods for Design and Analysis of Complex Surveys features intermediate and advanced statistical techniques for use in designing and analysing complex surveys. This extensively updated edition features much new material, and detailed practical exercises with links to a Web site, helping instructors and enabling use for distance learning. * Provides a comprehensive introduction to sampling and estimation in descriptive surveys, including design effect statistic and use of auxiliary data. * Includes detailed coverage of complex survey analysis, including design-based ANOVA and logistic regression with GEE estimation. * Contains much new material, including handling of non-sampling errors, and model-assisted estimation for domains. * Features detailed real-li fe case studies, such as multilevel modeling in a multinational educational survey. * Supported by a Web site containing software codes, real data sets, computerized exercises with solutions, and online training materials. Practical Methods for Design and Analysis of Complex Surveys provides a useful practical resource for researchers and practitioners working in the planning, implementation or analysis of complex surveys and opinion polls, including business, educational, health, social, and socio-economic surveys and official statistics. In addition, the book is well suited for use on intermediate and advanced courses in survey sampling.
A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.
The Thinker’s Guide to Analytic Thinking explores the practice of analyzing problems and opportunities and provides a framework for finding common denominators, inconsistencies, biases, and underlying causes. It helps readers learn to think within the logic of subjects and professions. By offering proper tools for analysis and assessment of thought, it empowers readers to address any decision with confidence. As part of the Thinker’s Guide Library, this book advances the mission of the Foundation for Critical Thinking to promote fairminded critical societies through cultivating essential intellectual abilities and virtues across every field of study across world.
