Fundamentals of Calculus

A comprehensive guide to ranks and group theory Ranks of Groups features a logical, straightforward presentation, beginning with a succinct discussion of the standard ranks before moving on to specific aspects of ranks of groups. Topics covered include section ranks, groups of finite 0-rank, minimax rank, special rank, groups of finite section p-rank, groups having finite section p-rank for all primes p, groups of finite bounded section rank, groups whose abelian subgroups have finite rank, groups whose abelian subgroups have bounded finite rank, finitely generated groups having finite rank, residual properties of groups of finite rank, groups covered by normal subgroups of bounded finite rank, and theorems of Schur and Baer. This book presents fundamental concepts and notions related to the area of ranks in groups. Class-tested worldwide by highly qualified authors in the fields of abstract algebra and group theory, this book focuses on critical concepts with the most interesting, striking, and central results. In order to provide readers with the most useful techniques related to the various different ranks in a group, the authors have carefully examined hundreds of current research articles on group theory authored by researchers around the world, providing an up-to-date, comprehensive treatment of the subject. • All material has been thoroughly vetted and class-tested by well-known researchers who have worked in the area of rank conditions in groups • Topical coverage reflects the most modern, up-to-date research on ranks of groups • Features a unified point-of-view on the most important results in ranks obtained using various methods so as to illustrate the role those ranks play within group theory • Focuses on the tools and methods concerning ranks necessary to achieve significant progress in the study and clarification of the structure of groups Ranks of Groups: The Tools, Characteristics, and Restrictions is an excellent textbook for graduate courses in mathematics, featuring numerous exercises, whose solutions are provided. This book will be an indispensable resource for mathematicians and researchers specializing in group theory and abstract algebra. MARTYN R. DIXON, PhD, is Professor in the Department of Mathematics at the University of Alabama. LEONID A. KURDACHENKO, PhD, DrS, is Distinguished Professor and Chair of the Department of Algebra at the University of Dnepropetrovsk, Ukraine. IGOR YA SUBBOTIN, PhD, is Professor in the Department of Mathematics and Natural Sciences at National University in Los Angeles, California.

Presents a comprehensive treatment of issues related to the inception, design, implementation and reporting of large-scale education assessments. In recent years many countries have decided to become involved in international educational assessments to allow them to ascertain the strengths and weaknesses of their student populations. Assessments such as the OECD's Programme for International Student Assessment (PISA), the IEA's Trends in Mathematics and Science Study (TIMSS) and Progress in International Reading Literacy (PIRLS) have provided opportunities for comparison between students of different countries on a common international scale. This book is designed to give researchers, policy makers and practitioners a well-grounded knowledge in the design, implementation, analysis and reporting of international assessments. Readers will be able to gain a more detailed insight into the scientific principles employed in such studies allowing them to make better use of the results. The book will also give readers an understanding of the resources needed to undertake and improve the design of educational assessments in their own countries and regions. Implementation of Large-Scale Education Assessments: Brings together the editors’ extensive experience in creating, designing, implementing, analysing and reporting results on a wide range of assessments. Emphasizes methods for implementing international studies of student achievement and obtaining highquality data from cognitive tests and contextual questionnaires. Discusses the methods of sampling, weighting, and variance estimation that are commonly encountered in international large-scale assessments. Provides direction and stimulus for improving global educational assessment and student learning Is written by experts in the field, with an international perspective. Survey researchers, market researchers and practitioners engaged in comparative projects will all benefit from the unparalleled breadth of knowledge and experience in large-scale educational assessments gathered in this one volume.

Introducing a revolutionary new model for the statistical analysis of experimental data In this important book, internationally acclaimed statistician, Chihiro Hirotsu, goes beyond classical analysis of variance (ANOVA) model to offer a unified theory and advanced techniques for the statistical analysis of experimental data. Dr. Hirotsu introduces the groundbreaking concept of advanced analysis of variance (AANOVA) and explains how the AANOVA approach exceeds the limitations of ANOVA methods to allow for global reasoning utilizing special methods of simultaneous inference leading to individual conclusions. Focusing on normal, binomial, and categorical data, Dr. Hirotsu explores ANOVA theory and practice and reviews current developments in the field. He then introduces three new advanced approaches, namely: testing for equivalence and non-inferiority; simultaneous testing for directional (monotonic or restricted) alternatives and change-point hypotheses; and analyses emerging from categorical data. Using real-world examples, he shows how these three recognizable families of problems have important applications in most practical activities involving experimental data in an array of research areas, including bioequivalence, clinical trials, industrial experiments, pharmaco-statistics, and quality control, to name just a few. • Written in an expository style which will encourage readers to explore applications for AANOVA techniques in their own research • Focuses on dealing with real data, providing real-world examples drawn from the fields of statistical quality control, clinical trials, and drug testing • Describes advanced methods developed and refined by the author over the course of his long career as research engineer and statistician • Introduces advanced technologies for AANOVA data analysis that build upon the basic ANOVA principles and practices Introducing a breakthrough approach to statistical analysis which overcomes the limitations of the ANOVA model, Advanced Analysis of Variance is an indispensable resource for researchers and practitioners working in fields within which the statistical analysis of experimental data is a crucial research component. Chihiro Hirotsu is a Senior Researcher at the Collaborative Research Center, Meisei University, and Professor Emeritus at the University of Tokyo. He is a fellow of the American Statistical Association, an elected member of the International Statistical Institute, and he has been awarded the Japan Statistical Society Prize (2005) and the Ouchi Prize (2006). His work has been published in Biometrika, Biometrics, and Computational Statistics & Data Analysis, among other premier research journals.

This book is a new edition of a title originally published in1992. No other book has been published that treats inverse spectral and inverse scattering results by using the so called Poisson summation formula and the related study of singularities. This book presents these in a closed and comprehensive form, and the exposition is based on a combination of different tools and results from dynamical systems, microlocal analysis, spectral and scattering theory. The content of the first edition is still relevant, however the new edition will include several new results established after 1992; new text will comprise about a third of the content of the new edition. The main chapters in the first edition in combination with the new chapters will provide a better and more comprehensive presentation of importance for the applications inverse results. These results are obtained by modern mathematical techniques which will be presented together in order to give the readers the opportunity to completely understand them. Moreover, some basic generic properties established by the authors after the publication of the first edition establishing the wide range of applicability of the Poison relation will be presented for first time in the new edition of the book.

Praise for the First Edition “…this book is quite inspiring, giving many practical ideas for survey research, especially for designing better questionnaires.” —International Statistical Review Reflecting modern developments in the field of survey research, the Second Edition of Design, Evaluation, and Analysis of Questionnaires for Survey Research continues to provide cutting-edge analysis of the important decisions researchers make throughout the survey design process. The new edition covers the essential methodologies and statistical tools utilized to create reliable and accurate survey questionnaires, which unveils the relationship between individual question characteristics and overall question quality. Since the First Edition, the computer program Survey Quality Prediction (SQP) has been updated to include new predictions of the quality of survey questions on the basis of analyses of Multi-Trait Multi-Method experiments. The improved program contains over 60,000 questions, with translations in most European languages. Featuring an expanded explanation of the usage and limitations of SQP 2.0, the Second Edition also includes: • New practice problems to provide readers with real-world experience in survey research and questionnaire design • A comprehensive outline of the steps for creating and testing survey questionnaires • Contemporary examples that demonstrate the many pitfalls of questionnaire design and ways to avoid similar decisions Design, Evaluation, and Analysis of Questionnaires for Survey Research, Second Edition is an excellent textbook for upper-undergraduate and graduate-level courses in methodology and research questionnaire planning, as well as an ideal resource for social scientists or survey researchers needing to design, evaluate, and analyze questionnaires. Design, Evaluation, and Analysis of Questionnaires for Survey Research, Second Edition is an excellent textbook for upper-undergraduate and graduate-level courses in methodology and research questionnaire planning, as well as an ideal resource for social scientists or survey researchers needing to design, evaluate, and analyze questionnaires.Reflecting modern developments in the field of survey research, the Second Edition ofDesign, Evaluation, and Analysis of Questionnaires for Survey Research continues toprovide cutting-edge analysis of the important decisions researchers make throughout thesurvey design process.The new edition covers the essential methodologies and statistical tools utilized to createreliable and accurate survey questionnaires, which unveils the relationship between individualquestion characteristics and overall question quality. Since the First Edition, the computerprogram Survey Quality Prediction (SQP) has