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Ideal Theoretic Methods in Commutative Algebra (Lecture Notes in Pure and Applied Mathematics)
by Daniel D. Anderson Ira J. PapickIncludes current work of 38 renowned contributors that details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. Summarizes recent findings on classes of going-down domains and the going-down property, emphasizing new characterizations and applications, as well as generalizations for commutative rings wi
Ideals of Powers and Powers of Ideals: Intersecting Algebra, Geometry, and Combinatorics (Lecture Notes of the Unione Matematica Italiana #27)
by Enrico Carlini Huy Tài Hà Brian Harbourne Adam Van TuylThis book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms. Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)
by David A. Cox John Little Donal O'SheaThis text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry--the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz--this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of Maple(tm), Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used. From the reviews of previous editions: ". . . The book gives an introduction to Buchberger's algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. . . . The book is well-written. . . . The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry. " --Peter Schenzel, zbMATH, 2007 "I consider the book to be wonderful. . . . The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging . . . offers the heart and soul of modern commutative and algebraic geometry. " --The American Mathematical Monthly
Identifiability and Observability in Epidemiological Models: A Primer (SpringerBriefs on PDEs and Data Science)
by Alain Rapaport Nik Cunniffe Frédéric Hamelin Abderrahman Iggidr Gauthier SalletThis book introduces the concepts of identifiability and observability in mathematical epidemiology, as well as those of observers’ constructions. It first exposes and illustrates on several examples the mathematical definitions and properties of observability and identifiability. A chapter is dedicated to the well-known Kermack McKendrick model, for which the complete analysis of identifiability and observability is not available in the literature. Then, several techniques of observer constructions, in view of online estimation of state and parameters, are presented and deployed on several models. New developments relevant for applications in epidemiology are also given. Finally, practical considerations are discussed with data and numerical simulations related to models previously analysed in the book. The book will be appealing to epidemiological modellers and mathematicians working on models in epidemiology.This book contributes to Sustainable Development Goal 3 (SDG3): Good Health and Well Being.
Identifiability and Regression Analysis of Biological Systems Models: Statistical and Mathematical Foundations and R Scripts (SpringerBriefs in Statistics)
by Paola LeccaThis richly illustrated book presents the objectives of, and the latest techniques for, the identifiability analysis and standard and robust regression analysis of complex dynamical models. The book first provides a definition of complexity in dynamic systems by introducing readers to the concepts of system size, density of interactions, stiff dynamics, and hybrid nature of determination. In turn, it presents the mathematical foundations of and algorithmic procedures for model structural and practical identifiability analysis, multilinear and non-linear regression analysis, and best predictor selection.Although the main fields of application discussed in the book are biochemistry and systems biology, the methodologies described can also be employed in other disciplines such as physics and the environmental sciences. Readers will learn how to deal with problems such as determining the identifiability conditions, searching for an identifiable model, and conducting their own regression analysis and diagnostics without supervision. Featuring a wealth of real-world examples, exercises, and codes in R, the book addresses the needs of doctoral students and researchers in bioinformatics, bioengineering, systems biology, biophysics, biochemistry, the environmental sciences and experimental physics. Readers should be familiar with the fundamentals of probability and statistics (as provided in first-year university courses) and a basic grasp of R.
Identification and Other Probabilistic Models: Rudolf Ahlswede’s Lectures on Information Theory 6 (Foundations in Signal Processing, Communications and Networking #16)
by Rudolf AhlswedeThe sixth volume of Rudolf Ahlswede's lectures on Information Theory is focused on Identification Theory. In contrast to Shannon's classical coding scheme for the transmission of a message over a noisy channel, in the theory of identification the decoder is not really interested in what the received message is, but only in deciding whether a message, which is of special interest to him, has been sent or not. There are also algorithmic problems where it is not necessary to calculate the solution, but only to check whether a certain given answer is correct. Depending on the problem, this answer might be much easier to give than finding the solution. ``Easier'' in this context means using fewer resources like channel usage, computing time or storage space. Ahlswede and Dueck's main result was that, in contrast to transmission problems, where the possible code sizes grow exponentially fast with block length, the size of identification codes will grow doubly exponentially fast. The theory of identification has now developed into a sophisticated mathematical discipline with many branches and facets, forming part of the Post Shannon theory in which Ahlswede was one of the leading experts. New discoveries in this theory are motivated both by concrete engineering problems and by explorations of the inherent properties of the mathematical structures. Rudolf Ahlswede wrote: It seems that the whole body of present day Information Theory will undergo serious revisions and some dramatic expansions. In this book we will open several directions of future research and start the mathematical description of communication models in great generality. For some specific problems we provide solutions or ideas for their solutions. The lectures presented in this work, which consists of 10 volumes, are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used as the basis for courses or to supplement courses in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs. The book also contains an afterword by Gunter Dueck.
Identification Problems in the Social Sciences
by Charles F. ManskiThis book provides a language and a set of tools for finding bounds on the predictions that social and behavioral scientists can logically make from nonexperimental and experimental data. The economist Charles F. Manski draws on examples from criminology, demography, epidemiology, social psychology, and sociology as well as economics to illustrate this language and to demonstrate the broad usefulness of the tools. There are many traditional ways to present identification problems in econometrics, sociology, and psychometrics. Some of these are primarily statistical in nature, using concepts such as flat likelihood functions and nondistinct parameter estimates. Manski’s strategy is to divorce identification from purely statistical concepts and to present the logic of identification analysis in ways that are accessible to a wide audience in the social and behavioral sciences. In each case, problems are motivated by real examples with real policy importance, the mathematics is kept to a minimum, and the deductions on identifiability are derived giving fresh insights. Manski begins with the conceptual problem of extrapolating predictions from one population to some new population or to the future. He then analyzes in depth the fundamental selection problem that arises whenever a scientist tries to predict the effects of treatments on outcomes. He carefully specifies assumptions and develops his nonparametric methods of bounding predictions. Manski shows how these tools should be used to investigate common problems such as predicting the effect of family structure on children’s outcomes and the effect of policing on crime rates. Successive chapters deal with topics ranging from the use of experiments to evaluate social programs, to the use of case-control sampling by epidemiologists studying the association of risk factors and disease, to the use of intentions data by demographers seeking to predict future fertility. The book closes by examining two central identification problems in the analysis of social interactions: the classical simultaneity problem of econometrics and the reflection problem faced in analyses of neighborhood and contextual effects.
Identifying and Supporting Productive STEM Programs in Out-of-School Settings
by Committee on Successful Out-of-School STEM LearningMore and more young people are learning about science, technology, engineering, and mathematics (STEM) in a wide variety of afterschool, summer, and informal programs. At the same time, there has been increasing awareness of the value of such programs in sparking, sustaining, and extending interest in and understanding of STEM. To help policy makers, funders and education leaders in both school and out-of-school settings make informed decisions about how to best leverage the educational and learning resources in their community, this report identifies features of productive STEM programs in out-of-school settings. "Identifying and Supporting Productive STEM Programs in Out-of-School Settings" draws from a wide range of research traditions to illustrate that interest in STEM and deep STEM learning develop across time and settings. The report provides guidance on how to evaluate and sustain programs. This report is a resource for local, state, and federal policy makers seeking to broaden access to multiple, high-quality STEM learning opportunities in their community.
Identifying Potential for Equitable Access to Tertiary Level Science
by Marissa RollnickHigher education internationally is in a state of transition and transformation, leading to an increase in the level of participation, and a consequent increase in number of non traditional and underprepared students. The appearance of these students provides a particular challenge in the sciences where adequate grounding is crucial. One response to this challenge has been the provision of access, foundation or "second chance programmes" which operate on different models internationally. In South Africa, where the push for equity is strong in the wake of the apartheid era, programmes have generally been established at all tertiary institutions with some of the most successful of these programmes based at universities characterised by a high research output. Consequently in the last decade there has been a great deal of research into the effectiveness of these programmes both at a micro and macro level. Similar research in other countries exists, but is patchy and often based on small groups of students. This book provides valuable information on what research has to say about disadvantaged and under prepared science students and how they learn - what works and what does not work. It provides an examination of issues related to the programmes, their structure, student selection and adjustment. Issues such the learning of these students, their communicative ability and laboratory work come under the spotlight. Although examining the issue internationally, the book draws heavily on lessons from South Africa where there has been considerably experience of such programmes.
Identität als Diskursgegenstand der Didaktik des Sachunterrichts: Eine historisch-diskursanalytische Untersuchung (Sachlernen & kindliche Bildung – Bedingungen, Strukturen, Kontexte)
by Martin SiebachDer Auseinandersetzung mit Identität kommt im Kontext gesellschaftlicher Transformationsprozesse der letzten Jahrzehnte eine immer größere Bedeutung zu. Identität ist zu einem zentralen Thema in Gesellschaft und Wissenschaft geworden. Eine Beteiligung der Sachunterrichtsdidaktik an diesem Diskurs wäre aufgrund der Bildungsauftrags des Unterrichtsfachs, zentrale gesellschaftliche Probleme zu thematisieren und eine breite und vielfältige Interessenförderung aller Schüler*innen zu gewährleisten zu erwarten. Außerdem haben viele curriculare Themen des Schulfachs Sachunterricht identitätsbezogene Aspekte, so körperliche Entwicklung, Geschlecht, Gender, Sexualität, Trans- bzw. Interkulturalität, Arbeit und Berufe. In der Sachunterrichtsdidaktik wäre dementsprechend eine identitätsbezogene Kontextualisierung solcher fachlichen Aspekte nötig und erwartbar. In dieser Arbeit wird für die Sachunterrichtsdidaktik geklärt, inwiefern die Thematisierung von „Identität“ in der Sachunterrichtsdidaktik diesen Erwartungen entspricht und somit als dem aktuellen Stand des sozialwissenschaftlichen Diskurses entsprechend gelten kann.
Identitätsarbeit beim Übergang in die Pension: Prozesse und Inhalte der prospektiven Auseinandersetzung mit Identitätsentwürfen und die Bedeutung der individuellen Kapitalausstattung (Vechtaer Beiträge zur Gerontologie)
by Julia ReinerAngesichts des Spannungsfelds aus Gewinnen und Verlusten, neuen Gestaltungsfreiheiten und -notwendigkeiten kann der Übergang in die Pension als besonders sensible Phase für Identitätsarbeit erachtet werden. Dies gilt speziell für die zukunftsorientierte Auseinandersetzung mit Identitätsentwürfen im Sinne von prospektiver Identitätsarbeit. Im Rahmen einer mehrphasigen Mixed-Methods-Studie untersucht Julia Reiner Prozesse und Inhalte von prospektiver Identitätsarbeit beim Übergang in die Pension und stellt in diesem Zusammenhang auch die Frage nach der Bedeutung der individuellen Kapitalausstattung. Durch die Verschränkung unterschiedlicher theoretischer Perspektiven und deren empirische Bearbeitung leistet die Untersuchung einen wertvollen Beitrag für die Identitäts- und Pensionierungsforschung sowie für Fragen sozialer Ungleichheit in diesen beiden Forschungsfeldern.
Identity and Ethnic Relations in Southeast Asia
by Chee Kiong TongModern nation states do not constitute closed entities. This is true especially in Southeast Asia, where Chinese migrants have continued to make their new homes over a long period of time, resulting in many different ethnic groups co-existing in new nation states. Focusing on the consequences of migration, and cultural contact between the various ethnic groups, this book describes and analyses the nature of ethnic identity and state of ethnic relations, both historically and in the present day, in multi-ethnic, pluralistic nation states in Southeast Asia. Drawing on extensive primary fieldwork in Malaysia, Singapore, Indonesia, Burma, Vietnam, Thailand and the Philippines, the book examines the mediations, and transformation of ethnic identity and the social incorporation, tensions and conflicts and the construction of new social worlds resulting from cultural contact among different ethnic groups.
Ideology and Spatial Voting in American Elections
by Stephen A. JesseeIdeology and Spatial Voting in American Elections addresses two core issues related to the foundations of democratic governance: how the political views of Americans are structured and how citizens' voting decisions relate to their ideological proximity to the candidates. Focusing on testing the assumptions and implications of spatial voting, this book connects the theory with empirical analysis of voter preferences and behavior, showing Americans cast their ballots largely in accordance with spatial voting theory. Stephen A. Jessee's research shows voters possess meaningful ideologies that structure their policy beliefs, moderated by partisanship and differing levels of political information. Jessee finds that while voters with lower levels of political information are more influenced by partisanship, independents and better informed partisans are able to form reasonably accurate perceptions of candidates' ideologies. His findings should reaffirm citizens' faith in the broad functioning of democratic elections.
If You Hopped like a Frog
by David M. SchwartzDid you know that a frog can jump 29 times its body length? Or that an ant can lift an object 50 times its weight?
If You Hopped Like A Frog (If You... Ser.)
by David M. SchwartzHow far could you hop?If you hopped like a frog...you could jump from home plate to first base in one mighty leap!Did you know that a frog can jump 20 times its body length? Or that an ant can lift an object 50 times its own weight?Read this book and find out what you could do -- if you had the amazing abilities of animals! And there are endless possibilities for making more hilarious comparisons of your own. Get ready for ratio and proportion like you've never seen them before!
If You Were a Minus Sign (Math Fun)
by Trisha Speed Shaskan Francesca CarabelliWhat could you do if you were a minus sign? You could subtract one number from another. You could subtract food and balloons. In every problem, you would find the difference. Discover even more answers in this installment of the bestselling MATH FUN series by Trisha Speed Shaskan! With creative examples, easy-to-understand text, and engaging art, these entertaining and educational picture books books are perfect for young math lovers to read aloud or read alone.
If You Were A Plus Sign (Math Fun)
by Trisha Speed Shaskan Francesca CarabelliWhat could you do if you were a plus sign? You could add things together. You could add people and animals. You could add up and down or side to side. Discover even more answers in this installment of the bestselling MATH FUN series by Trisha Speed Shaskan! With creative examples, easy-to-understand text, and engaging art, these entertaining and educational picture books books are perfect for young math lovers to read aloud or read alone.
IGA: Non-Invasive Coupling with FEM and Regularization of Digital Image Correlation Problems, Volume 2
by Robin Bouclier Jean-Charles PassieuxIsogeometric analysis (IGA) consists of using the same higher-order and smooth spline functions for the representation of geometry in Computer Aided Design as for the approximation of solution fields in Finite Element Analysis. Now, almost twenty years after its creation, substantial works are being reported in IGA, making it very competitive in scientific computing. This book proposes to use IGA jointly with standard finite element methods (FEM), presenting IGA as a projection of FEM on a more regular reduced basis. By shedding new light on how IGA relates to FEM, we can see how IGA can be implemented on top of an FE code in order to improve the solution of problems that require more regularity. This is illustrated by using IGA with FEM in a non-invasive fashion to perform efficient and robust multiscale global/local simulations in solid mechanics. Furthermore, we show that IGA can regularize the inverse problem of FE digital image correlation in experimental mechanics.
IGCSE Core Mathematics 3ed + CD
by Ric Pimentel Terry WallEndorsed by Cambridge International ExaminationsGive your core level students the support and framework they require to get their best grades with this book dedicated to the core level content of the latest syllabus and written specifically to ensure a more appropriate pace.- Gives students the practice they require to deepen their understanding through plenty of practice questionsThis title has been written for Core content of the revised Cambridge IGCSE Mathematics (0580) syllabus.
iGen: Why Today's Super-Connected Kids Are Growing Up Less Rebellious, More Tolerant, Less Happy--and Completely Unprepared for Adulthood--and What That Means for the Rest of Us
by Jean M. TwengeA highly readable and entertaining first look at how today’s members of iGen—the children, teens, and young adults born in the mid-1990s and later—are vastly different from their Millennial predecessors, and from any other generation, from the renowned psychologist and author of Generation Me.With generational divides wider than ever, parents, educators, and employers have an urgent need to understand today’s rising generation of teens and young adults. Born in the mid-1990s to the mid-2000s and later, iGen is the first generation to spend their entire adolescence in the age of the smartphone. With social media and texting replacing other activities, iGen spends less time with their friends in person—perhaps why they are experiencing unprecedented levels of anxiety, depression, and loneliness. But technology is not the only thing that makes iGen distinct from every generation before them; they are also different in how they spend their time, how they behave, and in their attitudes toward religion, sexuality, and politics. They socialize in completely new ways, reject once sacred social taboos, and want different things from their lives and careers. More than previous generations, they are obsessed with safety, focused on tolerance, and have no patience for inequality. iGen is also growing up more slowly than previous generations: eighteen-year-olds look and act like fifteen-year-olds used to. As this new group of young people grows into adulthood, we all need to understand them: Friends and family need to look out for them; businesses must figure out how to recruit them and sell to them; colleges and universities must know how to educate and guide them. And members of iGen also need to understand themselves as they communicate with their elders and explain their views to their older peers. Because where iGen goes, so goes our nation—and the world.
Ignorance and Uncertainty (Econometric Society Monographs #61)
by Olivier Compte Andrew PostlewaiteBorn of a belief that economic insights should not require much mathematical sophistication, this book proposes novel and parsimonious methods to incorporate ignorance and uncertainty into economic modeling, without complex mathematics. Economics has made great strides over the past several decades in modeling agents' decisions when they are incompletely informed, but many economists believe that there are aspects of these models that are less than satisfactory. Among the concerns are that ignorance is not captured well in most models, that agents' presumed cognitive ability is implausible, and that derived optimal behavior is sometimes driven by the fine details of the model rather than the underlying economics. Compte and Postlewaite lay out a tractable way to address these concerns, and to incorporate plausible limitations on agents' sophistication. A central aspect of the proposed methodology is to restrict the strategies assumed available to agents.
Iitaka Conjecture: An Introduction (SpringerBriefs in Mathematics)
by Osamu FujinoThe ambitious program for the birational classification of higher-dimensional complex algebraic varieties initiated by Shigeru Iitaka around 1970 is usually called the Iitaka program. Now it is known that the heart of the Iitaka program is the Iitaka conjecture, which claims the subadditivity of the Kodaira dimension for fiber spaces. The main purpose of this book is to make the Iitaka conjecture more accessible. First, Viehweg's theory of weakly positive sheaves and big sheaves is described, and it is shown that the Iitaka conjecture follows from the Viehweg conjecture. Then, the Iitaka conjecture is proved in some special and interesting cases. A relatively simple new proof of Viehweg's conjecture is given for fiber spaces whose geometric generic fiber is of general type based on the weak semistable reduction theorem due to Abramovick–Karu and the existence theorem of relative canonical models by Birkar–Cascini–Hacon–McKernan. No deep results of the theory of variations of Hodge structure are needed. The Iitaka conjecture for fiber spaces whose base space is of general type is also proved as an easy application of Viehweg's weak positivity theorem, and the Viehweg conjecture for fiber spaces whose general fibers are elliptic curves is explained. Finally, the subadditivity of the logarithmic Kodaira dimension for morphisms of relative dimension one is proved. In this book, for the reader's convenience, known arguments as well as some results are simplified and generalized with the aid of relatively new techniques.
Il concetto di curvatura: Genesi, sviluppo e intreccio fisico-matematico (UNITEXT #146)
by Franco CardinQuesto breve libro propone con uno spirito via via d’immagine storiografica e di dettaglio matematico, la nascita e l’evoluzione del concetto di curvatura: le sue origini ancestrali nella meccanica, nell’astronomia, nella geodesia, e infine, chiaramente nella geometria. Gli aspetti tecnici, a volte estremamente semplici, altre volte complessi, sono sempre accompagnati da spiegazioni che si sperano esaurienti.È ben noto che su entrambi i versanti culturali proposti nel libro, molto si è scritto e ad altissimo livello; qui, c’è un tentativo di sintesi, della storiografia e della matematica sul tema della curvatura. Il racconto del filo che intercorre tra Huygens, Gauss, Riemann, Christoffel, Ricci Curbastro, Levi-Civita e infine Einstein, è stato sicuramente già ben proposto sul versante puramente storico o in quello prettamente matematico: è una speranza che la narrazione qui presentata, con questi punti di vista intrecciati, sia infine soddisfacente. Il tentativo andava fatto. L’augurio forte è che gli argomenti narrati risultino coinvolgenti per il lettore, spingendolo ad esplorare autonomamente altri aspetti magari nascosti nelle pieghe della nozione di curvatura e del mondo che ci vive attorno. Il volume muove inizialmente dal racconto di qualche frammento di cosmologia antica e medioevale. Tutto ciò è solo apparentemente estraneo al corpo vivo della materia: ritroveremo per esempio che la concezione cosmologica di Dante, riassunta qui matematicamente, propose un universo come un’ipersfera 3-dimensionale che, quasi incidentalmente, risulterà proprio il modello cosmologico offerto da Einstein nel 1917 per il suo universo chiuso e statico. Ed è proprio la curvatura che domina quella scena, oggetto matematico protagonista della teoria della relatività generale einsteniana. I personaggi prima elencati vengono comunque narrati anche nelle loro salienti vicende umane, a volte altamente drammatiche, come accadde per esempio per Riemann e Tullio Levi-Civita. In un certo senso, la storia della curvatura accompagna la storia dell’umanità.Benché inizialmente sia stato generato da un disegno didattico, il volume è indirizzato ad un pubblico non necessariamente studentesco, con una cultura scientifica di base.
Illinois Math Connects: Concepts, Skills, And Problems Solving, Course 2
by Mcgraw-Hill StaffMath Connects: Concepts, Skills, and Problem Solving was written by the authorship team with the end results in mind. They looked at the content needed to be successful in Geometry and Algebra and backmapped the development of mathematical content, concepts, and procedures to PreK to ensure a solid foundation and seamless transition from grade level to grade level. The series is organized around the new NCTM Focal Points and is designed to meet most state standards. Math Connects focuses on three key areas of vocabulary to build mathematical literacy, intervention options aligned to RtI, and a comprehensive assessment system of diagnostic, formative, and summative assessments.
Illuminating Statistical Analysis Using Scenarios and Simulations
by Jeffrey E. KottemannFeatures an integrated approach of statistical scenarios and simulations to aid readers in developing key intuitions needed to understand the wide ranging concepts and methods of statistics and inference Illuminating Statistical Analysis Using Scenarios and Simulations presents the basic concepts of statistics and statistical inference using the dual mechanisms of scenarios and simulations. This approach helps readers develop key intuitions and deep understandings of statistical analysis. Scenario-specific sampling simulations depict the results that would be obtained by a very large number of individuals investigating the same scenario, each with their own evidence, while graphical depictions of the simulation results present clear and direct pathways to intuitive methods for statistical inference. These intuitive methods can then be easily linked to traditional formulaic methods, and the author does not simply explain the linkages, but rather provides demonstrations throughout for a broad range of statistical phenomena. In addition, induction and deduction are repeatedly interwoven, which fosters a natural "need to know basis" for ordering the topic coverage. Examining computer simulation results is central to the discussion and provides an illustrative way to (re)discover the properties of sample statistics, the role of chance, and to (re)invent corresponding principles of statistical inference. In addition, the simulation results foreshadow the various mathematical formulas that underlie statistical analysis. In addition, this book: • Features both an intuitive and analytical perspective and includes a broad introduction to the use of Monte Carlo simulation and formulaic methods for statistical analysis • Presents straight-forward coverage of the essentials of basic statistics and ensures proper understanding of key concepts such as sampling distributions, the effects of sample size and variance on uncertainty, analysis of proportion, mean and rank differences, covariance, correlation, and regression • Introduces advanced topics such as Bayesian statistics, data mining, model cross-validation, robust regression, and resampling • Contains numerous example problems in each chapter with detailed solutions as well as an appendix that serves as a manual for constructing simulations quickly and easily using Microsoft® Office Excel® Illuminating Statistical Analysis Using Scenarios and Simulations is an ideal textbook for courses, seminars, and workshops in statistics and statistical inference and is appropriate for self-study as well. The book also serves as a thought-provoking treatise for researchers, scientists, managers, technicians, and others with a keen interest in statistical analysis. Jeffrey E. Kottemann, Ph.D., is Professor in the Perdue School at Salisbury University. Dr. Kottemann has published articles in a wide variety of academic research journals in the fields of business administration, computer science, decision sciences, economics, engineering, information systems, psychology, and public administration. He received his Ph.D. in Systems and Quantitative Methods from the University of Arizona.