This volume is an outgrowth of the Conference on Research on the Enacted Mathematics Curriculum, funded by the National Science Foundation and held in Tampa, Florida in November 2010. The volume has the potential to be useful to a range of researchers, from established veterans in curriculum research to new researchers in this area of mathematics education. The chapters can be used to generate conversation about researching the enacted mathematics curriculum, including similarities and differences in the variables that can and should be studied across various curricula. As such, it might be used by a curriculum project team as it outlines a research agenda for curriculum or program evaluation. It might also be used as a text in a university graduate course on curriculum research and design. The chapters in this volume are a natural complement to those in Approaches to Studying the Enacted Mathematics Curriculum (Heck, Chval, Weiss, & Ziebarth, 2012), also published by Information Age Publishing. While the present volume focuses on a range of issues related to researching the enacted mathematics curriculum, including theoretical and conceptual issues, the volume by Heck et al. provides insights into different instrumentations used by groups of researchers to study curriculum enactment.

This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as square-integrable martingales and fractional Brownian motion, as well as alpha-stable processes. SMs include many well-known stochastic integrators as partial cases.General Stochastic Measures provides a comprehensive theoretical overview of SMs, including the basic properties of the integrals of real functions with respect to SMs. A number of results concerning the Besov regularity of SMs are presented, along with equations driven by SMs, types of solution approximation and the averaging principle. Integrals in the Hilbert space and symmetric integrals of random functions are also addressed.The results from this book are applicable to a wide range of stochastic processes, making it a useful reference text for researchers and postgraduate or postdoctoral students who specialize in stochastic analysis.

Rank-Based Methods for Shrinkage and Selection A practical and hands-on guide to the theory and methodology of statistical estimation based on rank Robust statistics is an important field in contemporary mathematics and applied statistical methods. Rank-Based Methods for Shrinkage and Selection: With Application to Machine Learning describes techniques to produce higher quality data analysis in shrinkage and subset selection to obtain parsimonious models with outlier-free prediction. This book is intended for statisticians, economists, biostatisticians, data scientists and graduate students. Rank-Based Methods for Shrinkage and Selection elaborates on rank-based theory and application in machine learning to robustify the least squares methodology. It also includes: Development of rank theory and application of shrinkage and selection Methodology for robust data science using penalized rank estimators Theory and methods of penalized rank dispersion for ridge, LASSO and Enet Topics include Liu regression, high-dimension, and AR(p) Novel rank-based logistic regression and neural networks Problem sets include R code to demonstrate its use in machine learning

This accessible reference includes selected contributions from Bayesian Thinking - Modeling and Computation, Volume 25 in the Handbook of Statistics Series, with a focus on key methodologies and applications for Bayesian models and computation. It describes parametric and nonparametric Bayesian methods for modeling, and how to use modern computational methods to summarize inferences using simulation. The book covers a wide range of topics including objective and subjective Bayesian inferences, with a variety of applications in modeling categorical, survival, spatial, spatiotemporal, Epidemiological, small area and micro array data.

Aids critical thinking on causal effects
Provides simulation based computing techniques
Covers Bioinformatics and Biostatistics

This volume is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic - as this handbook attests - is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.

Chapter on the Port Royal contributions to probability theory and decision theory

Serves as a singular contribution to the intellectual history of the 20th century Contains the latest scholarly discoveries and interpretative insights"

This book describes methods for statistical brain imaging data analysis from both the perspective of methodology and from the standpoint of application for software implementation in neuroscience research. These include those both commonly used (traditional established) and state of the art methods. The former is easier to do due to the availability of appropriate software. To understand the methods it is necessary to have some mathematical knowledge which is explained in the book with the help of figures and descriptions of the theory behind the software. In addition, the book includes numerical examples to guide readers on the working of existing popular software. The use of mathematics is reduced and simplified for non-experts using established methods, which also helps in avoiding mistakes in application and interpretation. Finally, the book enables the reader to understand and conceptualize the overall flow of brain imaging data analysis, particularly for statisticians and data-scientists unfamiliar with this area. The state of the art method described in the book has a multivariate approach developed by the authors' team. Since brain imaging data, generally, has a highly correlated and complex structure with large amounts of data, categorized into big data, the multivariate approach can be used as dimension reduction by following the application of statistical methods. The R package for most of the methods described is provided in the book. Understanding the background theory is helpful in implementing the software for original and creative applications and for an unbiased interpretation of the output. The book also explains new methods in a conceptual manner. These methodologies and packages are commonly applied in life science data analysis. Advanced methods to obtain novel insights are introduced, thereby encouraging the development of new methods and applications for research into medicine as a neuroscience.

Calculations for Molecular Biology and Biotechnology: A Guide to Mathematics in the Laboratory, Second Edition, provides an introduction to the myriad of laboratory calculations used in molecular biology and biotechnology. The book begins by discussing the use of scientific notation and metric prefixes, which require the use of exponents and an understanding of significant digits. It explains the mathematics involved in making solutions; the characteristics of cell growth; the multiplicity of infection; and the quantification of nucleic acids. It includes chapters that deal with the mathematics involved in the use of radioisotopes in nucleic acid research; the synthesis of oligonucleotides; the polymerase chain reaction (PCR) method; and the development of recombinant DNA technology. Protein quantification and the assessment of protein activity are also discussed, along with the centrifugation method and applications of PCR in forensics and paternity testing.

This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

This book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.

This book discusses diverse concepts and notions - and their applications - concerning probability and random variables at the intermediate to advanced level. It explains basic concepts and results in a clearer and more complete manner than the extant literature. In addition to a range of concepts and notions concerning probability and random variables, the coverage includes a number of key advanced concepts in mathematics. Readers will also find unique results on e.g. the explicit general formula of joint moments and the expected values of nonlinear functions for normal random vectors. In addition, interesting applications of the step and impulse functions in discussions on random vectors are presented. Thanks to a wealth of examples and a total of 330 practice problems of varying difficulty, readers will have the opportunity to significantly expand their knowledge and skills. The book is rounded out by an extensive index, allowing readers to quickly and easily find what they are looking for. Given its scope, the book will appeal to all readers with a basic grasp of probability and random variables who are looking to go one step further. It also offers a valuable reference guide for experienced scholars and professionals, helping them review and refine their expertise.