Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.

Each chapter consists of basic statistical theory, simple examples of S-PLUS code, plus more complex examples of S-PLUS code, and exercises. All data sets are taken from genuine medical investigations and will be available on a web site. The examples in the book contain extensive graphical analysis to highlight one of the prime features of S-PLUS. Written with few details of S-PLUS and less technical descriptions, the book concentrates solely on medical data sets, demonstrating the flexibility of S-PLUS and its huge advantages, particularly for applied medical statisticians.

The theory of U-statistics goes back to the fundamental work of Hoeffding 1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc."

This book provides clear explanatory text, illustrative mathematics and algorithms, demonstrations of the iterative process, pseudocode, and well-developed examples for applications of the branch-and-bound paradigm to important problems in combinatorial data analysis.

Supplementary material, such as computer programs, are provided on the world wide web.

Dr. Brusco is an editorial board member for the Journal of Classification, and a member of the Board of Directors for the Classification Society of North America.

A guide to using S environments to perform statistical analyses providing both an introduction to the use of S and a course in modern statistical methods. The emphasis is on presenting practical problems and full analyses of real data sets.

Most global optimization literature focuses on theory. This book, however, contains descriptions of new implementations of general-purpose or problem-specific global optimization algorithms. It discusses existing software packages from which the entire community can learn. The contributors are experts in the discipline of actually getting global optimization to work, and the book provides a source of ideas for people needing to implement global optimization software.

This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What's more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too.

There are many books that are excellent sources of knowledge about individual stastical tools (survival models, general linear models, etc.), but the art of data analysis is about choosing and using multiple tools. In the words of Chatfield ..".students typically know the technical details of regressin for example, but not necessarily when and how to apply it. This argues the need for a better balance in the literature and in statistical teaching between techniques and problem solving strategies." Whether analyzing risk factors, adjusting for biases in observational studies, or developing predictive models, there are common problems that few regression texts address. For example, there are missing data in the majority of datasets one is likely to encounter (other than those used in textbooks!) but most regression texts do not include methods for dealing with such data effectively, and texts on missing data do not cover regression modeling.

Although statistical design is one of the oldest branches of statistics, its importance is ever increasing, especially in the face of the data flood that often faces statisticians. It is important to recognize the appropriate design, and to understand how to effectively implement it, being aware that the default settings from a computer package can easily provide an incorrect analysis. The goal of this book is to describe the principles that drive good design, paying attention to both the theoretical background and the problems arising from real experimental situations. Designs are motivated through actual experiments, ranging from the timeless agricultural randomized complete block, to microarray experiments, which naturally lead to split plot designs and balanced incomplete blocks.

Without question, statistics is one of the most challenging courses for students in the social and behavioral sciences. Enrolling in their first statistics course, students are often apprehensive or extremely anxious toward the subject matter. And while IBM SPSS is one of the more easy-to-use statistical software programs available, for anxious students who realize they not only have to learn statistics but also new software, the task can seem insurmountable. Keenly aware of students' anxiety with statistics (and the fact that this anxiety can affect performance), Ronald D. Yockey has written SPSS Demystified: A Simple Guide and Reference, now in its fourth edition. Through a comprehensive, step-by-step approach, this text is consistently and specifically designed to both alleviate anxiety toward the subject matter and build a successful experience analyzing data in SPSS. Topics covered in the text are appropriate for most introductory and intermediate statistics and research methods courses. Key features of the text: Step-by-step instruction and screenshots Designed to be hands-on with the user performing the analyses alongside on their computer as they read through each chapter Call-out boxes provided, highlighting important information as appropriate SPSS output explained, with written results provided using the popular, widely recognized APA format End-of-chapter exercises included, allowing for additional practice SPSS datasets available on the publisher's website New to the Fourth Edition: Fully updated to SPSS 28 Updated screenshots in full color to reflect changes in SPSS software system (version 28) Exercises updated with up-to-date examples Exact p-values provided (consist with APA recommendations)

Systems of polynomial equations arise throughout mathematics, science, and engineering. Algebraic geometry provides powerful theoretical techniques for studying the qualitative and quantitative features of their solution sets. Re cently developed algorithms have made theoretical aspects of the subject accessible to a broad range of mathematicians and scientists. The algorith mic approach to the subject has two principal aims: developing new tools for research within mathematics, and providing new tools for modeling and solv ing problems that arise in the sciences and engineering. A healthy synergy emerges, as new theorems yield new algorithms and emerging applications lead to new theoretical questions. This book presents algorithmic tools for algebraic geometry and experi mental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. A wide range of mathematical scientists should find these expositions valuable. This includes both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all."

Proceedings of the 19th international symposium on computational statistics, held in Paris august 22-27, 2010.Together with 3 keynote talks, there were 14 invited sessions and more than 100 peer-reviewed contributed communications.

Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa tion and obtains a closed form analytic answer. It is these Computer Algebra systems, their capabilities, and applications which are the subject of the papers in this volume."

Optical Scanning Holography is an exciting new field with many potential novel applications. This book contains tutorials, research materials, as well as new ideas and insights that will be useful for those working in the field of optics and holography. The book has been written by one of the leading researchers in the field. It covers the basic principles of the topic which will make the book relevant for years to come.

In many fields of modern mathematics specialised scientific software becomes increasingly important. Hence, tremendous effort is taken by numerous groups all over the world to develop appropriate solutions.
This book contains surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Grobner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. Therefore the volume's other focus is on solutions towards the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general framework for modular systems."

Computer-Aided Control Systems Design: Practical Applications Using MATLAB (R) and Simulink (R) supplies a solid foundation in applied control to help you bridge the gap between control theory and its real-world applications. Working from basic principles, the book delves into control systems design through the practical examples of the ALSTOM gasifier system in power stations and underwater robotic vehicles in the marine industry. It also shows how powerful software such as MATLAB (R) and Simulink (R) can aid in control systems design. Make Control Engineering Come Alive with Computer-Aided Software Emphasizing key aspects of the design process, the book covers the dynamic modeling, control structure design, controller design, implementation, and testing of control systems. It begins with the essential ideas of applied control engineering and a hands-on introduction to MATLAB and Simulink. It then discusses the analysis, model order reduction, and controller design for a power plant and the modeling, simulation, and control of a remotely operated vehicle (ROV) for pipeline tracking. The author explains how to obtain the ROV model and verify it by using computational fluid dynamic software before designing and implementing the control system. In addition, the book details the nonlinear subsystem modeling and linearization of the ROV at vertical plane equilibrium points. Throughout, the author delineates areas for further study. Appendices provide additional information on various simulation models and their results. Learn How to Perform Simulations on Real Industry Systems A step-by-step guide to computer-aided applied control design, this book supplies the knowledge to help you deal with control problems in industry. It is a valuable reference for anyone who wants a better understanding of the theory and practice of basic control systems design, analysis, and implementation.

Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Edited by the principal designers of the program, this book explores Magma. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory. Includes case studies describing computations underpinning new theoretical results.

The first edition was released in 1996 and has sold close to 2200 copies.

Provides an up-to-date comprehensive treatment of MDS, a statistical technique used to analyze the structure of similarity or dissimilarity data in multidimensional space.

The authors have added three chapters and exercise sets. The text is being moved from SSS to SSPP.

The book is suitable for courses in statistics for the social or managerial sciences as well as for advanced courses on MDS.

All the mathematics required for more advanced topics is developed systematically in the text.

The contributions in this book state the complementary rather than competitive relationship between Probability and Fuzzy Set Theory and allow solutions to real life problems with suitable combinations of both theories.

Patients are not alike! This simple truth is often ignored in the analysis of me- cal data, since most of the time results are presented for the "average" patient. As a result, potential variability between patients is ignored when presenting, e.g., the results of a multiple linear regression model. In medicine there are more and more attempts to individualize therapy; thus, from the author's point of view biostatis- cians should support these efforts. Therefore, one of the tasks of the statistician is to identify heterogeneity of patients and, if possible, to explain part of it with known explanatory covariates. Finite mixture models may be used to aid this purpose. This book tries to show that there are a large range of applications. They include the analysis of gene - pression data, pharmacokinetics, toxicology, and the determinants of beta-carotene plasma levels. Other examples include disease clustering, data from psychophysi- ogy, and meta-analysis of published studies. The book is intended as a resource for those interested in applying these methods.

This book helps readers understand the mathematics of machine learning, and apply them in different situations. It is divided into two basic parts, the first of which introduces readers to the theory of linear algebra, probability, and data distributions and it's applications to machine learning. It also includes a detailed introduction to the concepts and constraints of machine learning and what is involved in designing a learning algorithm. This part helps readers understand the mathematical and statistical aspects of machine learning. In turn, the second part discusses the algorithms used in supervised and unsupervised learning. It works out each learning algorithm mathematically and encodes it in R to produce customized learning applications. In the process, it touches upon the specifics of each algorithm and the science behind its formulation. The book includes a wealth of worked-out examples along with R codes. It explains the code for each algorithm, and readers can modify the code to suit their own needs. The book will be of interest to all researchers who intend to use R for machine learning, and those who are interested in the practical aspects of implementing learning algorithms for data analysis. Further, it will be particularly useful and informative for anyone who has struggled to relate the concepts of mathematics and statistics to machine learning.

In recent years portfolio optimization and construction methodologies have become an increasingly critical ingredient of asset and fund management, while at the same time portfolio risk assessment has become an essential ingredient in risk management. This trend will only accelerate in the coming years. This practical handbook fills the gap between current university instruction and current industry practice. It provides a comprehensive computationally-oriented treatment of modern portfolio optimization and construction methods using the powerful NUOPT for S-PLUS optimizer.

This book reviews some of today's more complex problems, and reflects some of the important research directions in the field. Twenty-nine authors - largely from Montreal's GERAD Multi-University Research Center and who work in areas of theoretical statistics, applied statistics, probability theory, and stochastic processes - present survey chapters on various theoretical and applied problems of importance and interest to researchers and students across a number of academic domains.

This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Multivariate Survival Analysis and Competing Risks introduces univariate survival analysis and extends it to the multivariate case. It covers competing risks and counting processes and provides many real-world examples, exercises, and R code. The text discusses survival data, survival distributions, frailty models, parametric methods, multivariate data and distributions, copulas, continuous failure, parametric likelihood inference, and non- and semi-parametric methods. There are many books covering survival analysis, but very few that cover the multivariate case in any depth. Written for a graduate-level audience in statistics/biostatistics, this book includes practical exercises and R code for the examples. The author is renowned for his clear writing style, and this book continues that trend. It is an excellent reference for graduate students and researchers looking for grounding in this burgeoning field of research.