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The high-level language of R is recognized as one of the mostpowerful and flexible statistical software environments, and israpidly becoming the standard setting for quantitative analysis,statistics and graphics. R provides free access to unrivalledcoverage and cutting-edge applications, enabling the user to applynumerous statistical methods ranging from simple regression to timeseries or multivariate analysis. Building on the success of the author’s bestsellingStatistics: An Introduction using R, The R Book ispacked with worked examples, providing an all inclusive guide to R,ideal for novice and more accomplished users alike. The bookassumes no background in statistics or computing and introduces theadvantages of the R environment, detailing its applications in awide range of disciplines. Provides the first comprehensive reference manual for the Rlanguage, including practical guidance and full coverage of thegraphics facilities. Introduces all the statistical models covered by R, beginningwith simple classical tests such as chi-square and t-test. Proceeds to examine more advance methods, from regression andanalysis of variance, through to generalized linear models,generalized mixed models, time series, spatial statistics,multivariate statistics and much more. The R Book is aimed at undergraduates, postgraduates andprofessionals in science, engineering and medicine. It is alsoideal for students and professionals in statistics, economics,geography and the social sciences.
This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.
The present book is the outcome of efforts to introduce topological connectedness as one of the basic tools for the study of necessary conditions for an extremum. Apparently this monograph is the first book in the theory of maxima and minima where topological connectedness is used so widely for this purpose. Its application permits us to obtain new results in this sphere and to consider the classical results from a nonstandard point of view. Regarding the style of the present book it should be remarked that it is comparatively elementary. The author has made constant efforts to make the book as self-contained as possible. Certainly, familiarity with the basic facts of topology, functional analysis, and the theory of optimization is assumed. The book is written for applied mathematicians and graduate students interested in the theory of optimization and its applications. We present the synthesis of the well known Dybovitskii'-Milyutin ap proach for the study of necessary conditions for an extremum, based on functional analysis, and topological methods. This synthesis allows us to show that in some cases we have the following important result: if the Euler equation has no non trivial solution at a point of an extremum, then some inclusion is valid for the functionals belonging to the dual space. This general result is obtained for an optimization problem considered in a lin ear topological space. We also show an application of our result to some problems of nonlinear programming and optimal control.
Colloquia Mathematica Societatis Jânos Bolyai, 37: Finite and Infinite Sets, Vol. I focuses on the principles, operations, and approaches involved in finite and infinite sets. The selection first elaborates on essential chains and squares, cellular automata in trees, almost disjoint families of countable sets, and application of Lovasz local lemma. Discussions focus on deleting operations, number of all and self-dual E-chains, transversality of E-chains and E-squares, and binary E-chains and E-squares. The text then elaborates on induced subgraphs, inverse extremal digraph problems, two Sperner-type conditions, and minimal decomposition of all graphs with equinumerous vertices and edges into mutually isomorphic subgraphs. Topics include general digraph extremal problem, matrix graphs and quadratic forms, augmentation of matrices, set of attained densities, proof of the continuity theorem, and inverse extremal multigraph problems. The text examines circular flows in graphs, two-colorings of simple arrangements, monochromatic paths in infinite colored graphs, and graphs associated with an integral domain and their applications. The selection is a dependable reference for researchers interested in finite and infinite sets.
Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
This volume addresses some of the most important approaches to the following key questions in contemporary generative syntactic theory: What are the operations available for (syntactic) structure-building in natural languages? What are the triggers behind them? and Which constraints are involved in the operations? Internationally recognised scholars and young researchers propose new answers on the basis of detailed discussions of a wide range of phenomena (Gapping, Right-Node-Raising, Comparative Deletion, Across-The-Board movement, Tough-constructions, Nominalizations, Scope interactions, Wh-movement, A-movement, Case and Agreement relations, among others). Their discussions draw on evidence from a rich variety of languages, including Brazilian Portuguese, Bulgarian, Croatian, English, German, Icelandic, Japanese, Spanish, Vata, and Vietnamese. The proposals presented illustrate the shift in the locus of the explanation of linguistic phenomena that characterizes contemporary linguistic theory: a shift, in many cases, from a model which relies on properties of systems external to narrow syntax (such as the Lexicon or the Phonetic Form component) to one which relies on properties of the structure-building mechanisms themselves. The volume will interest researchers and students of theoretical linguistics from advanced undergraduate and above.
Get ready for C++20 with all you need to know for complete mastery! Your comprehensive and updated guide to one of the world’s most popular programming languages is here! Whether you’re a novice or expert, you’ll find what you need to get going with the latest features of C++20. The workhorse of programming languages, C++ gives you the utmost control of data usage and interface and resource allocation. If your job involves data, proficiency in C++ means you’re indispensable! This edition gives you 7 books in 1 for total C++ mastery. Inside, internationally renowned expert John Paul Mueller takes you from the fundamentals of working with objects and classes to writing applications that use paradigms not normally associated with C++, such as those used for functional programming strategies. The book also includes online resources such as source code. You discover how to use a C++ GNU compiler to build applications and even how to use your mobile device for coding. Conquer advanced programming and troubleshooting Streamline your code with lambda expressions Use C++ where you need it: for gaming, enterprise applications, and Web services Uncover object secrets including the use of design patterns Discover how to use functional programming techniques to make code concise and easy to read If you want to be your organization’s C++ guru, C++ All-In-One for Dummies is where it’s at!