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Combinatorial Nullstellensatz With Applications to Graph Colouring

Combinatorial Nullstellensatz With Applications to Graph Colouring

Combinatorial Nullstellensatz is a novel theorem in algebra introduced by Noga Alon to tackle combinatorial problems in diverse areas of mathematics. This book focuses on the applications of this theorem to graph colouring. A key step in the applications of Combinatorial Nullstellensatz is to show that the coefficient of a certain monomial in the expansion of a polynomial is nonzero. The major part of the book concentrates on three methods for calculating the coefficients: Alon-Tarsi orientation: The task is to show that a graph has an orientation with given maximum out-degree and for which the number of even Eulerian sub-digraphs is different from the number of odd Eulerian sub-digraphs. In particular this method is used to show that a graph whose edge set decomposes into a Hamilton cycle and vertex-disjoint triangles is 3-choosable and that every planar graph has a matching whose deletion results in a 4-choosable graph. Interpolation formula for the coefficient: This method is in particular used to show that toroidal grids of even order are 3-choosable r-edge colourable r-regular planar graphs are r-edge choosable and complete graphs of order p+1 where p is a prime are p-edge choosable. Coefficients as the permanents of matrices: This method is in particular used in the study of the list version of vertex-edge weighting and to show that every graph is (2 3)-choosable. It is suited as a reference book for a graduate course in mathematics. | Combinatorial Nullstellensatz With Applications to Graph Colouring

GBP 52.99
1

Computational Aspects of Polynomial Identities Volume l Kemer's Theorems 2nd Edition

Computational Aspects of Polynomial Identities Volume l Kemer's Theorems 2nd Edition

Computational Aspects of Polynomial Identities: Volume l Kemer’s Theorems 2nd Edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. This edition gives all the details involved in Kemer’s proof of Specht’s conjecture for affine PI-algebras in characteristic 0. The book first discusses the theory needed for Kemer’s proof including the featured role of Grassmann algebra and the translation to superalgebras. The authors develop Kemer polynomials for arbitrary varieties as tools for proving diverse theorems. They also lay the groundwork for analogous theorems that have recently been proved for Lie algebras and alternative algebras. They then describe counterexamples to Specht’s conjecture in characteristic p as well as the underlying theory. The book also covers Noetherian PI-algebras Poincaré–Hilbert series Gelfand–Kirillov dimension the combinatoric theory of affine PI-algebras and homogeneous identities in terms of the representation theory of the general linear group GL. Through the theory of Kemer polynomials this edition shows that the techniques of finite dimensional algebras are available for all affine PI-algebras. It also emphasizes the Grassmann algebra as a recurring theme including in Rosset’s proof of the Amitsur–Levitzki theorem a simple example of a finitely based T-ideal the link between algebras and superalgebras and a test algebra for counterexamples in characteristic p. | Computational Aspects of Polynomial Identities Volume l Kemer's Theorems 2nd Edition

GBP 59.99
1

Galois Theory

Galois Theory

Since 1973 Galois theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory Fifth Edition mathematician and popular science author Ian Stewart updates this well-established textbook for today’s algebra students. New to the Fifth Edition Reorganised and revised Chapters 7 and 13 New exercises and examples Expanded updated references Further historical material on figures besides Galois: Omar Khayyam Vandermonde Ruffini and Abel A new final chapter discussing other directions in which Galois theory has developed: the inverse Galois problem differential Galois theory and a (very) brief introduction to p-adic Galois representations This bestseller continues to deliver a rigorous yet engaging treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs formulas and theorems.

GBP 52.99
1

Higher Order Derivatives

Higher Order Derivatives

The concept of higher order derivatives is useful in many branches of mathematics and its applications. As they are useful in many places nth order derivatives are often defined directly. Higher Order Derivatives discusses these derivatives their uses and the relations among them. It covers higher order generalized derivatives including the Peano d. l. V. P. and Abel derivatives; along with the symmetric and unsymmetric Riemann Cesàro Borel LP- and Laplace derivatives. Although much work has been done on the Peano and de la Vallée Poussin derivatives there is a large amount of work to be done on the other higher order derivatives as their properties remain often virtually unexplored. This book introduces newcomers interested in the field of higher order derivatives to the present state of knowledge. Basic advanced real analysis is the only required background and although the special Denjoy integral has been used knowledge of the Lebesgue integral should suffice.

GBP 59.99
1

Text Analytics An Introduction to the Science and Applications of Unstructured Information Analysis

Text Analytics An Introduction to the Science and Applications of Unstructured Information Analysis

Text Analytics: An Introduction to the Science and Applications of Unstructured Information Analysis is a concise and accessible introduction to the science and applications of text analytics (or text mining) which enables automatic knowledge discovery from unstructured information sources for both industrial and academic purposes. The book introduces the main concepts models and computational techniques that enable the reader to solve real decision-making problems arising from textual and/or documentary sources. Features: Easy-to-follow step-by-step concepts and methods Every chapter is introduced in a very gentle and intuitive way so students can understand the WHYs WHAT-IFs WHAT-IS-THIS-FORs HOWs etc. by themselves Practical programming exercises in Python for each chapter Includes theory and practice for every chapter summaries practical coding exercises for target problems QA and sample code and data available for download at https://www. routledge. com/Atkinson-Abutridy/p/book/9781032249797 | Text Analytics An Introduction to the Science and Applications of Unstructured Information Analysis

GBP 44.99
1

Inferential Models Reasoning with Uncertainty

Inferential Models Reasoning with Uncertainty

A New Approach to Sound Statistical ReasoningInferential Models: Reasoning with Uncertainty introduces the authors’ recently developed approach to inference: the inferential model (IM) framework. This logical framework for exact probabilistic inference does not require the user to input prior information. The authors show how an IM produces meaningful prior-free probabilistic inference at a high level. The book covers the foundational motivations for this new IM approach the basic theory behind its calibration properties a number of important applications and new directions for research. It discusses alternative meaningful probabilistic interpretations of some common inferential summaries such as p-values. It also constructs posterior probabilistic inferential summaries without a prior and Bayes’ formula and offers insight on the interesting and challenging problems of conditional and marginal inference. This book delves into statistical inference at a foundational level addressing what the goals of statistical inference should be. It explores a new way of thinking compared to existing schools of thought on statistical inference and encourages you to think carefully about the correct approach to scientific inference. | Inferential Models Reasoning with Uncertainty

GBP 44.99
1

Advanced Number Theory with Applications

Advanced Number Theory with Applications

Exploring one of the most dynamic areas of mathematics Advanced Number Theory with Applications covers a wide range of algebraic analytic combinatorial cryptographic and geometric aspects of number theory. Written by a recognized leader in algebra and number theory the book includes a page reference for every citing in the bibliography and more than 1 500 entries in the index so that students can easily cross-reference and find the appropriate data. With numerous examples throughout the text begins with coverage of algebraic number theory binary quadratic forms Diophantine approximation arithmetic functions p-adic analysis Dirichlet characters density and primes in arithmetic progression. It then applies these tools to Diophantine equations before developing elliptic curves and modular forms. The text also presents an overview of Fermat’s Last Theorem (FLT) and numerous consequences of the ABC conjecture including Thue–Siegel–Roth theorem Hall’s conjecture the Erdös–Mollin-–Walsh conjecture and the Granville–Langevin Conjecture. In the appendix the author reviews sieve methods such as Eratothesenes’ Selberg’s Linnik’s and Bombieri’s sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring. By focusing on salient techniques in number theory this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.

GBP 69.99
1

Software Engineering for Science

Software Engineering for Science

Software Engineering for Science provides an in-depth collection of peer-reviewed chapters that describe experiences with applying software engineering practices to the development of scientific software. It provides a better understanding of how software engineering is and should be practiced and which software engineering practices are effective for scientific software. The book starts with a detailed overview of the Scientific Software Lifecycle and a general overview of the scientific software development process. It highlights key issues commonly arising during scientific software development as well as solutions to these problems. The second part of the book provides examples of the use of testing in scientific software development including key issues and challenges. The chapters then describe solutions and case studies aimed at applying testing to scientific software development efforts. The final part of the book provides examples of applying software engineering techniques to scientific software including not only computational modeling but also software for data management and analysis. The authors describe their experiences and lessons learned from developing complex scientific software in different domains. About the EditorsJeffrey Carver is an Associate Professor in the Department of Computer Science at the University of Alabama. He is one of the primary organizers of the workshop series on Software Engineering for Science (http://www. SE4Science. org/workshops). Neil P. Chue Hong is Director of the Software Sustainability Institute at the University of Edinburgh. His research interests include barriers and incentives in research software ecosystems and the role of software as a research object. George K. Thiruvathukal is Professor of Computer Science at Loyola University Chicago and Visiting Faculty at Argonne National Laboratory. His current research is focused on software metrics in open source mathematical and scientific software.

GBP 44.99
1

Understanding Regression Analysis A Conditional Distribution Approach

Understanding Regression Analysis A Conditional Distribution Approach

Understanding Regression Analysis unifies diverse regression applications including the classical model ANOVA models generalized models including Poisson Negative binomial logistic and survival neural networks and decision trees under a common umbrella - namely the conditional distribution model. It explains why the conditional distribution model is the correct model and it also explains (proves) why the assumptions of the classical regression model are wrong. Unlike other regression books this one from the outset takes a realistic approach that all models are just approximations. Hence the emphasis is to model Nature’s processes realistically rather than to assume (incorrectly) that Nature works in particular constrained ways. Key features of the book include: Numerous worked examples using the R software Key points and self-study questions displayed just-in-time within chapters Simple mathematical explanations (baby proofs) of key concepts Clear explanations and applications of statistical significance (p-values) incorporating the American Statistical Association guidelines Use of data-generating process terminology rather than population Random-X framework is assumed throughout (the fixed-X case is presented as a special case of the random-X case) Clear explanations of probabilistic modelling including likelihood-based methods Use of simulations throughout to explain concepts and to perform data analyses This book has a strong orientation towards science in general as well as chapter-review and self-study questions so it can be used as a textbook for research-oriented students in the social biological and medical and physical and engineering sciences. As well its mathematical emphasis makes it ideal for a text in mathematics and statistics courses. With its numerous worked examples it is also ideally suited to be a reference book for all scientists. | Understanding Regression Analysis A Conditional Distribution Approach

GBP 39.99
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Linear Regression Models Applications in R

Linear Regression Models Applications in R

Research in social and behavioral sciences has benefited from linear regression models (LRMs) for decades to identify and understand the associations among a set of explanatory variables and an outcome variable. Linear Regression Models: Applications in R provides you with a comprehensive treatment of these models and indispensable guidance about how to estimate them using the R software environment. After furnishing some background material the author explains how to estimate simple and multiple LRMs in R including how to interpret their coefficients and understand their assumptions. Several chapters thoroughly describe these assumptions and explain how to determine whether they are satisfied and how to modify the regression model if they are not. The book also includes chapters on specifying the correct model adjusting for measurement error understanding the effects of influential observations and using the model with multilevel data. The concluding chapter presents an alternative model—logistic regression—designed for binary or two-category outcome variables. The book includes appendices that discuss data management and missing data and provides simulations in R to test model assumptions. Features Furnishes a thorough introduction and detailed information about the linear regression model including how to understand and interpret its results test assumptions and adapt the model when assumptions are not satisfied. Uses numerous graphs in R to illustrate the model’s results assumptions and other features. Does not assume a background in calculus or linear algebra rather an introductory statistics course and familiarity with elementary algebra are sufficient. Provides many examples using real-world datasets relevant to various academic disciplines. Fully integrates the R software environment in its numerous examples. The book is aimed primarily at advanced undergraduate and graduate students in social behavioral health sciences and related disciplines taking a first course in linear regression. It could also be used for self-study and would make an excellent reference for any researcher in these fields. The R code and detailed examples provided throughout the book equip the reader with an excellent set of tools for conducting research on numerous social and behavioral phenomena. John P. Hoffmann is a professor of sociology at Brigham Young University where he teaches research methods and applied statistics courses and conducts research on substance use and criminal behavior. | Linear Regression Models Applications in R

GBP 66.99
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