Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

Books Journals

Computer Arithmetic and Formal Proofs

1st Edition
November 16, 2017
Sylvie Boldo + 1 more
English
Hardback
9 7 8 1 7 8 5 4 8 1 1 2 3
eBook
9 7 8 0 0 8 1 0 1 1 7 0 6

Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs. This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation.

Occupancy Estimation and Modeling

2nd Edition
November 13, 2017
Darryl I. MacKenzie + 5 more
English
Paperback
9 7 8 0 1 2 8 1 4 6 9 1 0
eBook
9 7 8 0 1 2 4 0 7 2 4 5 9

Occupancy Estimation and Modeling: Inferring Patterns and Dynamics of Species Occurrence, Second Edition, provides a synthesis of model-based approaches for analyzing presence-absence data, allowing for imperfect detection. Beginning from the relatively simple case of estimating the proportion of area or sampling units occupied at the time of surveying, the authors describe a wide variety of extensions that have been developed since the early 2000s. This provides an improved insight about species and community ecology, including, detection heterogeneity; correlated detections; spatial autocorrelation; multiple states or classes of occupancy; changes in occupancy over time; species co-occurrence; community-level modeling, and more. Occupancy Estimation and Modeling: Inferring Patterns and Dynamics of Species Occurrence, Second Edition has been greatly expanded and detail is provided regarding the estimation methods and examples of their application are given. Important study design recommendations are also covered to give a well rounded view of modeling.

Mathematical Optimization Terminology

1st Edition
November 10, 2017
Andre A. Keller
English
Paperback
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eBook
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Mathematical Optimization Terminology: A Comprehensive Glossary of Terms is a practical book with the essential formulations, illustrative examples, real-world applications and main references on the topic. This book helps readers gain a more practical understanding of optimization, enabling them to apply it to their algorithms. This book also addresses the need for a practical publication that introduces these concepts and techniques.

Handbook of Statistical Analysis and Data Mining Applications

2nd Edition
November 9, 2017
Ken Yale + 2 more
English
eBook
9 7 8 0 1 2 4 1 6 6 4 5 5

Handbook of Statistical Analysis and Data Mining Applications, Second Edition, is a comprehensive professional reference book that guides business analysts, scientists, engineers and researchers, both academic and industrial, through all stages of data analysis, model building and implementation. The handbook helps users discern technical and business problems, understand the strengths and weaknesses of modern data mining algorithms and employ the right statistical methods for practical application. This book is an ideal reference for users who want to address massive and complex datasets with novel statistical approaches and be able to objectively evaluate analyses and solutions. It has clear, intuitive explanations of the principles and tools for solving problems using modern analytic techniques and discusses their application to real problems in ways accessible and beneficial to practitioners across several areas—from science and engineering, to medicine, academia and commerce.

Disease Modelling and Public Health, Part B

1st Edition
Volume 37
October 31, 2017
Arni S.R. Srinivasa Rao + 2 more
English
Hardback
9 7 8 0 4 4 4 6 3 9 7 5 2
eBook
9 7 8 0 4 4 4 6 3 9 7 6 9

Handbook of Statistics: Disease Modelling and Public Health, Part B, Volume 37 addresses new challenges in existing and emerging diseases. As a two part volume, this title covers an extensive range of techniques in the field, with this book including chapters on Reaction diffusion equations and their application on bacterial communication, Spike and slab methods in disease modeling, Mathematical modeling of mass screening and parameter estimation, Individual-based and agent-based models for infectious disease transmission and evolution: an overview, and a section on Visual Clustering of Static and Dynamic High Dimensional Data. This volume covers the lack of availability of complete data relating to disease symptoms and disease epidemiology, one of the biggest challenges facing vaccine developers, public health planners, epidemiologists and health sector researchers.

Writing Small Omegas

1st Edition
October 24, 2017
Alberto Cogliati
English
Paperback
9 7 8 0 1 2 8 1 4 2 4 4 8
eBook
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Writing Small Omegas: Elie Cartan's Contributions to the Theory of Continuous Groups 1894-1926 provides a general account of Lie’s theory of finite continuous groups, critically examining Cartan’s doctoral attempts to rigorously classify simple Lie algebras, including the use of many unpublished letters. It evaluates pioneering attempts to generalize Lie's classical ideas to the infinite-dimensional case in the works of Lie, Engel, Medolaghi and Vessiot. Within this context, Cartan’s groundbreaking contributions in continuous group theory, particularly in his characteristic and unique recourse to exterior differential calculus, are introduced and discussed at length. The work concludes by discussing Cartan’s contributions to the structural theory of infinite continuous groups, his method of moving frames, and the genesis of his geometrical theory of Lie groups.

Maximum Principles for the Hill's Equation

1st Edition
October 19, 2017
Alberto Cabada + 2 more
English
Paperback
9 7 8 0 1 2 8 0 4 1 1 7 8
eBook
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Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,…) and for problems with parametric dependence. The authors discuss the properties of the related Green’s functions coupled with different boundary value conditions. In addition, they establish the equations’ relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included.

Disease Modelling and Public Health, Part A

1st Edition
Volume 36
October 13, 2017
Arni S.R. Srinivasa Rao + 2 more
English
Hardback
9 7 8 0 4 4 4 6 3 9 6 8 4
eBook
9 7 8 0 4 4 4 6 3 9 6 9 1

Disease Modelling and Public Health, Part A, Volume 36 addresses new challenges in existing and emerging diseases with a variety of comprehensive chapters that cover Infectious Disease Modeling, Bayesian Disease Mapping for Public Health, Real time estimation of the case fatality ratio and risk factor of death, Alternative Sampling Designs for Time-To-Event Data with Applications to Biomarker Discovery in Alzheimer's Disease, Dynamic risk prediction for cardiovascular disease: An illustration using the ARIC Study, Theoretical advances in type 2 diabetes, Finite Mixture Models in Biostatistics, and Models of Individual and Collective Behavior for Public Health Epidemiology. As a two part volume, the series covers an extensive range of techniques in the field. It present a vital resource for statisticians who need to access a number of different methods for assessing epidemic spread in population, or in formulating public health policy.

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology

1st Edition
September 19, 2017
Abdon Atangana
English
Paperback
9 7 8 0 1 2 8 0 9 6 7 0 3
eBook
9 7 8 0 1 2 8 0 9 7 9 6 0

Fractional Operators with Constant and Variable Order with Application to Geo-hydrology provides a physical review of fractional operators, fractional variable order operators, and uncertain derivatives to groundwater flow and environmental remediation. It presents a formal set of mathematical equations for the description of groundwater flow and pollution problems using the concept of non-integer order derivative. Both advantages and disadvantages of models with fractional operators are discussed. Based on the author’s analyses, the book proposes new techniques for groundwater remediation, including guidelines on how chemical companies can be positioned in any city to avoid groundwater pollution.

Means in Mathematical Analysis

1st Edition
September 14, 2017
Gheorghe Toader + 1 more
English
Paperback
9 7 8 0 1 2 8 1 1 0 8 0 5
eBook
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Means in Mathematical Analysis addresses developments in global analysis, non-linear analysis, and the many problems of associated fields, including dynamical systems, ergodic theory, combinatorics, differential equations, approximation theory, analytic inequalities, functional equations and probability theory. The series comprises highly specialized research monographs written by eminent scientists, handbooks and selected multi-contributor reference works (edited volumes), bringing together an extensive body of information. It deals with the fundamental interplay of nonlinear analysis with other headline domains, particularly geometry and analytic number theory, within the mathematical sciences.

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