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

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

1st Edition
May 17, 2016
Michal Feckan + 1 more
English
Hardback
9 7 8 0 1 2 8 0 4 2 9 4 6
eBook
9 7 8 0 1 2 8 0 4 3 6 4 6

Poincaré-Andronov-Me... Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switch... boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity.

Data Gathering, Analysis and Protection of Privacy Through Randomized Response Techniques: Qualitative and Quantitative Human Traits

1st Edition
Volume 34
April 13, 2016
Arijit Chaudhuri + 2 more
English
Hardback
9 7 8 0 4 4 4 6 3 5 7 0 9
eBook
9 7 8 0 4 4 4 6 3 5 7 1 6

Data Gathering, Analysis and Protection of Privacy through Randomized Response Techniques: Qualitative and Quantitative Human Traits tackles how to gather and analyze data relating to stigmatizing human traits. S.L. Warner invented RRT and published it in JASA, 1965. In the 50 years since, the subject has grown tremendously, with continued growth. This book comprehensively consolidates the literature to commemorate the inception of RR.

Geometric Measure Theory

5th Edition
April 7, 2016
Frank Morgan
English
Hardback
9 7 8 0 1 2 8 0 4 4 8 9 6
eBook
9 7 8 0 1 2 8 0 4 5 2 7 5

Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe. The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers. Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincaré conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications.

Introduction to Finite and Infinite Dimensional Lie (Super)algebras

1st Edition
April 4, 2016
Neelacanta Sthanumoorthy
English
Hardback
9 7 8 0 1 2 8 0 4 6 7 5 3
eBook
9 7 8 0 1 2 8 0 4 6 8 3 8

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras.

Environmental Data Analysis with MatLab

2nd Edition
March 7, 2016
William Menke + 1 more
English
Hardback
9 7 8 0 1 2 8 0 4 4 8 8 9
eBook
9 7 8 0 1 2 8 0 4 5 5 0 3

Environmental Data Analysis with MatLab is a new edition that expands fundamentally on the original with an expanded tutorial approach, new crib sheets, and problem sets providing a clear learning path for students and researchers working to analyze real data sets in the environmental sciences. Since publication of the bestselling Environmental Data Analysis with MATLAB®, many advances have been made in environmental data analysis. One only has to consider the global warming debate to realize how critically important it is to be able to derive clear conclusions from often noisy data drawn from a broad range of sources. The work teaches the basics of the underlying theory of data analysis and then reinforces that knowledge with carefully chosen, realistic scenarios. MATLAB®, a commercial data processing environment, is used in these scenarios. Significant content is devoted to teaching how it can be effectively used in an environmental data analysis setting. This new edition, though written in a self-contained way, is supplemented with data and MATLAB® scripts that can be used as a data analysis tutorial. New features include boxed crib sheets to help identify major results and important formulas and give brief advice on how and when they should be used. Numerical derivatives and integrals are derived and illustrated. Includes log-log plots with further examples of their use. Discusses new datasets on precipitation and stream flow. Topical enhancement applies the chi-squared test to the results of the generalized least squares method. New coverage of cluster analysis and approximation techniques that are widely applied in data analysis, including Taylor Series and low-order polynomial approximations; non-linear least-squares with Newton’s method; and pre-calculation and updating techniques applicable to real time data acquisition.

Elementary Linear Algebra

5th Edition
February 25, 2016
Stephen Andrilli + 1 more
English
eBook
9 7 8 0 1 2 8 0 1 0 4 7 1

Elementary Linear Algebra, 5th edition, by Stephen Andrilli and David Hecker, is a textbook for a beginning course in linear algebra for sophomore or junior mathematics majors. This text provides a solid introduction to both the computational and theoretical aspects of linear algebra. The textbook covers many important real-world applications of linear algebra, including graph theory, circuit theory, Markov chains, elementary coding theory, least-squares polynomials and least-squares solutions for inconsistent systems, differential equations, computer graphics and quadratic forms. Also, many computational techniques in linear algebra are presented, including iterative methods for solving linear systems, LDU Decomposition, the Power Method for finding eigenvalues, QR Decomposition, and Singular Value Decomposition and its usefulness in digital imaging. The most unique feature of the text is that students are nurtured in the art of creating mathematical proofs using linear algebra as the underlying context. The text contains a large number of worked out examples, as well as more than 970 exercises (with over 2600 total questions) to give students practice in both the computational aspects of the course and in developing their proof-writing abilities. Every section of the text ends with a series of true/false questions carefully designed to test the students’ understanding of the material. In addition, each of the first seven chapters concludes with a thorough set of review exercises and additional true/false questions. Supplements to the text include an Instructor’s Manual with answers to all of the exercises in the text, and a Student Solutions Manual with detailed answers to the starred exercises in the text. Finally, there are seven additional web sections available on the book’s website to instructors who adopt the text.

Theory of Approximate Functional Equations

1st Edition
February 23, 2016
Madjid Eshaghi Gordji + 1 more
English
Hardback
9 7 8 0 1 2 8 0 3 9 2 0 5
eBook
9 7 8 0 1 2 8 0 3 9 7 1 7

Presently no other book deals with the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups. Moreover, in most stability theorems for functional equations, the completeness of the target space of the unknown functions contained in the equation is assumed. Recently, the question, whether the stability of a functional equation implies this completeness, has been investigated by several authors. In this book the authors investigate these developments in the theory of approximate functional equations.

The Gradient Test

1st Edition
February 2, 2016
Artur Lemonte
English
Paperback
9 7 8 0 1 2 8 0 3 5 9 6 2
eBook
9 7 8 0 1 2 8 0 3 6 1 3 6

The Gradient Test: Another Likelihood-Based Test presents the latest on the gradient test, a large-sample test that was introduced in statistics literature by George R. Terrell in 2002. The test has been studied by several authors, is simply computed, and can be an interesting alternative to the classical large-sample tests, namely, the likelihood ratio (LR), Wald (W), and Rao score (S) tests. Due to the large literature about the LR, W and S tests, the gradient test is not frequently used to test hypothesis. The book covers topics on the local power of the gradient test, the Bartlett-corrected gradient statistic, the gradient statistic under model misspecification, and the robust gradient-type bounded-influence test.

Financial Mathematics

1st Edition
January 25, 2016
Yuliya Mishura
English
Hardback
9 7 8 1 7 8 5 4 8 0 4 6 1
eBook
9 7 8 0 0 8 1 0 0 4 8 8 3

Finance Mathematics is devoted to financial markets both with discrete and continuous time, exploring how to make the transition from discrete to continuous time in option pricing. This book features a detailed dynamic model of financial markets with discrete time, for application in real-world environments, along with Martingale measures and martingale criterion and the proven absence of arbitrage. With a focus on portfolio optimization, fair pricing, investment risk, and self-finance, the authors provide numerical methods for solutions and practical financial models, enabling you to solve problems both from mathematical and from financial point of view.

Advances in Mathematical Chemistry and Applications: Volume 2

1st Edition
January 18, 2016
Subhash C. Basak + 2 more
English
Paperback
9 7 8 1 6 8 1 0 8 0 5 3 6
eBook
9 7 8 1 6 8 1 0 8 0 5 2 9

Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have brought together 27 chapters written by 68 internationally renowned experts in these two volumes. Each volume comprises a wise integration of mathematical and chemical concepts and covers numerous applications in the field of drug discovery, bioinformatics, chemoinformatics, computational biology, mathematical proteomics, and ecotoxicology. Volume 2 explores deeper the topics introduced in Volume 1, with numerous additional topics such as topological approaches for classifying fullerene isomers; chemical reaction networks; discrimination of small molecules using topological molecular descriptors; GRANCH methods for the mathematical characterization of DNA, RNA and protein sequences; linear regression methods and Bayesian techniques; in silico toxicity prediction methods; drug design; integration of bioinformatics and systems biology, molecular docking, and molecular dynamics; metalloenzyme models; protein folding models; molecular periodicity; generalized topologies and their applications; and many more.

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