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

Stochastic Models of Financial Mathematics

1st Edition
October 12, 2016
Vigirdas Mackevicius
English
Hardback
9 7 8 1 7 8 5 4 8 1 9 8 7
eBook
9 7 8 0 0 8 1 0 2 0 8 6 9

This book presents a short introduction to continuous-time financial models. An overview of the basics of stochastic analysis precedes a focus on the Black–Scholes and interest rate models. Other topics covered include self-financing strategies, option pricing, exotic options and risk-neutral probabilities. Vasicek, Cox−Ingersoll−Ross, and Heath–Jarrow–Morton interest rate models are also explored.The author presents practitioners with a basic introduction, with more rigorous information provided for mathematicians. The reader is assumed to be familiar with the basics of probability theory. Some basic knowledge of stochastic integration and differential equations theory is preferable, although all preliminary information is given in the first part of the book. Some relatively simple theoretical exercises are also provided.

Ruin Probabilities

1st Edition
October 10, 2016
Yuliya Mishura + 1 more
English
Hardback
9 7 8 1 7 8 5 4 8 2 1 8 2
eBook
9 7 8 0 0 8 1 0 2 0 9 8 2

Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments.

Analysis for Time-to-Event Data under Censoring and Truncation

1st Edition
September 26, 2016
Hongsheng Dai + 1 more
English
Paperback
9 7 8 0 1 2 8 0 5 4 8 0 2
eBook
9 7 8 0 0 8 1 0 1 0 0 8 2

Survival Analysis for Bivariate Truncated Data provides readers with a comprehensive review on the existing works on survival analysis for truncated data, mainly focusing on the estimation of univariate and bivariate survival function. The most distinguishing feature of survival data is known as censoring, which occurs when the survival time can only be exactly observed within certain time intervals. A second feature is truncation, which is often deliberate and usually due to selection bias in the study design. Truncation presents itself in different ways. For example, left truncation, which is often due to a so-called late entry bias, occurs when individuals enter a study at a certain age and are followed from this delayed entry time. Right truncation arises when only individuals who experienced the event of interest before a certain time point can be observed. Analyzing truncated survival data without considering the potential selection bias may lead to seriously biased estimates of the time to event of interest and the impact of risk factors.

An Invitation to Applied Mathematics

1st Edition
September 24, 2016
Carmen Chicone
English
Hardback
9 7 8 0 1 2 8 0 4 1 5 3 6
eBook
9 7 8 0 1 2 8 0 4 1 5 4 3

An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics.

Fractional Calculus and Fractional Processes with Applications to Financial Economics

1st Edition
September 22, 2016
Hasan Fallahgoul + 2 more
English
Hardback
9 7 8 0 1 2 8 0 4 2 4 8 9
eBook
9 7 8 0 1 2 8 0 4 2 8 4 7

Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization.

Differential Equations with Mathematica

4th Edition
September 13, 2016
Martha L. Abell + 1 more
English
eBook
9 7 8 0 1 2 8 0 4 7 7 7 4

Differential Equations with Mathematica, Fourth Edition is a supplementing reference which uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists. Mathematica’s diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica’s built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, mathematica can be used to perform the calculations encountered when solving a differential equation. Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica’s outstanding graphics capabilities.

Cognitive Computing: Theory and Applications

1st Edition
Volume 35
September 9, 2016
Vijay V Raghavan + 3 more
English
Hardback
9 7 8 0 4 4 4 6 3 7 4 4 4
eBook
9 7 8 0 4 4 4 6 3 7 5 1 2

Cognitive Computing: Theory and Applications, written by internationally renowned experts, focuses on cognitive computing and its theory and applications, including the use of cognitive computing to manage renewable energy, the environment, and other scarce resources, machine learning models and algorithms, biometrics, Kernel Based Models for transductive learning, neural networks, graph analytics in cyber security, neural networks, data driven speech recognition, and analytical platforms to study the brain-computer interface.

Introduction to Robust Estimation and Hypothesis Testing

4th Edition
September 2, 2016
Rand R. Wilcox
English
eBook
9 7 8 0 1 2 8 0 4 7 8 1 1

Introduction to Robust Estimating and Hypothesis Testing, 4th Editon, is a ‘how-to’ on the application of robust methods using available software. Modern robust methods provide improved techniques for dealing with outliers, skewed distribution curvature and heteroscedasticity that can provide substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. Since the last edition, there have been numerous advances and improvements. They include new techniques for comparing groups and measuring effect size as well as new methods for comparing quantiles. Many new regression methods have been added that include both parametric and nonparametric techniques. The methods related to ANCOVA have been expanded considerably. New perspectives related to discrete distributions with a relatively small sample space are described as well as new results relevant to the shift function. The practical importance of these methods is illustrated using data from real world studies. The R package written for this book now contains over 1200 functions. New to this edition 35% revised content Covers many new and improved R functions New techniques that deal with a wide range of situations

Biostatistics and Computer-based Analysis of Health Data using Stata

1st Edition
August 24, 2016
Christophe Lalanne + 1 more
English
Hardback
9 7 8 1 7 8 5 4 8 1 4 2 0
eBook
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This volume of the Biostatistics and Health Sciences Set focuses on statistics applied to clinical research. The use of Stata for data management and statistical modeling is illustrated using various examples. Many aspects of data processing and statistical analysis of cross-sectional and experimental medical data are covered, including regression models commonly found in medical statistics. This practical book is primarily intended for health researchers with basic knowledge of statistical methodology. Assuming basic concepts, the authors focus on the practice of biostatistical methods essential to clinical research, epidemiology and analysis of biomedical data (including comparison of two groups, analysis of categorical data, ANOVA, linear and logistic regression, and survival analysis). The use of examples from clinical trials and epideomological studies provide the basis for a series of practical exercises, which provide instruction and familiarize the reader with essential Stata packages and commands.

Theory and Computation of Tensors

1st Edition
August 12, 2016
Yimin Wei + 1 more
English
Paperback
9 7 8 0 1 2 8 0 3 9 5 3 3
eBook
9 7 8 0 1 2 8 0 3 9 8 0 9

Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships.

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