Modern Analysis Series – serie

The history of mathematics is, to a considerable extent, connected with the study of solutions of the equation f(x)=a=const for functions f(x) of one real or complex variable. Therefore, it is surprising that we know very little about solutions of u(x,y)=A=const for functions of two real variables. These two solutions, called level of sets, are very important with regard to applications in physics, biology and economics as they make a map of appropriate processes described by the function u(x,y) for given parameters (x,y). This text explores a concept, Gamma-lines, which generalizes the concept of levels of sets and, at the same time, the concept of a-points. The authors provide a book on Gamma-lines for the broad specialist and show the large range of their field of applications. The general methods proposed in this volume are useful for both physicists and engineers.

Although the basic statistical theory behind modern genetics is not very difficult, most statistical genetics papers are not easy to read for beginners in the field, and formulae quickly become very tedious to fit a particular area of application. Introduction to Statistical Methods in Modern Genetics distinguishes between the necessary and unnecessary complexity in a presentation designed for graduate-level statistics students. The author keeps derivations simple, but does so without losing the mathematical details. He also provides the required background in modern genetics for those looking forward to entering this arena. Along with some of the statistical tools important in genetics applications, students will learn:How a gene is found How scientists have separated the genetic and environmental aspects of a person's intelligence How genetics are used in agriculture to improve crops and domestic animals What a DNA fingerprint is and why there are controversies about itAlthough the author assumes students have a foundation in basic statistics, an appendix provides the necessary background beyond the elementary, including multinomial distributions, inference on frequency tables, and discriminant analysis. With clear explanations, a multitude of figures, and exercise sets in each chapter, this text forms an outstanding entrée into the rapidly expanding world of genetic data analysis.

The history of mathematics is, to a considerable extent, connected with the study of solutions of the equation f(x)=a=const for functions f(x) of one real or complex variable. Therefore, it is surprising that we know very little about solutions of u(x,y)=A=const for functions of two real variables. These two solutions, called level of sets, are very important with regard to applications in physics, biology and economics as they make a map of appropriate processes described by the function u(x,y) for given parameters (x,y). This text explores a concept, Gamma-lines, which generalizes the concept of levels of sets and, at the same time, the concept of a-points. The authors provide a book on Gamma-lines for the broad specialist and show the large range of their field of applications. The general methods proposed in this volume are useful for both physicists and engineers.

Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole.To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison.Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.

Although the basic statistical theory behind modern genetics is not very difficult, most statistical genetics papers are not easy to read for beginners in the field, and formulae quickly become very tedious to fit a particular area of application. Introduction to Statistical Methods in Modern Genetics distinguishes between the necessary and unnecessary complexity in a presentation designed for graduate-level statistics students. The author keeps derivations simple, but does so without losing the mathematical details. He also provides the required background in modern genetics for those looking forward to entering this arena. Along with some of the statistical tools important in genetics applications, students will learn:How a gene is found How scientists have separated the genetic and environmental aspects of a person's intelligence How genetics are used in agriculture to improve crops and domestic animals What a DNA fingerprint is and why there are controversies about itAlthough the author assumes students have a foundation in basic statistics, an appendix provides the necessary background beyond the elementary, including multinomial distributions, inference on frequency tables, and discriminant analysis. With clear explanations, a multitude of figures, and exercise sets in each chapter, this text forms an outstanding entrée into the rapidly expanding world of genetic data analysis.