This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable ("elementary") and complex variable ("analytic") methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.
Numerical Solution of Elliptic Differential Equations by Reduction to the Interface
This is the first book that deals with the numerical solution of elliptic partial differential equations by their reduction to the interface. Inheriting the beneficial features of finite element, boundary element and domain decomposition methods, the new approach exhibits linear-logarithmic complexity in the number of the interface degrees of freedom and it is well suited for parallel computations.
This text presents, for the first time at an elementary level, current topics in applied mathematics such as singular perturbation, nonlinear wave propagation, bifurcation, similarity methods and the numerical solution of partial differential equations. It emphasizes the interdependency of mathematics and its application to physical phenomena, and is written in a style accessible to readers with a wide range of interests and backgrounds.
The assessment of risks posed by natural hazards such as floods, droughts, earthquakes, tsunamis or cyclones, may not reflect the full range or magnitude of events possible. As human populations grow, especially in hazard-prone areas, methods for accurately assessing natural hazard risks are becoming increasingly important. Jonathan Nott describes the many methods used to reconstruct such hazards from natural long-term records. He demonstrates how long-term records are essential in gaining a realistic understanding of the variability of natural hazards...
This book covers all the basic concepts of statistics - descriptive study of data, probability, sampling variation, statistical inference and special techniques for handling data - and illustrates them with practical examples that stimulate students' appreciation of the subject. It pays careful attention to the role of assumptions so that readers can develop a sophisticated approach to interpreting statistical results. Each chapter begins by identifying the practical goal underlying topics covered and ends with a summary of key ideas and formulas.
