This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization.

This book fulfils its aim of providing good and interesting material for advanced undergraduate study. This is probably one of the best books to begin learning about the sometimes complex topic of stochastic calculus and stochastic processes from a more mathematical approach. Some literature are often accused of unnecessarily complicating the subject when applied to areas of finance. With this book you are allowed to explore the rigorous side of stochastic calculus, yet main.

Contents: Introduction; Symplectic analysis; Fourier transform, stationary phase; Semiclassical Quantization; Semiclassical defect measures; Eigenvalues and eigenfunctions; Estimates for eigenfunctions; More on the symbol calculus; Quantum ergodicity; Quantizing symplectic transformations

These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Topics: WDVV equations and Frobenius manifolds; Polynomial solutions of WDVV; Symmetries of WDVV; etc.

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S.
These types of structures occur in our everyday life, that’s why we study them in this book.

This volume is a reprint with few corrections of the original work published in 1964. Starting with the notion of differential manifolds, the first six chapters lay a foundation for the study of Riemannian manifolds through specializing the theory of connections on principle bundles and affine connections. The geometry of Riemannian manifolds is emphasized, as opposed to global analysis, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory. Isometric immersions are treated elegantly and from a global viewpoint. In the final chapter are the more complicated estimates on which much of the research in Riemannian geometry is based: the Morse index theorem, Synge's theorems on closed geodesics, Rauch's comparison theorem, and the original proof of the Bishop volume-comparison theorem (with Myer's Theorem as a corollary).

Even with a limited mathematics background, readers can understand what statistical methods are and how they may be used to obtain the best possible results from experimental measurements and data. The author describes the physical bases on which statistical theories are developed, and derives from them useful mathematical results and formulas for the evaluation and analysis of experimental data. Special mathematical techniques are explained as they are needed.

The need to validate an analytical or bioanalytical method is encountered by analysts in the pharmaceutical industry on an almost daily basis, because adequately validated methods are a necessity for approvable regulatory filings. What constitutes a validated method, however, is subject to analyst interpretation because there is no universally accepted industry practice for assay validation. This book is intended to serve as a guide to the analyst in terms of the issues and parameters that must be considered in the development and validation of analytical methods. In addition to the critical issues surrounding method validation, this book also deals with other related factors such as method development, data acquisition, automation, cleaning validation and regulatory considerations.