Lang, Serge

Undergraduate Algebra, 3rd ed

Series: Undergraduate Texts in Mathematics,
2005, XI, 408 p., Hardcover
ISBN: 0-387-22025-9

About this textbook

Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text.

For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyderfs proof of the Mason-Stothers polynomial abc theorem.

Table of contents

* Foreword * The Integers * Groups * Rings * Polynomials * Vector Spaces and Modules * Some Linear Groups * Field Theory * Finite Fields * The Real and Complex Numbers * Sets * Appendix * Index


Antman, Stuart

Nonlinear Problems of Elasticity, 2nd ed.

Series: Applied Mathematical Sciences, Vol. 107
2005, XVIII, 836 p. 110 illus., Hardcover
ISBN: 0-387-20880-1

About this book

This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity, directed toward the scientist, engineer, and mathematician who wish to see careful treatments of precisely formulated problems. Special emphasis is placed on the role of nonlinear material response. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.

Table of contents



Lutz Edler (Editor), Christos Kitsos (Editor)

Recent Advances in Quantitative Methods in Cancer
and Human Health Risk Assessment

ISBN: 0-470-85756-0
Hardcover
502 pages
June 2005

Human health risk assessment involves the measuring of risk of exposure to disease, with a view to improving disease prevention. Mathematical, biological, statistical, and computational methods play a key role in exposure assessment, hazard assessment and identification, and dose-response modelling.
Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment is a comprehensive text that accounts for the wealth of new biological data as well as new biological, toxicological, and medical approaches adopted in risk assessment. It provides an authoritative compendium of state-of-the-art methods proposed and used, featuring contributions from eminent authors with varied experience from academia, government, and industry.

Provides a comprehensive summary of currently available quantitative methods for risk assessment of both cancer and non-cancer problems.
Describes the applications and the limitations of current mathematical modelling and statistical analysis methods (classical and Bayesian).
Includes an extensive introduction and discussion to each chapter.
Features detailed studies of risk assessments using biologically-based modelling approaches.
Discusses the varying computational aspects of the methods proposed.
Provides a global perspective on human health risk assessment by featuring case studies from a wide range of countries.
Features an extensive bibliography with links to relevant background information within each chapter.
Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment will appeal to researchers and practitioners in public health & epidemiology, and postgraduate students alike. It will also be of interest to professionals working in risk assessment agencies.

Don L. McLeish

Monte Carlo Simulation and Finance

ISBN: 0-471-67778-7
Hardcover
387 pages
2005

Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon.

Table of contents

Chapter 1. Introduction.
Chapter 2. Some Basic Theory of Finance.
Introduction to Pricing: Single PeriodModels.
Multiperiod Models.
Determining the Process Bt.
Minimum Variance Portfolios and the Capital Asset Pricing Model.
Entropy: choosing a Q measure.
Models in Continuous Time.
Problems.
Chapter 3. Basic Monte Carlo Methods.
Uniform Random Number Generation.
Apparent Randomness of Pseudo-Random Number Generators.
Generating Random Numbers from Non-Uniform Continuous Distributions.
Generating Random Numbers from Discrete Distributions.
Random Samples Associated with Markov Chains.
Simulating Stochastic Partial Differential Equations.
Problems.
Chapter 4. Variance Reduction Techniques.
Introduction.
Variance reduction for one-dimensional Monte-Carlo Integration.
Problems.
Chapter 5. Simulating the value of Options.
Asian Options.
Pricing a Call option under stochastic interest rates.
Simulating Barrier and lookback options.
Survivorship Bias.
Problems.
Chapter 6. Quasi- Monte Carlo Multiple Integration.
Introduction.
Theory of Low discrepancy sequences.
Examples of low discrepancy sequences.
Problems.
Chapter 7. Estimation and Calibration.
Introduction.
Finding a Root.
Maximization of Functions.
MaximumLikelihood Estimation.
Using Historical Data to estimate the parameters in Diffusion Models.
Estimating Volatility.
Estimating Hedge ratios and Correlation Coefficients.
Problems.
Chapter 8. Sensitivity Analysis, Estimating Derivatives and the Greeks.
Estimating Derivatives.
Infinitesimal Perturbation Analysis: Pathwise differentiation.
Calibrating aModel using simulations.
Problems.
Chapter 9. Other Directions and Conclusions.
Alternative Models.
ARCH and GARCH.
Conclusions.
Notes.
References.
Index.

Kamel Rekab / Florida Institute of Technology
Muzaffar Shaikh / Florida Institute of Technology

Statistical Design of Experiments with Engineering Applications

Series: Statistics: Textbooks and Monographs Volume: 182
ISBN: 1574446258
Publication Date: 4/8/2005
Number of Pages: 272

Includes an introduction to the design of experiments and quadratic optimization
Discusses two- and three-level design types
Explores statistical and non-statistical approaches for location optimization and variability reduction
Elucidates Taguchi's approach to design of experiments
Includes coverage of simplistic graphical methods and formal statistical tests for studying the validity of the prediction equation

In today's high-technology world, with flourishing e-business and intense competition at a global level, the search for the competitive advantage has become a crucial task of corporate executives. Quality, formerly considered a secondary expense, is now universally recognized as a necessary tool. Although many statistical methods are available for determining quality, there has been no guide to easy learning and implementation until now. Filling that gap, Statistical Design of Experiments with Engineering Applications, provides a ready made, quick and easy-to-learn approach for applying design of experiments techniques to problems. The book uses quality as the main theme to explain various design of experiments concepts.

The authors examine the entire product lifecycle and the tools and techniques necessary to measure quality at each stage. They explain topics such as optimization, Taguchi's method, variance reduction, and graphical applications based on statistical techniques. Wherever applicable the book supplies practical rules of thumb, step-wise procedures that allow you to grasp concepts quickly and apply them appropriately, and examples that demonstrate how to apply techniques. Emphasizing the importance of quality to products and services, the authors include concepts from the field of Quality Engineering. Written with an emphasis on application and not on bogging you down with the theoretical underpinnings, the book enables you to solve 80% of design problems without worrying about the derivation of mathematical formulas.