ISBN: 1584886412
Publication Date: 11/27/2006
Number of Pages: 424
・Leads students from standard probability and statistics topics
to stochastic processes, queuing systems, and simulations techniques
・Describes the most commonly used types of distributions,
including binomial, geometric, Poisson, uniform, exponential,
gamma, and normal
・Introduces Monte Carlo methods to estimate probabilities,
expectations, and other distribution characteristics
・Teaches how to estimate parameters of interest, test
hypotheses, fit regression models, and make forecasts
・Provides MATLAB computer codes for simulation and computation
・Contains many detailed examples and exercises that have direct
applications to computer science and related fields
・Summarizes the main concepts at the end of each chapter and
reviews calculus and linear algebra in the appendix
・Satisfies the Accreditation Board for Engineering and
Technology (ABET) requirements for probability and statistics
・Includes a solutions manual with qualifying course adoptions
In modern computer science, software engineering, and other
fields, the need arises to make decisions under uncertainty.
Presenting probability and statistical methods, simulation
techniques, and modeling tools, Probability and Statistics for
Computer Scientists helps students solve problems and make
optimal decisions in uncertain conditions, select stochastic
models, compute probabilities and forecasts, and evaluate
performance of computer systems and networks.
After introducing probability and distributions, this easy-to-follow
textbook provides two course options. The first approach is a
probability-oriented course that begins with stochastic
processes, Markov chains, and queuing theory, followed by
computer simulations and Monte Carlo methods. The second approach
is a more standard, statistics-emphasized course that focuses on
statistical inference, estimation, hypothesis testing, and
regression. Assuming one or two semesters of college calculus,
the book is illustrated throughout with numerous examples,
exercises, figures, and tables that stress direct applications in
computer science and software engineering. It also provides
MATLABｮ codes and demonstrations written in simple commands
that can be directly translated into other computer languages.
By the end of this course, advanced undergraduate and beginning
graduate students should be able to read a word problem or a
corporate report, realize the uncertainty involved in the
described situation, select a suitable probability model,
estimate and test its parameters based on real data, compute
probabilities of interesting events and other vital
characteristics, and make appropriate conclusions and forecasts.
Table of contents
ISBN: 1584886072
Publication Date: 11/1/2006
Number of Pages: 552
・Discusses three common numerical areas: interpolation and
quadratures, linear and nonlinear solvers, and finite differences
・Explains the most fundamental and universal concepts,
including error, efficiency, complexity, stability, and
convergence
・Addresses advanced topics, such as intrinsic accuracy limits,
saturation of numerical methods by smoothness, and the method of
difference potentials
・Provides rigorous proofs for all important mathematical
results
・Includes numerous examples and exercises to illustrate key
theoretical ideas and to enable independent study
・Contains a solutions manual for qualifying instructors
A Theoretical Introduction to Numerical Analysis presents the
general methodology and principles of numerical analysis,
illustrating these concepts using numerical methods from real
analysis, linear algebra, and differential equations. The book
focuses on how to efficiently represent mathematical models for
computer-based study.
An accessible yet rigorous mathematical introduction, this book
provides a pedagogical account of the fundamentals of numerical
analysis. The authors thoroughly explain basic concepts, such as
discretization, error, efficiency, complexity, numerical
stability, consistency, and convergence. The text also addresses
more complex topics like intrinsic error limits and the effect of
smoothness on the accuracy of approximation in the context of
Chebyshev interpolation, Gaussian quadratures, and spectral
methods for differential equations. Another advanced subject
discussed, the method of difference potentials, employs discrete
analogues of Calderon's potentials and boundary projection
operators. The authors often delineate various techniques through
exercises that require further theoretical study or computer
implementation.
By lucidly presenting the central mathematical concepts of
numerical methods, A Theoretical Introduction to Numerical
Analysis provides a foundational link to more specialized
computational work in fluid dynamics, acoustics, and
electromagnetism.
Table of contents
ISBN: 1584887729
Publication Date: 12/12/2006
Number of Pages: 248
・Presents mathematical fundamentals, including bivectors,
multivectors, and the spinor theory of rotations
・Provides examples along with applications of geometric algebra
to everyday situations in physics
・Explores the applications of geometric algebra to problems
central to the quantization of gravity
・Includes appendices on complex numbers in algebra formulations
of electrodynamics and plane-wave solutions to Maxwell's equations
Well-known for their research in general relativity, the authors
of Geometric Algebra and Its Applications to Physics provide an
in-depth examination of geometric algebra as a discipline within
mathematical physics and demonstrate how it can be applied to
fundamental problems in physics, especially in experimental
situations. This book presents topics, such as postulates,
bivectors, multivectors, operators, spinor and Lorentz rotations,
as well as two- and three-dimensional applications of these
topics. It provides examples and applications of geometric
algebra to everyday situations in physics, addressing Maxwell's
equations and exploring problems central to the quantization of
gravity.
Series: Chapman & Hall/CRC Statistics in the Social and Behavioral
Science
ISBN: 1584885629
Publication Date: 7/26/2007
Number of Pages: 608
Requiring only a background in introductory statistics, calculus,
and matrix algebra, Bayesian Methods: A Social and Behavioral
Sciences Approach provides detailed explanations of derivations
and theories using a computationally oriented approach. The
second edition of this popular text features new updates on such
topics as MCMC algorithms, perfect sampling, and Bayesian
nonparametrics. It emphasizes the R computing environment as well
as the Bugs simulation program. It also includes various examples
and exercise problems. This text remains an ideal resource for
statisticians, and is especially designed to help political and
social scientists develop a tool chest for statistical analysis.
Table of Contents
Background and Introduction to Bayesian Methods. Likelihood
Interference and the Generalized Linear Model. Bayesian Models
for Explaining Single Variables. Robustness and Sensitivity.
Assessing Model Quality. The Other MC: Markov Chain Theory.
Putting MC and MC Together: Markov Chain Monte Carlo. Numerical
Issues in MCMC. Recent Developments in MCMC Theory. Bayesian
Hierarchal Models and Empirical Bayes. Bayesian Time Series and
Survival Models.