ISBN: 9781420086782
Publication Date: 27/01/2009
Pages: 264
Trim Size: 6-1/8 x 9-1/4
Binding(s): Hardback
Based on a condensed one-week course taught by the author, this text provides a concise introduction to the statistical software package R and its use in computational statistics. It covers the basics of R, including importing data, programming, and graphics. The author also explores data analysis, linear and nonparametric regression, residual diagnostic, statistical comparisons, and multivariate statistics. Integrating R code throughout, the text includes numerous examples and figures to illustrate the methods, provides all data sets and code on the R archive, and contains many exercises, enabling its use as a course text or for self-study.
Introduction. Bases. Involution. Comparison of Distributions. Dimensions 1,2,3-infinity. R as a Programming Language. Bibliography. Index.
Metrics, Norms and Integrals is a textbook on contemporary analysis based on the author’s lectures given at the University of Melbourne for over two decades. It covers three main topics: metric and topological spaces, functional analysis, and the theory of the Lebesgue integral on measure spaces. This self-contained text contains a number of original presentations, including an early introduction of pseudometric spaces to motivate general topologies, an innovative introduction to the Lebesgue integral, and a discussion on the use of the Newton integral. It is thus a valuable book to inform and stimulate both undergraduate and graduate students.
Metrics and Topologies:
Metric Spaces
Convergence and Completeness
Continuity in Metric Spaces
Topological Spaces
Compactness
Connectedness
Linear Analysis:
Normed Spaces
Inner Product Spaces
Linear Operators and Functionals
Self-Adjoint Compact Operators
Introductory Functional Analysis
Integration:
Measure Spaces
The Abstract Lebesgue Integral
Integral on the Real Line
Construction of Measures
Product Measures. Integration on ?k
Lebesgue Spaces
Readership: Advanced undergraduates and graduate students in mathematics.
428pp Pub. date: Nov 2008
ISBN 978-981-283-656-4
Symmetry is as simple or as complicated as we are ready to absorb it in everything around us. From flowers to bridges, buildings, coke machines, and snowflakes; from molecules to walnuts, fences, pine cones, and sunflowers; from music to children’s drawings; from hubcaps to bank logos, propellers, wallpaper decorations, and pavements, we recognize it if we walk around with open eyes and an open mind. This book provides aesthetic pleasure and covert education, immersing the reader in both the familiar and the unknown and leading always to unexpected discoveries.
The authors, world-renowned scientists, have already produced a dozen books on symmetry for professionals as well as laypersons, for grownups as well as children, in English, Russian, German, Hungarian, and Swedish languages. They provide this attractive account of symmetry in few words and many ? as many as 650 ? images in full color from the most diverse corners of our globe. An encounter with this book will open up a whole new experience for the reader, who will never look at the world with the same eyes as before.
Introduction
Mirror Symmetry
Chirality
Multiple Mirrors
Rotational Symmetry
Shape and Movement Polyhedra
Repetitions
Helical Symmetry
Planar Patterns
Readership: Students, teachers, artists, designers, art historians, architects, and lay people.
220pp (approx.) Pub. date: Scheduled Spring 2009
ISBN 978-981-283-531-4
This proceedings volume contains selected talks and poster presentations from the 9th International Conference on Path Integrals ? New Trends and Perspectives, which took place at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, during the period September 23?28, 2007. Continuing the well-developed tradition of the conference series, the present status of both the different techniques of path integral calculations and their diverse applications to many fields of physics and chemistry is reviewed. This is reflected in the main topics in this volume, which range from more traditional fields such as general quantum physics and quantum or statistical field theory through technical aspects like Monte Carlo simulations to more modern applications in the realm of quantum gravity and astrophysics, condensed matter physics with topical subjects such as Bose?Einstein condensation or quantum wires, biophysics and econophysics. All articles are successfully tied together by the common method of path integration; as a result, special methodological advancements in one topic could be transferred to other topics.
History and Perspectives
Quantum Physics
Quantum Field Theory
Quantum Gravity
Statistical Field Theory
Monte Carlo Techniques
Bose?Einstein Condensation
Condensed Matter
Spin Models
Biophysics and Stochastics
Readership: Physicists, mathematicians and chemists.
628pp Pub. date: Nov 2008
ISBN 978-981-283-726-4
Explanation of the basic concepts and methods of statistics requires a reasonably good mathematical background, at least at a first-year-level knowledge of calculus. Most of the statistical software explain how to conduct data analysis, but do not explain when to apply and when not to apply it. Keeping this in view, we try to explain the basic concepts of probability and statistics for students with an understanding of a first course in calculus at the undergraduate level.
Designed as a textbook for undergraduate and first-year graduate students in statistics, bio-statistics, social sciences and business administration programs as well as undergraduates in engineering sciences and computer science programs, it provides a clear exposition of the theory of probability along with applications in statistics. The book contains a large number of solved examples and chapter-end exercises designed to reinforce the probability theory and emphasize statistical applications.
Probability, Conditional Probability, Independence
Discrete Probability Distributions, Probability Generating Function
Distribution Function, Probability Density Function, Expectation and Variance, Moments, Moment Generating Function, Functions of a Random Variable, Standard Continuous Probability Distributions
Bivariate Probability Distributions, Conditional Distributions, Independence, Expectation of a Function of a Random Vector, Correlation and Regression, Moment Generating Function, Multivariate Probability Distributions
Functions of Two Random Variables, Functions of Multivariate Random Vectors, Sampling Distributions, Chebyshev’s Inequality, Weak Law of Large Numbers, Poisson Approximation to a Binomial Distribution, Central Limit Theorem, Normal Approximation to a Binomial Distribution, Approximation to a Chi-Square Distribution by a Normal Distribution, Convergence of Sequences of Random Variables
Methods of Estimation, Cramer?Rao Inequality, Efficient Estimation, Sufficient Statistics, Properties of a Maximum Likelihood Estimator, Bayes Estimation, Estimation of a Probability Density Function
Interval Estimation (Confidence Intervals), Testing of Hypotheses, Chi-Square Tests
Simple Linear Regression Model, Multiple Linear Regression Model, Correlation
Readership: Advanced undergraduate and first-year graduate students in mathematics, statistics, bio-statistics, social sciences and business administration programs as well as undergraduates in engineering and computer science programs.
340pp (approx.)
Pub. date: Scheduled Winter 2008
ISBN 978-981-283-653-3
ISBN 978-981-283-654-0(pbk)
This is a first-ever textbook written in English about the theory of modular forms and Jacobi forms of several variables. It contains the classical theory as well as a new theory on Jacobi forms over Cayley numbers developed by the author from 1990 to 2000. Applications to the classical Euler sums are of special interest to those who are eager to evaluate double Euler sums or more general multiple zeta values. The celebrated sum formula proved by Granville in 1997 is given in a more general form here.
Theory of Modular Forms of One Variable:
Group Action of the Modular Group
The Gamma and Zeta Functions
Zeta Functions of Modular Forms
Dimension Formulae
Bernoulli Identities and Applications
Euler Sums and Recent Development
Theory of Modular Forms of Several Variables:
Theory of Modular Forms of Several Variables
The Full Modular Group
The Fourier Coefficients of Eisenstein Series
Theory of Jacobi Forms
Hecke Operators and Jacobi Forms
Singular Modular Forms on the Exceptional Domain
Readership: Researchers, postgraduate and graduate students in number theory.
250pp (approx.) Pub. date: Scheduled Spring 2009
ISBN 978-981-283-518-5