2015, Approx. 360 p.
Softcover
ISBN 978-3-319-11945-8
Due: April 9, 2015
First book on algebra or analysis explaining the theory and including the material used in the mathematical Olympiad
Presents some interesting ways to tackle known problems
Elementary treatment of complex numbers
Key observations regarding the solution of functional equation problems
This book presents useful techniques for solving mathematical Olympiad problems in algebra and analysis. Most of the examples, exercises and problems in the book originate from the mathematical Olympiad contests around the world. The material is divided in ten chapters. The first four chapters are related to basic material that can be used in the first stages of any mathematical contests at high school level. The next four chapters comprise more advanced topics which are required for the international mathematical competitions and can be also useful for students in their first year of university. The final chapters provide a comprehensive list of problems which were presented at national and international contests in recent years, and solutions to all exercises and problems in the book.
1. Preliminaries.- 2 Progressions and finite sums.- 3 Induction principle.- 4 Quadratic and cubic polynomials.- 5 Complex numbers.- 6 Functions and functional equations.- 7 Sequences and series.- 8 Polynomials.- 9 Problems.- 10 Solutions of the exercises and problems.- Notation.- Bibliography.- Index.
Series: Springer Texts in Statistics
2015, X, 710 p. 150 illus., 50 illus. in color.
Hardcover
ISBN 978-1-4939-2121-8
Due: April 6, 2015
New edition features color throughout, reworking of the material to emphasize R (but also utilize SAS), and new material
New chapters include Ch. 19 on Likert Scale Data to pick up on the importance of rating scales in fields from population studies to phsychometrics and Ch. 20 on Medical, Pharmaceutical and Social Science Examples
Unique features: chapters introducing the statistics and probability methods used, R package-specific appendices, exercises, code for the graphics used throughout the book, and the ability for readers to also use SAS code
This contemporary presentation of statistical methods features extensive use of graphical displays for exploring data and for displaying the analysis. The authors demonstrate how to analyze data?showing code, graphics, and accompanying computer listings?for all the methods they cover. They emphasize how to construct and interpret graphs, discuss principles of graphical design, and show how accompanying traditional tabular results are used to confirm the visual impressions derived directly from the graphs. Many of the graphical formats are novel and appear here for the first time in print. All chapters have exercises.
The second edition features new chapters, sections and revisions. New chapters cover Likert Scale Data to build on the importance of rating scales in fields from population studies to psychometrics.
This book can serve as a standalone text for statistics majors at the master's level and for other quantitatively oriented disciplines at the doctoral level, and as a reference book for researchers. In-depth discussions of regression analysis, analysis of variance, and design of experiments are followed by introductions to analysis of discrete bivariate data, nonparametrics, logistic regression, and ARIMA time series modeling. The authors illustrate classical concepts and techniques with a variety of case studies using both newer graphical tools and traditional tabular displays.
The authors provide and discuss R and SAS executable functions and macros for all new graphical display formats. All graphs and tabular output in the book were constructed using these programs. Complete transcripts for all examples and figures are provided for readers to use as models for their own analyses.
Introduction.- Data and Statistics.- Statistics Concepts.- Graphs.- Introductory Inference.- One-Way Analysis of Variance.- Multiple Comparisons.- Linear Regression by Least Squares.- Multiple Regression.- Two-Way Analysis of Variance.
2015, Approx. 300 p. 10 illus.
Hardcover
ISBN 978-4-431-55238-3
Due: September 7, 2015
Presents systematically the author’s contributions to various problems of mathematical statistics
Provides an English translation by the author of some known results originally published in Japanese
Deals in a systematic and comprehensive manner with problems that hitherto were not well articulated
This volume is a reorganized edition of Kei Takeuchi’s works on various problems in mathematical statistics based on papers and monographs written since the 1960s on several topics in mathematical statistics and published in various journals in English and in Japanese. They are organized into six parts, each of which is concerned with specific topics and edited to make a consistent thesis. Sometimes expository chapters have been added. The topics included are as follows: theory of statistical prediction from a non-Bayesian viewpoint and analogous to the classical theory of statistical inference; theory of robust estimation, concepts, and procedures, and its implications for practical applications; theory of location and scale covariant/invariant estimations with derivation of explicit forms in various cases; theory of selection and testing of parametric models and a comprehensive approach including the derivation of the Akaike's Information Criterion(AIC); theory of randomized designs, comparisons of random and conditional approaches, and of randomized and non-randomized designs, with random sampling from finite populations considered as a special case of randomized designs and with some separate independent papers included. Theory of asymptotically optimal and higher-order optimal estimators are not included, since most of them already have been published in the Joint Collected Papers of M. Akahira and K. Takeuchi . There are some topics that are not necessarily new, do not seem to have attracted many theoretical statisticians, and do not appear to have been systematically dealt with in textbooks or expository monographs. One purpose of this volume is to give a comprehensive view of such problems as well.
Part I Theory of Statistical Prediction.-Part II Theory of Location and/or
Scale Covariant, Invariant Estimation.-Part III Theory of Robust Estimation
of Location.-Part IV Theory of the Tests for Shapes of Distributions.-Part
V Theory of Randomized Designs.-Part VI Miscellaneous.-VI .1 Theory of
the Cornish-Fisher Expansion of the Distribution.-VI.2 Problem of Model
Selection.-VI.3 Determination of the Levels of Independent Variables to
Attain the Level of the Dependent Variables.-VI.4 Structure of UMV Unbiased
Estimators for Finite Rank Distributions.
Series: Springer Monographs in Mathematics
2014, X, 451 p.
Hardcover
ISBN 978-4-431-55287-1
Due: December 14, 2014
Explains topics that have been actively studied in the non-commutative harmonic analysis of solvable Lie groups
Gives the classical standard results with proof related to the so-called orbit method
Presents concrete examples that will help provide better understanding and ideas for further progress
This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers.
The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators.
The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that the group is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.
1. Preliminaries: Lie groups and Lie algebras 2. Haar measure and group algebra 3. Induced representations 4. Four exponential solvable Lie groups 5. Orbit method 6. Kirillov Theory for nilpotent Lie groups 7. Holomorphically induced representations 8. Irreducible decomposition 9. e-central elements 10. Frobenius reciprocity 11. Plancherel formula 12. Commutativity conjecture: induction case 13. Commutativity conjecture: restriction case.
2014 392 pages
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
978-1-43-985796-0
September 2014
Clustering remains a vibrant area of research in statistics. Although there are many books on this topic, there are relatively few that are well founded in the theoretical aspects. In Robust Cluster Analysis and Variable Selection, Gunter Ritter presents an overview of the theory and applications of probabilistic clustering and variable selection, synthesizing the key research results of the last 50 years.
The author focuses on the robust clustering methods he found to be the most useful on simulated data and real-time applications. The book provides clear guidance for the varying needs of both applications, describing scenarios in which accuracy and speed are the primary goals.
Robust Cluster Analysis and Variable Selection includes all of the important theoretical details, and covers the key probabilistic models, robustness issues, optimization algorithms, validation techniques, and variable selection methods. The book illustrates the different methods with simulated data and applies them to real-world data sets that can be easily downloaded from the web. This provides you with guidance in how to use clustering methods as well as applicable procedures and algorithms without having to understand their probabilistic fundamentals.
2015 300 pages
Series: Textbooks in Mathematics
Hardback:
978-1-48-224238-6
25th April 2015
Updated throughout, the new edition of this classic textbook provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space. It emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Along with a quick review of abstract measure theory, the book covers theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation.
This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes.
This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.
Mathematical Foundations
Linear Codes over Finite Fields
Designs and Their Codes
Difference Sets
Almost Difference Sets
Linear Codes of Difference Sets
Linear Codes of Almost Difference Sets
Codebooks from (Almost) Difference Sets
Readership: Students and professionals working on combinatorics, or coding theory, or digital communications.