Hardback
ISBN 9781032712420
530 Pages
January 27, 2025
Available for pre-order on January 6, 2025.
This accessible introduction to the topic covers the theory of measure and integral, as introduced by Lebesgue and developed in the first half of the 20th century. It leads naturally to Banach spaces of functions and linear operators acting on them.
This material in Measure and Integral: Theory and Practice is typically covered in a graduate course and is almost always treated in an abstract way, with little or no motivation. The author employs a plethora of examples and exercises and strives to motivate every concept with its historical background. This textbook is accessible to a wider range of students, including at the undergraduate level.
A major problem facing anyone teaching measure theory is how to combine the elementary approach (measure on the real line or in the plane) and the abstract measure theory. The author develops a theory of measure in the plane, then shows how to generalize these ideas to an abstract setting.
The result is a textbook accessible to a wider range of students.
The material requires a good understanding of topics often referred to as advanced calculus, such as Riemann integration on Euclidean spaces and series of functions. Also, a reader is expected to be proficient in the basics of set theory and point-set topology, preferably including metric spaces.
Prologue
I Preliminaries
1 Set Theory
1.1 Sets
1.2 Functions
1.3 Cardinal and Ordinal Numbers
1.4 The Axiom of Choice
2 Metric Spaces
2.1 Elementary Theory of Metric Spaces
2.2 Completeness
2.3 Compactness
2.4 Limits of Functions
2.5 Bairefs Theorem
3 Geometry of the Line and the Plane
II Measure Theory
4 Lebesgue Measure on R2
4.1 Jordan Measure
4.2 Lebesgue Measure
4.3 The Ð-Algebra of Lebesgue Measurable Sets
5 Abstract Measure
5.1 Measures and Measurable Sets
5.2 CarathLeodory Extension of Measure
5.3 Lebesgue Measure on Euclidean Spaces
5.4 Beyond Lebesgue Ð-Algebra
5.5 Signed Measures
6 Measurable Functions
6.1 Definition and Basic Facts
6.2 Fundamental Properties of Measurable Functions
6.3 Sequences of Measurable Functions
III Integration Theory
7 The Integral
7.1 About Riemann Integral
7.2 Integration of Nonnegative Measurable Functions
7.3 The Integral of a Real-Valued Function
7.4 Computing Lebesgue Integral
8 Integration on Product Spaces
8.1 Measurability on Cartesian Products
8.2 Product Measures
8.3 The Fubini Theorem
9 Differentiation and Integration
9.1 Dini Derivatives
9.2 Monotone Functions
9.3 Functions of Bounded Variation
9.4 Absolutely Continuous Functions
9.5 The Radon?Nikodym Theorem
IV An Introduction to Functional Analysis
10 Banach Spaces
10.1 Normed Linear Spaces
10.2 The Space Lp(X, Ê)
10.3 Completeness of Lp(X, Ê)
10.4 Dense Sets in Lp(X, Ê)
10.5 Hilbert Space
10.6 Besselfs Inequality and Orthonormal Bases
10.7 The Space C(X)
11 Continuous Linear Operators Between Banach Spaces
11.1 Linear Operators
11.2 Banach Space Isomorphisms
11.3 The Uniform Boundedness Principle
11.4 The Open Mapping and Closed Graph Theorems
12 Duality
12.1 Linear Functionals
12.2 The Hahn?Banach Theorem
12.3 The Dual of Lp(X, Ê)
12.4 The Dual Space of L(X, Ê)
12.5 The Dual Space of C(X)
12.6 Weak Convergence
Epilogue
Solutions and Answers to Selected Exercises
Bibliography
Subject Index
Author Index
ISBN 9780367344894
770 Pages 31 B/W Illustrations
February 26, 2025 by Chapman & Hall
Nonparametric statistical methods minimise the number of assumptions that need to be made about the distribution of data being analysed, unlike classical parametric methods. As such, they are an essential part of a statisticianfs armoury and this book is an essential resource in their application. Starting from the basics of statistics, it takes the reader through the main nonparametric approaches with an emphasis on carefully explained examples backed up by use of the R programming language.
Key features of this fully revised and extended fifth edition include:
An introductory chapter that provides a gentle introduction to the basics of statistics, including types of data, hypothesis testing, confidence intervals, and ethical issues
An R package containing functions that have been written for the examples in the text and the exercises
Summary bullet points at the end of each section to enable the reader to locate important principles quickly
A case study from medical research to demonstrate nonparametric approaches to the data analysis
Examples fully integrated into the text, drawn from published research on contemporary issues, with more detail given in their explanation
Extensive exercises along with complete solutions allow the reader to test their understanding of the material.
Articles used in the examples and exercises carefully chosen to enable readers to identify up to date literature in their field for research, publications, and teaching material
Numerous historical references throughout the text, from which to explore the origins of nonparametric methods.
Applied Nonparametric Statistical Methods, Fifth Edition is a comprehensive course text in nonparametric techniques suitable for undergraduate students of mathematics and statistics. It assumes only basic previous experience of statistics and with algebra kept to a minimum it is also ideal for quantitative methods modules delivered to undergraduate or postgraduate students in science, business, and health service training. It is an invaluable resource for researchers, medical practitioners, business managers, research and development staff, and others needing to interpret quantitative information. Suitable for self-directed learning in continuing professional development it also acts as a handy accessible reference manual.
1. Basic concepts of statistical inference
2. Fundamentals of nonparametric methods
3. Exploring averages for single samples
4. Other single-sample inferences
5. Methods for paired samples
6. Methods for two independent samples
7. Basic tests for three or more samples
8. Analysis of structured data
9. Analysis of survival data
10. Correlation and concordance
11. Bivariate linear regression
12. Categorical data
13. Association in categorical data
14. Robust estimation
15. Nonparametric methods in action
In the series De Gruyter Textbook
The idea of the book is to present a text that is useful for both students of quantitative sciences and practitioners who work with univariate or multivariate probabilistic models. Since the text should also be suitable for self-study, excessive formalism is avoided though mathematical rigor is retained. A deeper insight into the topics is provided by detailed examples and illustrations. The book covers the standard content of a course in probability and statistics. However, the second edition includes two new chapters about distribution theory and exploratory data analysis. The first-mentioned chapter certainly goes beyond the standard material. It is presented to reflect the growing practical importance of developing new distributions. The second new chapter studies intensively one- and bidimensional concepts like assymetry, kurtosis, correlation and determination coefficients. In particular, examples are intended to enable the reader to take a critical look at the appropriateness of the geometrically motivated concepts.
Many examples, exercises with detailed solutions.
Mathematically rigorous, but exaggerate formalism is avoided.
For students of Mathematics, Statistics, Engineering
Now covers distribution theory, a fertile field of research and new examples
This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.
Leading experts survey the state-of-the-art on finitely presented groups and directions for future research
Algorithmic techniques and group-based cryptography
Covers important connections to logic and to applications in AI
Volume 55 in the series De Gruyter Studies in Mathematical Physics
This monograph introduces mathematicians, physicists, and engineers to the ideas relating quantum mechanics and symmetries - both described in terms of Lie algebras and Lie groups. The exposition of quantum mechanics from this point of view reveals that classical mechanics and quantum mechanics are very much alike. Written by a mathematician and a physicist, this book is (like a math book) about precise concepts and exact results in classical mechanics and quantum mechanics, but motivated and discussed (like a physics book) in terms of their physical meaning. The reader can focus on the simplicity and beauty of theoretical physics, without getting lost in a jungle of techniques for estimating or calculating quantities of interest.
This work is not intended for a strictly linear reading: Start reading where your interest is!
All the material is covered at different levels of sophistication.
A mix of introductory material and many advanced topics.
About this book
This reference discusses how automata and language theory can be used to understand solutions to solving equations in groups and word problems in groups. Examples presented include, how Fine scale complexity theory has entered group theory via these connections and how cellular automata, has been generalized into a group theoretic setting. Chapters written by experts in group theory and computer science explain these connections.
Covers recent breakthroughs on describing solutions sets to systems of equations in free groups via ETD0L languages.
Survey of Stallings automata and their algorithmic properties.
Chapters on cellular automata over groups and automaton groups.
In the series De Gruyter Proceedings in Mathematics
This volume documents the contributions presented at The ICRTMPCS II International Conference on Advances in Mathematical and Computational Sciences. Entries focus on modern trends and techniques in branches of pure and applied mathematics, statistics, and computer science. Highlighting applications in coding theory, cryptography, graph theory, fuzzy theory, variance analysis, data analysis, and sampling theory.
Entries from pure and applied mathematics that are applicable in coding theory, cryptography, graph theory and fuzzy theory.
Entries in statistics that deal with applications in sampling theory, data analysis, stochastic processes, and networking
In the series De Gruyter Proceedings in Mathematics
This volume consists of twenty articles stemming from presentations given at the 2023 Integers Conference. They represent a variety of active areas of research in combinatorial number theory, including additive number theory, multiplicative number theory, elementary number theory, the theory of partitions, Ramsey theory, sequences, algebraic combinatorics, enumerative combinatorics, and Diophantine equations.
Includes contributions from several distinguished scholars
Focuses on many trending topics in number theory and combinatorics.
Of Interest to researchers and graduate students working in combinatoric game theory