Contemporary Mathematics, Volume: 679
2016; 217 pp; Softcover
MSC: Primary 11; 30; 35; 47;
ISBN: 978-1-4704-2305-6
This volume contains the Proceedings of the Conference on Completeness Problems, Carleson Measures, and Spaces of Analytic Functions, held from June 29?July 3, 2015, at the Institut Mittag-Leffler, Djursholm, Sweden.
The conference brought together experienced researchers and promising young mathematicians from many countries to discuss recent progress made in function theory, model spaces, completeness problems, and Carleson measures.
This volume contains articles covering cutting-edge research questions, as well as longer survey papers and a report on the problem session that contains a collection of attractive open problems in complex and harmonic analysis.
Contemporary Mathematics, Volume: 680
2016; 177 pp; Softcover
MSC: Primary 17; 57; 81;
Print ISBN: 978-1-4704-1459-7
Throughout recent history, the theory of knot invariants has been a fascinating melting pot of ideas and scientific cultures, blending mathematics and physics, geometry, topology and algebra, gauge theory, and quantum gravity.
The 2013 Seminaire de Mathematiques Superieures in Montreal presented an opportunity for the next generation of scientists to learn in one place about the various perspectives on knot homology, from the mathematical background to the most recent developments, and provided an access point to the relevant parts of theoretical physics as well.
This volume presents a cross-section of topics covered at that summer school and will be a valuable resource for graduate students and researchers wishing to learn about this rapidly growing field.
December 6, 2016 by Chapman and Hall/CRC
Textbook - 212 Pages - 20 B/W Illustrations
ISBN 9781498755771
Mathematically rigorous, but accessible.
Important concepts are introduced early on.
Emphasis on model building and interpretation.
Only the basic ideas are introduced, keeping the book short.
Extends basic theory using exercises.
Trains modeling skills using problems.
Uses some calculus, but can easily be tailored to students without this background.
This short book introduces the main ideas of statistical inference in a way that is both user friendly and mathematically sound. Particular emphasis is placed on the common foundation of many models used in practice. In addition, the book focuses on the formulation of appropriate statistical models to study problems in business, economics, and the social sciences, as well as on how to interpret the results from statistical analyses.
The book will be useful to students who are interested in rigorous applications of statistics to problems in business, economics and the social sciences, as well as students who have studied statistics in the past, but need a more solid grounding in statistical techniques to further their careers.
Jacco Thijssen is professor of finance at the University of York, UK. He holds a PhD in mathematical economics from Tilburg University, Netherlands. His main research interests are in applications of optimal stopping theory, stochastic calculus, and game theory to problems in economics and finance. Professor Thijssen has earned several awards for his statistics teaching.
Statistical Inference
Theory and Calculus of Probability
From Probability to Statistics
Statistical Inference for the Mean based on a Large Sample
Statistical Models and Sampling Distributions
Estimation of Parameters
Confidence Intervals
Hypothesis Testing
Linear Regression
Bayesian Inference
Appendix
March 17, 2017
Reference - 472 Pages - 25 B/W Illustrations
ISBN 9781498773140
Demonstrates the usefulness of pathological functions in various questions of real analysis
Shows the importance of such functions in the process of development of basic concepts of mathematical analysis
Presents the close and profound connections of pathological (paradoxical) functions with logical and settheoretic foundations of mathematical analysis
This book explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line, and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, he considers examples of functions whose existence cannot be established without the help of additional set theoretical axioms
Introduction: basic concepts
Cantor and Peano type functions
Functions of first Baire class
Semicontinuous functions that are not countably continuous
Singular monotone functions
A characterization of constant functions via Dinifs derived numbers
Everywhere differentiable nowhere monotone functions
Continuous nowhere approximately differentiable functions
Blumbergfs theorem and Sierpinski-Zygmund functions
The cardinality of first Baire class
Lebesgue nonmeasurable functions and functions without the Baire property
Hamel basis and Cauchy functional equation
Summation methods and Lebesgue nonmeasurable functions
Luzin sets, SierpiLnski sets, and their applications
Absolutely nonmeasurable additive functions
Egorov type theorems
A difference between the Riemann and Lebesgue iterated integrals
Sierpinskifs partition of the Euclidean plane
Bad functions defined on second category sets
Sup-measurable and weakly sup-measurable functions
Generalized step-functions and superposition operators
Ordinary differential equations with bad right-hand sides
Nondifferentiable functions from the point of view of category and measure
Absolute null subsets of the plane with bad orthogonal projections
Appendix 1: Luzinfs theorem on the existence of primitives
Appendix 2: Banach limits on the real line .
April 18, 2017
Textbook - 400 Pages
ISBN 9781498746342
Series: Chapman & Hall/CRC Texts in Statistical Science
Systematically develops core methodology of functional data analysis
Covers recent developments, including sparsely observed and dependent functions
Rigorously develops requisite mathematical concepts
Uses R for numerical examples and provides a dedicated R package
Each chapter contains theoretical and data analytic problems
Introduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework.
The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems.
The material of the book can be roughly divided into four parts of approximately equal length: 1) basic concepts and techniques of FDA, 2) functional regression models, 3) sparse and dependent functional data, and 4) introduction to the Hilbert space framework of FDA. The book assumes advanced undergraduate background in calculus, linear algebra, distributional probability theory, foundations of statistical inference, and some familiarity with R programming. Other required statistics background is provided in scalar settings before the related functional concepts are developed. Most chapters end with references to more advanced research for those who wish to gain a more in-depth understanding of a specific topic.