An Introduction to Independence for Analysts

An Introduction to Independence for Analysts
Author: H. G. Dales
Publisher: Cambridge University Press
Total Pages: 257
Release: 1987-12-10
Genre: Mathematics
ISBN: 0521339960

Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.

Introduction to Data Science

Introduction to Data Science
Author: Rafael A. Irizarry
Publisher: CRC Press
Total Pages: 836
Release: 2019-11-20
Genre: Mathematics
ISBN: 1000708039

Introduction to Data Science: Data Analysis and Prediction Algorithms with R introduces concepts and skills that can help you tackle real-world data analysis challenges. It covers concepts from probability, statistical inference, linear regression, and machine learning. It also helps you develop skills such as R programming, data wrangling, data visualization, predictive algorithm building, file organization with UNIX/Linux shell, version control with Git and GitHub, and reproducible document preparation. This book is a textbook for a first course in data science. No previous knowledge of R is necessary, although some experience with programming may be helpful. The book is divided into six parts: R, data visualization, statistics with R, data wrangling, machine learning, and productivity tools. Each part has several chapters meant to be presented as one lecture. The author uses motivating case studies that realistically mimic a data scientist’s experience. He starts by asking specific questions and answers these through data analysis so concepts are learned as a means to answering the questions. Examples of the case studies included are: US murder rates by state, self-reported student heights, trends in world health and economics, the impact of vaccines on infectious disease rates, the financial crisis of 2007-2008, election forecasting, building a baseball team, image processing of hand-written digits, and movie recommendation systems. The statistical concepts used to answer the case study questions are only briefly introduced, so complementing with a probability and statistics textbook is highly recommended for in-depth understanding of these concepts. If you read and understand the chapters and complete the exercises, you will be prepared to learn the more advanced concepts and skills needed to become an expert.

Handbook of Analysis and Its Foundations

Handbook of Analysis and Its Foundations
Author: Eric Schechter
Publisher: Academic Press
Total Pages: 907
Release: 1996-10-24
Genre: Mathematics
ISBN: 0080532993

Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/

An Introduction to Categorical Data Analysis

An Introduction to Categorical Data Analysis
Author: Alan Agresti
Publisher: John Wiley & Sons
Total Pages: 393
Release: 2018-10-11
Genre: Mathematics
ISBN: 1119405270

A valuable new edition of a standard reference The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data. Adding to the value in the new edition is: • Illustrations of the use of R software to perform all the analyses in the book • A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis • New sections in many chapters introducing the Bayesian approach for the methods of that chapter • More than 70 analyses of data sets to illustrate application of the methods, and about 200 exercises, many containing other data sets • An appendix showing how to use SAS, Stata, and SPSS, and an appendix with short solutions to most odd-numbered exercises Written in an applied, nontechnical style, this book illustrates the methods using a wide variety of real data, including medical clinical trials, environmental questions, drug use by teenagers, horseshoe crab mating, basketball shooting, correlates of happiness, and much more. An Introduction to Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and biostatisticians as well as methodologists in the social and behavioral sciences, medicine and public health, marketing, education, and the biological and agricultural sciences.

Number Theory

Number Theory
Author: Sinnou David
Publisher: Cambridge University Press
Total Pages: 227
Release: 1996-11-07
Genre: Mathematics
ISBN: 052158549X

This book covers the whole spectrum of number theory, and is composed of contributions from some of the best specialists worldwide.

Stochastic Analysis

Stochastic Analysis
Author: M. T. Barlow
Publisher: Cambridge University Press
Total Pages: 385
Release: 1991-10-25
Genre: Mathematics
ISBN: 0521425336

Papers from the Symposium on stochastic analysis, which took place at the University of Durham in July 1990.

An Introduction to Data Analysis

An Introduction to Data Analysis
Author: Tiffany Bergin
Publisher: SAGE
Total Pages: 363
Release: 2018-10-15
Genre: Social Science
ISBN: 1526452316

Covering the general process of data analysis to finding, collecting, organizing, and presenting data, this book offers a complete introduction to the fundamentals of data analysis. Using real-world case studies as illustrations, it helps readers understand theories behind and develop techniques for conducting quantitative, qualitative, and mixed methods data analysis. With an easy-to-follow organization and clear, jargon-free language, it helps readers not only become proficient data analysts, but also develop the critical thinking skills necessary to assess analyses presented by others in both academic research and the popular media. It includes advice on: - Data analysis frameworks - Validity and credibility of data - Sampling techniques - Data management - The big data phenomenon - Data visualisation - Effective data communication Whether you are new to data analysis or looking for a quick-reference guide to key principles of the process, this book will help you uncover nuances, complexities, patterns, and relationships among all types of data.