Paperback 2019
ISBN9780691183312 392 pp. 6 1/8 x 9 1/4 97 b/w illus., 16 tables
forthcoming September 2018
The Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography?the science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principles underpin the ways that different codes and ciphers work. He focuses on both code making and code breaking and discusses most of the ancient and modern ciphers that are currently known. He begins by looking at substitution ciphers, and then discusses how to introduce flexibility and additional notation. Holden goes on to explore polyalphabetic substitution ciphers, transposition ciphers, connections between ciphers and computer encryption, stream ciphers, public-key ciphers, and ciphers involving exponentiation. He concludes by looking at the future of ciphers and where cryptography might be headed. The Mathematics of Secrets reveals the mathematics working stealthily in the science of coded messages.
A blog describing new developments and historical discoveries in cryptography related to the material in this book is accessible at http://press.princeton.edu/titles/10826.html.
Joshua Holden is professor of mathematics at the Rose-Hulman Institute of Technology.
Hardcover 2019
ISBN9780691182131
328 pp. 6 1/8 x 9 1/4
forthcoming February 2019
Paperback 2019
ISBN9780691182148
A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil’s conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting ?-adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors.
Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil’s conjecture. The proof of the product formula will appear in a sequel volume.
Dennis Gaitsgory is professor of mathematics at Harvard University. He is the coauthor of A Study in Derived Algebraic Geometry. Jacob Lurie is professor of mathematics at Harvard University. He is the author of Higher Topos Theory (Princeton).
ISBN: 978-1-119-41788-0
Aug 2018
584 pages
HARDCOVER
A hands-on approach to statistical inference that addresses the latest developments in this ever-growing field
This clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal distribution, and their solutions, are developed in detail. Much emphasis throughout is on non-Gaussian distributions, including details on working with the stable Paretian distribution and fast calculation of the noncentral Student's t. An entire chapter is dedicated to optimization, including development of Hessian-based methods, as well as heuristic/genetic algorithms that do not require continuity, with MATLAB codes provided.
The book includes both theory and nontechnical discussions, along with a substantial reference to the literature, with an emphasis on alternative, more modern approaches. The recent literature on the misuse of hypothesis testing and p-values for model selection is discussed, and emphasis is given to alternative model selection methods, though hypothesis testing of distributional assumptions is covered in detail, notably for the normal distribution.
Presented in three parts?Essential Concepts in Statistics; Further Fundamental Concepts in Statistics; and Additional Topics?Fundamental Statistical Inference: A Computational Approach offers comprehensive chapters on: Introducing Point and Interval Estimation; Goodness of Fit and Hypothesis Testing; Likelihood; Numerical Optimization; Methods of Point Estimation; Q-Q Plots and Distribution Testing; Unbiased Point Estimation and Bias Reduction; Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The Method of Indirect Inference; and, as an appendix, A Review of Fundamental Concepts in Probability Theory, the latter to keep the book self-contained, and giving material on some advanced subjects such as saddlepoint approximations, expected shortfall in finance, calculation with the stable Paretian distribution, and convergence theorems and proofs.
ISBN: 978-1-118-88498-0
Aug 2018
1120 pages
Hardcover
Covers the latest methodologies and research on international comparative surveys with contributions from noted experts in the field
Advances in Comparative Survey Methodology examines the most recent advances in methodology and operations as well as the technical developments in international survey research. With contributions from a panel of international experts, the text includes information on the use of Big Data in concert with survey data, collecting biomarkers, the human subject regulatory environment, innovations in data collection methodology and sampling techniques, use of paradata across the survey lifecycle, metadata standards for dissemination, and new analytical techniques.
This important resource:
Contains contributions from key experts in their respective fields of study from around the globe
Highlights innovative approaches in resource poor settings, and innovative approaches to combining survey and other data
Includes material that is organized within the total survey error framework
Presents extensive and up-to-date references throughout the book
Written for students and academic survey researchers and market researchers engaged in comparative projects, this text represents a unique collaboration that features the latest methodologies and research on global comparative surveys.
ISBN: 978-1-119-40528-3
Oct 2018
384 pages
HARDCOVER
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.