A non-mathematician explores mathematical terrain, reporting accessibly and engagingly on topics from Sudoku to probability. Brian Hayes wants to convince us that mathematics is too important and too much fun to be left to the mathematicians. Foolproof, and Other Mathematical Meditations is his entertaining and accessible exploration of mathematical terrain both far-flung and nearby, bringing readers tidings of mathematical topics from Markov chains to Sudoku. Hayes, a non-mathematician, argues that mathematics is not only an essential tool for understanding the world but also a world unto itself, filled with objects and patterns that transcend earthly reality. In a series of essays, Hayes sets off to explore this exotic terrain, and takes the reader with him. Math has a bad reputation: dull, difficult, detached from daily life. As a talking Barbie doll opined, “Math class is tough.” But Hayes makes math seem fun. Whether he's tracing the genealogy of a well-worn anecdote about a famous mathematical prodigy, or speculating about what would happen to a lost ball in the nth dimension, or explaining that there are such things as quasirandom numbers, Hayes wants readers to share his enthusiasm. That's why he imagines a cinematic treatment of the discovery of the Riemann zeta function (“The year: 1972. The scene: Afternoon tea in Fuld Hall at the Institute for Advanced Study in Princeton, New Jersey”), explains that there is math in Sudoku after all, and describes better-than-average averages. Even when some of these essays involve a hike up the learning curve, the view from the top is worth it.

An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics.

The year’s finest mathematical writing from around the world This annual anthology brings together the year’s finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice—and taking readers behind the scenes of today’s hottest mathematical debates. James Grime shows how to build subtly mischievous dice for playing slightly unfair games and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world—with glimpses at science, philosophy, music, art, and even crocheting. And there’s much, much more. In addition to presenting the year’s most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics. This is a must-read for anyone interested in where math has taken us—and where it is headed.

The solitaire game “The Tower of Hanoi" was invented in the 19th century by the French number theorist Édouard Lucas. The book presents its mathematical theory and offers a survey of the historical development from predecessors up to recent research. In addition to long-standing myths, it provides a detailed overview of the essential mathematical facts with complete proofs, and also includes unpublished material, e.g., on some captivating integer sequences. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms, together with their correctness proofs, form an essential part of the book. In view of the most important practical applications, namely in physics, network theory and cognitive (neuro)psychology, the book also addresses other structures related to the Tower of Hanoi and its variants. The updated second edition includes, for the first time in English, the breakthrough reached with the solution of the “The Reve's Puzzle" in 2014. This is a special case of the famed Frame-Stewart conjecture which is still open after more than 75 years. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike. Excerpts from reviews of the first edition: “The book is an unusual, but very welcome, form of mathematical writing: recreational mathematics taken seriously and serious mathematics treated historically. I don’t hesitate to recommend this book to students, professional research mathematicians, teachers, and to readers of popular mathematics who enjoy more technical expository detail.” Chris Sangwin, The Mathematical Intelligencer 37(4) (2015) 87f. “The book demonstrates that the Tower of Hanoi has a very rich mathematical structure, and as soon as we tweak the parameters we surprisingly quickly find ourselves in the realm of open problems.” László Kozma, ACM SIGACT News 45(3) (2014) 34ff. “Each time I open the book I discover a renewed interest in the Tower of Hanoi. I am sure that this will be the case for all readers.” Jean-Paul Allouche, Newsletter of the European Mathematical Society 93 (2014) 56.

Modern Applied Regressions creates an intricate and colorful mural with mosaics of categorical and limited response variable (CLRV) models using both Bayesian and Frequentist approaches. Written for graduate students, junior researchers, and quantitative analysts in behavioral, health, and social sciences, this text provides details for doing Bayesian and frequentist data analysis of CLRV models. Each chapter can be read and studied separately with R coding snippets and template interpretation for easy replication. Along with the doing part, the text provides basic and accessible statistical theories behind these models and uses a narrative style to recount their origins and evolution. This book first scaffolds both Bayesian and frequentist paradigms for regression analysis, and then moves onto different types of categorical and limited response variable models, including binary, ordered, multinomial, count, and survival regression. Each of the middle four chapters discusses a major type of CLRV regression that subsumes an array of important variants and extensions. The discussion of all major types usually begins with the history and evolution of the prototypical model, followed by the formulation of basic statistical properties and an elaboration on the doing part of the model and its extension. The doing part typically includes R codes, results, and their interpretation. The last chapter discusses advanced modeling and predictive techniques—multilevel modeling, causal inference and propensity score analysis, and machine learning—that are largely built with the toolkits designed for the CLRV models previously covered. The online resources for this book, including R and Stan codes and supplementary notes, can be accessed at https://sites.google.com/site/socjunxu/home/statistics/modern-applied-regressions.

This book explores an alternative approach to the conventional, market-based, view of economic theory and economic policy, at theoretical, numerical and applicable levels. The chapters provide a theoretical, empirical, and algorithmic approach to marcodynamics, Sraffian economics, and current policy issues. Post-Keynesian macroeconomics, business cycle theory, the trade cycle, microfoundations, and the Philips Machine are also covered. This book aims to challenge orthodox ideas and provide a lens through which to honour the work of Stefano Zambelli. It will be of relevant to students and academics interested in economics.