What's Happening in the Mathematical Sciences – serie

Beautifully produced and marvelously written, ""What's Happening in the Mathematical Sciences, Volume 3"", contains 10 articles on recent developments in the field. In an engaging, reader-friendly style, Barry Cipra explores topics ranging from Fermat's Last Theorem to Computational Fluid Dynamics. The volumes in this series highlight the many roles mathematics plays in the modern world. This volume includes articles on: a new mathematical method that's taking Wall Street by storm 'Ultra-parallel' supercomputing with DNA, and how a mathematician found the famous flaw in the Pentium chip. Unique in kind, and lively in style, ""What's Happening in the Mathematical Sciences, Volume 3"" is a delight to read and a valuable source of information.

This volume is fourth in the much-acclaimed 'AMS' series, ""What's Happening in the Mathematical Sciences"". The lively style and in-depth coverage of some of the most important 'happenings' in mathematics today make this publication a delightful and intriguing read accessible to a wide audience. High school students, professors, researchers, engineers, statisticians, computer scientists - anyone with an interest in mathematics - will find captivating material in this book. As we enter the 21st century, ""What's Happening"" presents the state of modern mathematics and its worldwide significance in a timely and enduring fashion.Featured articles include: 'From Wired to Weird', on advances that are encouraging research in quantum computation; 'A Prime Case of Chaos', on new connections between number theory and theoretical physics; 'Beetlemania: Chaos in Ecology', on new evidence for chaotic dynamics in an actual population; 'A Blue-Letter Day for Computer Chess', on the mathematics underlying Deep Blue's victory over Garry Kasparov; and, much more!

Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the ""What's Happening"" series contradicts that view by showing that mathematics is indeed found everywhere - in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science: Mathematical biology - Mathematics was key to cracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code; Celestial mechanics and cosmology - New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology's most fundamental questions: What is the size and shape of the universe?Mathematics and Everyday Life: Traffic jams - New models are helping researchers understand where traffic jams come from-and maybe what to do about them; Small worlds - Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics: Beyond Fermat's Last Theorem - Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments in the elegant world of elliptic curves and modular functions; The Millennium Prize Problems - The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in this latest volume of ""What's Happening in the Mathematical Sciences"". The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.

The ""AMS"" series ""What's Happening in the Mathematical Sciences"" distills the amazingly rich brew of current research in mathematics down to a few choice samples. This volume leads off with an update on the Poincare Conjecture, a hundred-year-old problem that has apparently been solved by Grigory Perelman of St. Petersburg, Russia. So what did topologists do when the oldest and most famous problem about closed manifolds was vanquished? As the second chapter describes, they confronted a suite of problems concerning the 'ends' of open manifolds...and solved those, too. Not to be outdone, number theorists accomplished several unexpected feats in the first five years of the new century, from computing a trillion digits of pi to finding arbitrarily long equally-spaced sequences of prime numbers.Undergraduates made key discoveries, as explained in the chapters on Venn diagrams and primality testing. In applied mathematics, the Navier-Stokes equations of fluid mechanics continued to stir up interest. One team proved new theorems about the long-term evolution of vortices, while others explored the surprising ways that insects use vortices to move around. The random jittering of Brownian motion became a little less mysterious. Finally, an old and trusted algorithm of computer science had its trustworthiness explained in a novel way. Barry Cipra explains these new developments in his wry and witty style, familiar to readers of Volumes 1-5, and is joined in this volume by Dana Mackenzie. Volume 6 of ""What's Happening"" will convey to all readers - from mathematical novices to experts - the beauty and wonder that is mathematics.

Since 1993, the AMS has been publishing ""What's Happening in the Mathematical Sciences"", a series of lively and highly readable accounts of the latest developments in mathematics. This seventh volume describes some genuine surprises, such as the recent discovery that coin tosses are inherently unfair; a mathematical theory of invisibility that was soon followed by the creation of a prototype 'invisibility cloak'; and, an ultra-efficient approach to image sensing that led to the development of a single-pixel camera. The past few years have also seen deep results on some classical mathematics problems. For example, this volume describes a proof of the Sato-Tate Conjecture in number theory and a major advance in the Minimal Model Program of algebraic geometry. The computation of the character table of the exceptional Lie group $E_8$ brings 'the most beautiful structure in mathematics' to public attention, and proves that human persistence is just as important as gigabytes of RAM. The amazing story of the Archimedes Palimpsest shows how the modern tools of high-energy physics uncovered the centuries-old secrets of the mathematical writings of Archimedes. Dana Mackenzie, a science writer specializing in mathematics, makes each of these topics accessible to all readers, with a style that is friendly and at the same time attentive to the nuances that make mathematics fascinating. Anyone with an interest in mathematics, from high school teachers and college students to engineers and computer scientists, will find something of interest here. The stories are well told and the mathematics is compelling.

What's Happening in the Mathematical Sciences is a collection of articles highlighting some of the most recent developments in mathematics. These include important achievements in pure mathematics, as well as its fascinating applications.On the pure mathematics side, ``Prime Clusters and Gaps: Out-Experting the Experts'' talks about new insights into the distribution of prime numbers, the perpetual source of new problems, and new results. Recently, several mathematicians (including Yitang Zhang and James Maynard) significantly improved our knowledge of the distribution of prime numbers. Advances in the so-called Kadison-Singer problem and its applications in signal processing algorithms used to analyze and synthesize signals are described in ``The Kadison-Singer Problem: A Fine Balance''. ``Quod Erat Demonstrandum'' presents two examples of perseverance in mathematicians' pursuit of truth using, in particular, computers to verify their arguments. And ``Following in Sherlock Holmes' Bike Tracks'' shows how an episode in one of Sir Arthur Conan Doyle's stories about Sherlock Holmes naturally led to very interesting problems and results in the theory of completely integrable systems.On the applied side, ``Climate Past, Present, and Future'' shows the importance of mathematics in the study of climate change and global warming phenomena. Mathematical models help researchers to understand the past, present, and future changes of climate, and to analyze their consequences. ``The Truth Shall Set Your Fee'' talks about algorithms of information exchange in cyberspace. Economists have known for a long time that trust is a cornerstone of commerce, and this becomes even more important nowadays when a lot of transactions, big and small, are done over the Internet. Recent efforts of theoretical computer scientists led to the development of so-called ``rational protocols'' for information exchange, where the parties in the information exchange process find that lies do not pay off.Over the last 100 years many professional mathematicians and devoted amateurs contributed to the problem of finding polygons that can tile the plane, e.g., used as floor tiles in large rooms and walls. Despite all of these efforts, the search is not yet complete, as the very recent discovery of a new plane-tiling pentagon shows in ``A Pentagonal Search Pays Off''. Mathematics can benefit coaches and players in some of the most popular team sports as shown in ``The Brave New World of Sports Analytics''. The increased ability to collect and process statistics, big data, or ``analytics'' has completely changed the world of sports analytics. The use of modern methods of statistical modeling allows coaches and players to create much more detailed game plans as well as create many new ways of measuring a player's value. Finally, ``Origami: Unfolding the Future'' talks about the ancient Japanese paper-folding art and origami's unexpected connections to a variety of areas including mathematics, technology, and education.

As always, What's Happening in the Mathematical Sciences presents a selection of topics in mathematics that have attracted particular attention in recent years. This volume is dominated by an event that shook the world in 2020 and 2021, the coronavirus (or COVID-19) pandemic. While the world turned to politicians and physicians for guidance, mathematicians played a key role in the background, forecasting the epidemic and providing rational frameworks for making decisions. The first three chapters of this book highlight several of their contributions, ranging from advising governors and city councils to predicting the effect of vaccines to identifying possibly dangerous ""escape variants"" that could re-infect people who already had the disease.In recent years, scientists have sounded louder and louder alarms about another global threat: climate change. Climatologists predict that the frequency of hurricanes and waves of extreme heat will change. But to even define an ""extreme"" or a ""change"", let alone to predict the direction of change, is not a climate problem: it's a math problem. Mathematicians have been developing new techniques, and reviving old ones, to help climate modelers make such assessments.In a more light-hearted vein, Descartes' ""Homework"" describes how a famous mathematician's blunder led to the discovery of new properties of foam-like structures called Apollonian packings. ""Square Pegs and Squiggly Holes"" shows that square pegs fit virtually any kind of hole, not just circular ones. ""Much Ado About Zero"" explains how difficult problems about eigenvalues of matrices can sometimes be answered by playing a simple game that involves coloring dots on a grid or a graph.Finally, ""Dancing on the Edge of the Impossible"" provides a progress report on one of the oldest and still most important challenges in number theory: to devise an effective algorithm for finding all of the rational-number points on an algebraic curve. In the great majority of cases, number theorists know that the number of solutions is finite, yet they cannot tell when they have found the last one. However, two recently proposed methods show potential for breaking the impasse.