What's happening in the mathematical sciences

著者

• American Mathematical Society
• Cipra, Barry
• Zorn, Paul
• MacKenzie, Dana

書誌事項

What's happening in the mathematical sciences

American Mathematical Society

American Mathematical Society, c1993-

• v. 1
• v. 2
• v. 3
• v. 4
• v. 5
• v. 6
• v. 7
• v. 8
• v. 9
• v. 10
• v. 11

注記

Title from cover

v. 4. 1998-1999

Statement of responsibility/author: v. 2: written by Barry Cipra ; edited by Paul Zorn -- v. 3-5: Barry Cipra ; edited by Paul Zorn -- v. 6, 10: Dana MacKenzie, Barry Cipra -- v. 7-9, 11: Dana MacKenzie

内容説明・目次

巻冊次

v. 3 ISBN 9780821803554

内容説明

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.

目次

Fermat's Theorem-at last! A tale of two theories Computer science discovers DNA Divide and conquer The gentle art of control Computational fluid dynamics--verging on turbulence Cellular automata offer new outlook on life, the universe, and everything Are group theorists simpleminded? The secret life of large numbers In math we trust.

巻冊次

v. 4 ISBN 9780821807668

内容説明

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!

目次

A blue-letter day for computer chess A prime case of chaos Proof by example: A mathematician's mathematician Computers take algebraic geometry back to its roots As easy as EQP Beetlemania: Chaos in ecology From wired to weird Tales from the cryptosystem But is it math? Mathematical discovery (by Henri Poincare) Science and method.

巻冊次

v. 5 ISBN 9780821829042

内容説明

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.

目次

Introduction New heights for number theory Nothing to sphere but sphere itself A mathematical twist to protein folding Finite math The mathematics of traffic jams Rewriting history It's a small, big, small, big world A celestial Pas de trois Think and grow rich Ising on the cake.

巻冊次

v. 7 ISBN 9780821844786

内容説明

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.

巻冊次

v. 8 ISBN 9780821849996

内容説明

What's Happening in the Mathematical Sciences showcases the remarkable recent progress in pure and applied mathematics. Once again, there are some surprises, where we discover new properties of familiar things, in this case tightly-packed tetrahedra or curious turtle-like shapes that right themselves. Mathematics also has played significant roles in current events, most notably the financial crisis, but also in screening for breast cancer. The Netflix competition to find a better algorithm for recommending videos to subscribers demonstrated how deeply mathematics is used behind the scenes in our everyday lives.Mathematicians have settled several important conjectures in the past few years. In topology, the recently solved Kervaire invariant conjecture tells us about exotic spheres in high dimension. The Weinstein conjecture, proved by Cliff Taubes, guarantees periodicity in certain important dynamical systems. A very old dynamical system--the game of billiards--received two innovative makeovers. First, mathematicians proved the existence of ""wandering"" trajectories in an inside-out version of the game, called ""outer billiards,"" which some researchers consider a toy model for planetary motion. Second, mathematicians proved two different versions of the Quantum Unique Ergodicity conjecture, which says that a quantum-mechanical billiard ball behaves, in the long term (and at high energies) similarly to a classical billiard ball. The proof uses ideas from pure number theory dating back to Ramanujan. Finally, in another area of statistical physics, mathematicians showed that the transition from an unmixed to a mixed system often happens, relatively speaking, in the blink of an eye.Dana Mackenzie, a science and mathematics writer, makes the mathematics and the applications easily comprehensible, by calling on common sense or on similar but familiar phenomena. The stories invite you into the exciting world of modern mathematics, with its thrill of discovery and the anticipation of what is still to come. 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 gripping.

巻冊次

v. 9 ISBN 9780821887394

内容説明

What's Happening in the Mathematical Sciences looks at some highlights of the most recent developments in mathematics. These include the mathematics behind stories that made headlines, as well as fascinating mathematical stories that never made it into the newspapers. In 2009, a flu pandemic, the world's first in more than 40 years, tested a new generation of mathematical models that take some of the guesswork out of public health decisions. As health officials rushed to quell the outbreak of H1N1 flu, mathematicians were working just as hurriedly to answer questions like these: Was the epidemic serious enough to justify school closings or quarantines? Who should be vaccinated first, the elderly or the young? Their findings substantially affected the response of local governments, national governments, and the World Health Organization. Mathematics can also help society prepare for other kinds of natural and manmade disasters. A major tsunami in 2011 in Japan, like the one seven years earlier in the Indian Ocean, highlighted flaws in our understanding of these catastrophic events and inadequacies in our early warning systems. Geoscientists are working together with mathematicians to improve our short-term forecasting ability and quantify the long-term risks of tsunamis. Meanwhile, in California, another group of mathematicians succeeded in adapting earthquake prediction algorithms to forecast criminal activity. Their ""predictive policing"" software was tested in Los Angeles and is being adopted by other cities across the United States. Fortunately, not all mathematics has to do with emergencies. Pure mathematicians have been busy cleaning out their closets of long-standing open problems. In 2012, two conjectures about different kinds of minimising surfaces were solved: the Willmore Conjecture (minimising energy) and the Lawson Conjecture (minimising area). Also in 2012, following up on the extraordinary proofs of the Poincare Conjecture and Thurston's Geometrization Conjecture, topologists proved a collection of conjectures that ensure that three-dimensional spaces can all be constructed in a uniform way. Meanwhile, for the last ten years, a new way of understanding algebraic curves and surfaces has developed, leading to a subject now known as tropical geometry. With the new ideas, certain hard problems in algebraic geometry suddenly become easy and certain ""mathematical mysteries"" of string theory begin to make sense. In physics, the nine-billion-dollar search for the elusive Higgs boson finally bagged its quarry in 2012. This discovery, one of the most widely publicised science stories of the year, provides experimental evidence for the ""Higgs mechanism,"" a nearly 50-year-old mathematical argument that explains how certain subatomic particles acquire mass. Rounding out this volume are chapters on a new statistical technique called topic modelling, which is breaking down the academic barriers between math and the humanities, and new discoveries about mathematicians' (and a lot of other people's) favourite toy: the Rubik's Cube.

目次

A massive breakthrough (about the mathematics of the Higgs particle) Tubing through hyperspace (about the proofs of the Willmore conjecture, Lawson's conjecture, and the Pinkall-Sterling conjecture) Tsunamis: Learning from math, learning from the past (title is self explanatory) Today's forecast: Ten percent chance of burglary (about protective policing) Topologists cross four off ``bucket list'' (about the proof of the Virtual Haken Conjecture and three related conjectures) Speedcubing, anyone? (about the mathematics of the Rubik's cube) The right epidemic at the right time (about the 2009 flu epidemic and mathematical models of epidemics) Thinking topically: Latent Dirichlet allocation (about topic models) Thinking tropically (about tropical geometry)

巻冊次

v. 2 ISBN 9780821889985

内容説明

After rave reviews for first issue of "What's Happening", volume 2 was eagerly awaited. 'Very well written', said one reader of volume 1. 'The writing is brilliant, positively brilliant'. 'A terrific publication', said another. 'This is a wonderful tool for showing people what mathematics is about and what mathematicians can do'. One reader called it 'a must for all mathematics department reading and coffee lounges'. Volume 2 of "What's Happening" features the same lively writing and all new topics. Here you can read about a new class of solitons, the contributions wavelets are making to solving scientific problems, how mathematics is improving medical imaging, and Andrew Wiles' acclaimed work on Fermat's Last Theorem."What's Happening" is great for mathematics majors, graduate students, and mathematics clubs - not to mention mathematics faculty, who will enjoy reading about developments in fields other than their own. Highlighting the excitement and wonder of mathematics, "What's Happening" is in a class by itself.

目次

"A truly remarkable proof" From knot to unknot New wave mathematics Mathematical insights for medical imaging Parlez-vous wavelets? Random algorithms leave little to chance Soap solution Straightening out nonlinear codes Quite easily done (Vector) field of dreams.

巻冊次

v. 1 ISBN 9780821889992

内容説明

This is the inaugural issue of "What's Happening in the Mathematical Sciences", an annual publication that surveys some of the important developments in the mathematical sciences over the past year or so. Mathematics is constantly growing and changing, reaching out to other areas of science and helping to solve some of the major problems facing society. Here you can read about how computers can't always be trusted to provide the right answer, how mathematics is contributing to solving environmental problems, and how mathematicians have solved a longstanding problem about the way a drum's shape affects its sound. "What's Happening in the Mathematical Sciences" aims to inform the general public about the beauty and power of mathematics.

目次

New trends emerging in mathematical biology New computer insights from "transparent" proofs You can't hear the shape of a drum Environmentally sound mathematics Disproving the obvious in higher dimensions Collaboration closes in on closed geodesics Crystal clear computations Camp geometry Number theorists uncover a slew of prime impostors Map-coloring theorists look at new worlds.

巻冊次

v. 10 ISBN 9781470422042

内容説明

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.

目次

Origami: Unfolding the future by D. Mackenzie Prime clusters and gaps: Out-experting the experts by D. Mackenzie The truth shall set your fee by B. Cipra Climate past, present, and future by D. Mackenzie Following in Sherlock Holmes' bike tracks by D. Mackenzie Quod erat demonstrandum by B. Cipra The Kadison-Singer problem: A fine balance by D. Mackenzie A pentagonal search pays off by B. Cipra The brave new world of sports analytics by D. Mackenzie

巻冊次

v. 11 ISBN 9781470441630

内容説明

This new volume of What's Happening in the Mathematical Sciences features a rich selection of articles about recent topics in pure and applied mathematics. "Expanding Horizons" and "Needles in an Infinite Haystack" explain new developments in the theory of expander graphs and in number theory (asymptotic Fermat's last theorem), respectively. "The SetR Game Has Met Its Match" presents a solution of the so-called Cap Set Conjecture, a statement about arithmetic progressions in finite vector spaces, which resulted from the mathematical analysis of the popular game "Set". "The Shape of Data" and "Quantum Computers and Golden Gates" present recent advances in theoretical computer science and related areas of data science. The mathematical aspects of one of the most fascinating recent developments in general relativity, the discovery of gravitational waves, is discussed in "When Black Holes Collide". Three articles talk about applications of mathematical methods in various aspects of everyday life: bike-sharing systems and ride-sharing services (like Lyft and Uber) in "The Mathematics of Commuting", weight control in "The Calculus of Calories", and an analysis of various partisan election practices in "Gerrymandering: Mathematics on Trial". We anticipate that many readers will find an interesting topic to read about and, hopefully, more than one.

目次

Introduction Gerrymandering: Mathematics on trial The calculus of calories When black holes collide The shape of data The "SetR" game has met its match The mathematics of commuting Expanding horizons Quantum computers and golden gates Needles in an infinite haystack.

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詳細情報

• NII書誌ID(NCID): BA21976049
• ISBN:
  • 0821889990
  • 0821889982
  • 0821803557
  • 0821807668
  • 0821829041
  • 0821835858
  • 9780821844786
  • 9780821849996
  • 9780821887394
  • 9781470422042
  • 9781470441630
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, RI
• ページ数/冊数: v.
• 大きさ: 26-28 cm