What's Happening in the Mathematical Sciences PDF Download

Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821889985
Category : Mathematics
Languages : en
Pages : 56

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Book Description
This volume covers a new class of solitons, the contributions wavelets are making to solving scientific problems, how mathematics is improving medical imaging, and Andrew Wiles's work on Fermat's "Last Theorem". This work is aimed at undergraduates, graduate students and mathematics clubs.

Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 56

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Book Description
This document consists of the first two volumes of a new annual serial devoted to surveying some of the important developments in the mathematical sciences in the previous 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. Volumes 1 and 2 survey some of the important developments in the mathematical sciences over the past year or so. The contents of volume 1 are: (1) "Equations Come to Life in Mathematical Biology"; (2) "New Computer Insights from 'Transparent' Proofs"; (3) "You Can't Always Hear the Shape of a Drum"; (4) "Environmentally Sound Mathematics"; (5) "Disproving the Obvious in Higher Dimensions"; (6) "Collaboration Closes in on Closed Geodesics"; (7)"Crystal Clear Computations"; (8) "Camp Geometry"; (9) "Number Theorists Uncover a Slew of Prime Impostors"; and (10) "Map-Coloring Theorists Look at New Worlds." The contents of volume 2 are: (1) "A Truly Remarkable Proof" (Fermat's Last Theorem); (2) "From Knot to Unknot"; (3) "New Wave Mathematics"; (4) "Mathematical Insights for Medical Imaging"; (5) "Parlez-vous Wavelets?" (6) "Random Algorithms Leave Little to Chance"; (7) "Soap Solution"; (8) "Straightening Out Nonlinear Codes"; (9) "Quite Easily Done"; and (10) "(Vector) Field of Dreams." (MKR)

Author: Dana Mackenzie
Publisher: American Mathematical Soc.
ISBN: 0821849999
Category : Mathematics
Languages : en
Pages : 137

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Book Description
This volume showcases the latest remarkable progress in pure and applied mathematics, written in an engaging style that conveys modern mathematics' thrill of discovery. Among the stories in this volume are several showing mathematics' significant role in current events, from the financial crisis to breast cancer screening. The book chronicles several important conjectures that mathematicians have settled in the past several years.

Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821890431
Category : Science
Languages : en
Pages : 108

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Book Description
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 tocracking 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'smost 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 inthe 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 thislatest 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.

Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821889992
Category : Mathematics
Languages : en
Pages : 52

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Book Description
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.

Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821803554
Category : Mathematical recreations
Languages : en
Pages : 124

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Book Description
Beautifully produced and marvelously written this volume contains 10 articles on recent developments in the field. In an engaging, reader-friendly style, Cipra explores topics ranging from Fermat's Last Theorem to Computational Fluid Dynamics. The volumes in this series are intended to highlight the many roles mathematics plays in the modern world. Volume 3 includes articles on: a new mathematical methods 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, lively in style, Volume 3 of What's Happening in the Mathematical Sciences is a delight to read and a valuable source of information.

Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 248

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Book Description
This document consists of the first two volumes of a new annual serial devoted to surveying some of the important developments in the mathematical sciences in the previous 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. Volumes 1 and 2 survey some of the important developments in the mathematical sciences over the past year or so. The contents of volume 1 are: (1) "Equations Come to Life in Mathematical Biology"; (2) "New Computer Insights from 'Transparent' Proofs"; (3) "You Can't Always Hear the Shape of a Drum"; (4) "Environmentally Sound Mathematics"; (5) "Disproving the Obvious in Higher Dimensions"; (6) "Collaboration Closes in on Closed Geodesics"; (7)"Crystal Clear Computations"; (8) "Camp Geometry"; (9) "Number Theorists Uncover a Slew of Prime Impostors"; and (10) "Map-Coloring Theorists Look at New Worlds." The contents of volume 2 are: (1) "A Truly Remarkable Proof" (Fermat's Last Theorem); (2) "From Knot to Unknot"; (3) "New Wave Mathematics"; (4) "Mathematical Insights for Medical Imaging"; (5) "Parlez-vous Wavelets?" (6) "Random Algorithms Leave Little to Chance"; (7) "Soap Solution"; (8) "Straightening Out Nonlinear Codes"; (9) "Quite Easily Done"; and (10) "(Vector) Field of Dreams." (MKR)

Author: Dana Mackenzie
Publisher: American Mathematical Soc.
ISBN: 1470422042
Category : Mathematical models
Languages : en
Pages : 119

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Book Description
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.

Author: National Research Council
Publisher: National Academies Press
ISBN: 0309284570
Category : Mathematics
Languages : en
Pages : 223

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Book Description
The mathematical sciences are part of nearly all aspects of everyday life-the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. The Mathematical Sciences in 2025 examines the current state of the mathematical sciences and explores the changes needed for the discipline to be in a strong position and able to maximize its contribution to the nation in 2025. It finds the vitality of the discipline excellent and that it contributes in expanding ways to most areas of science and engineering, as well as to the nation as a whole, and recommends that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, the report emphasizes that universities and the government need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term.

Author: Dana Mackenzie
Publisher: American Mathematical Society
ISBN: 1470464985
Category : Mathematics
Languages : en
Pages : 0

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Book Description
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.