What's Happening in the Mathematical Sciences, Volume 3 PDF Download

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

View

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

View

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: Dana Mackenzie
Publisher: American Mathematical Soc.
ISBN: 9780821885970
Category : Mathematics
Languages : en
Pages : 140

View

Book Description
A new twist in knot theory -- Error-term roulette and the Sato-Tate conjecture -- The fifty-one percent solution -- Dominos, anyone? -- No seeing is believing -- Getting with the (Mori) program -- The book that time couldn't erase -- Charting a 248-dimensional world -- Compressed sensing makes every pixel count.

Author: Barry Cipra
Publisher: American Mathematical Soc.
ISBN: 9780821807668
Category : Mathematics
Languages : en
Pages : 140

View

Book Description
This volume is fourth in the series "What's Happening in the Mathematical Sciences". As the 20th century draws to a close, it presents the state of modern mathematics and its world-wide significance. It includes "Beetlemania: Chaos in Ecology", on evidence for chaotic dynamics in a population.

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

View

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: Giandomenico Sica
Publisher: Polimetrica s.a.s.
ISBN: 8876990143
Category : Mathematics
Languages : en
Pages : 353

View

Book Description

Author: Cesare Cozzo
Publisher: Cambridge Scholars Publishing
ISBN: 1443863351
Category : Science
Languages : en
Pages : 295

View

Book Description
How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy – the heuristic conception. This path from logic to a naturalistic conception of knowledge and philosophy explains the title, From a Heuristic Point of View, which recalls the celebrated collection of essays, From a Logical Point of View, by Willard Van Orman Quine, the father of modern naturalized epistemology. The word ‘heuristic’ points to Cellucci’s favorite theme and the main difference between him and Quine: the emphasis on discovery and building a ‘logic’ for generating new knowledge. This book is a collection of essays from leading figures in this field who discuss, criticize, or expand on the main topics in Cellucci’s work, dealing with some of the most challenging questions in logic, science and philosophy.

Author: Shahid Rahman
Publisher: Springer Science & Business Media
ISBN: 9048124867
Category : Philosophy
Languages : en
Pages : 617

View

Book Description
The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.

Author: Dana Mackenzie
Publisher: Princeton University Press
ISBN: 0691160163
Category : Mathematics
Languages : en
Pages : 224

View

Book Description
Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics--the universal language of science--keep the masterpieces of the subject hidden behind a veil? The Universe in Zero Words tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society--from the elementary (1+1=2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E=mc2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called "a popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives. Illustrated in color throughout, the book tells the human and often-surprising stories behind the invention or discovery of the equations, from how a bad cigar changed the course of quantum mechanics to why whales (if they could communicate with us) would teach us a totally different concept of geometry. At the same time, the book shows why these equations have something timeless to say about the universe, and how they do it with an economy (zero words) that no other form of human expression can match. The Universe in Zero Words is the ultimate introduction and guide to equations that have changed the world.

Author: Rossella Lupacchini
Publisher: Springer Science & Business Media
ISBN: 8847007844
Category : Philosophy
Languages : en
Pages : 285

View

Book Description
This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G ̈ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers collected in this book are intended to search for some answers, to discuss conceptual and logical issues underlying such questions and, perhaps, to call attention to other relevant questions.