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Mathematics Unlimited - 2001 and Beyond Hardcover – Jan 25 2001


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Product Details

  • Hardcover: 1236 pages
  • Publisher: Springer; 2001 edition (Jan. 25 2001)
  • Language: English
  • ISBN-10: 3540669132
  • ISBN-13: 978-3540669135
  • Product Dimensions: 7 x 21 x 25.4 cm
  • Shipping Weight: 3.1 Kg
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: #443,325 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

"Mathematics: Frontiers and Perspectives Mathematics Unlimited: 2001 and Beyond

"...many individuals and teams created lists of problems and trends similar in spirit to Hilbert's set. Mathematics Unlimited has by no means the widest range of all that I have seen. ... The competence of the authors supports the hope that the predictions and problems collected here will indeed set the development of matheamtics in the coming years. ... The book will interest anybody using or interested in true mathematics as opposed to its textbook representation. ... Apart from its excellent content the book is also wonderfully set and bound, which adds the pleasure to reading and gives hope that it will endure many years and survive many readers."

Daniel Wójcik, Pure and Applied Geophysics, Vol. 160, pp. 1373-1374, 2003

 "… In all, this will keep readers with even a modest knowledge of mathematics entertained for a long time."

Mathematika 48, 2001

"This book is an essential purchase for every library and mathematics department. It is a very valuable source for those of us engaged in careers talks, information evenings or pep talks to high school students. It provides a unique snapshot of mathematics as it stands today and perhaps the best view available of where mathematics will be going in the next century. For all mathematicians from the undergraduate level onwards, this book will serve as an inspiration for the further pursuit of mathematics."
Australian Mathematical Society GAZETTE, October 2001

"Frontiers and 2001 are both inspired by David Hilbert's famous address to the International Congress of Mathematicians in 1900 in Paris. Hilbert asked, "What new methods and new facts in the wide and rich field of mathematical thought will the new centuries disclose?" These books in one sense answer Hilberts question, as they form a huge montage of where mathematics is now. But in another sense, they raise Hilbert's question again: where is mathematics going?

...So 2001 is larger than Frontiers and is working with a more inclusive notion of mathematics. These are important differences, but otherwise the two books are quite similar. A typical paper in either book is quite broad in subject matter. ... Many papers are also broad in that they address the history of their subject and also make predictions about future developments.
........Frontiers is an excellent book, but it is 2001 which has a better claim to capturing and defining the mathematical spirit of our times. ..."

David P. Roberts, MAA Online Book Review Column, for detailed review have a look at http://www.maa.org/reviews/2000bks.html

"[...] Natürlich konnten die Herausgeber trotz der erwähnten Vielfalt Vollständigkeit nicht anstreben, jedoch durch die Auswahl der Schlaglichter ein eindrucksvolles Bild moderner Mathematik gestalten. Weitgehend einheitlich legen auch die Autoren großen Wert auf die Darstellung der Verknüpfungen ihres jeweiligen Gegenstandes mit anderen Gebieten und auf die Bedeutung der Interdisziplinarität für die bisher erzielten Fortschritte wie insbesondere für die Fortentwicklung im neuen Jahrhundert.

Obwohl es kaum einem Leser gelingen wird, die mehr als 1200 Seiten dieses umfassenden Werkes wirklich Seite für Seite durchzuarbeiten, ist es doch von großer Faszination, Einblick in die Sicht der Autoren für zukünftige wesentliche Entwicklungen nehmen zu können.

Es liegt mithin ein wirklich tiefliegendes und den zukünftigen Weg unserer Wissenschaft gewiß beeinflussendes und mitgestaltendes Werk vor, in das jeder Mathematiker und Anwender zumindest Einblick nehmen sollte."

R.Ansorge, ZAMM 81 (2001), 732

 "Mathematics Unlimited - ein einzigartiger Sammelband "Mathematics Unlimited - 2001 and Beyond" ist einzigartig in der mathematischen Literatur. Unter der Federführung von Björn Engquist (...) und Wilfried Schmid (...) entwerfen zweiundneunzig renommierte Autorinnen und Autoren aus allen Teilen der Welt ein faszinierendes und farbenprächtiges Bild der modernen Mathematik und ihrer vielfältigen Wechselwirkungen mit anderen Wissenschaften. Der besondere Wert dieses Buches liegt darin, daß es im Sinne von Gauß keine Trennung in reine und angewandte Mathematik gibt, sondern in überzeugender Weise die Einheit der Mathematik betont wird. Die einzelnen Beiträge richten sich nicht an Spezialisten, sondern an ein breites Publikum von Mathematikern und interessierten Wissenschaftlern anderer Disziplinen. Es gibt keinen vergleichbaren Band, der ein so breites Spektrum an mathematischen Themen überdeckt. Dem Springer-Verlag gebührt ein herzliches Dankeschön für die verlegerische Meisterleistung. Ich bin sicher, daß jeder Leser etwas Neues entdeckt, welches sein Interesse findet und ihm bei der Lektüre Freude bereitet. Kurze, sorgfältig ausgewählte Literaturangaben laden zur Vertiefung des Gelesenen ein. ...."

DMV-Mitteilungen 4/2001

 

From the Publisher

This is THE mathematics book of the century, giving a unique overview on all of mathematics and its related fields The authors are all top-experts who write with an orientation towards the future

Inside This Book (Learn More)
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Continuum physics, which includes the disciplines of continuum mechanics, continuum thermodynamics, continuum electromagnetism, and certain fields of chemistry, furnishes refined mathematical models for the behavior of material bodies that are not invisibly small. Read the first page
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Format: Hardcover
This book is a look to the future of mathematics based on the trends in mathematical thinking at the present time. I did not read all the articles in the book, so my review will be limited to those I did. The article "Experimental Mathematics" by D. Bailey and J. Borwein is an overview of a somewhat controversial activity in mathematics. This activity, characterized as "experimental" mathematics, has, the authors argue, enabled very interesting mathematical problems to be eventually solved. They outline in the article the recent discovery of how to calculate the the nth digit of Pi without computing any of the first n-1 digits without multiple-precision arithmetic and needing only low memory. The calculation scheme was based on a formula that was discovered by a computer, the first time this has happened.according to the authors. Experimental mathematics can be viewed as "real-time" discovery of mathematics, as well as letting us visualize the mathematical structures involved using computer graphics. Mathematicians interested in network modeling will appreciate the article by F. Kelly entitled "Mathematical Modeling of the Internet". Interestingly, his approach makes use of dynamical systems, with the goal of studying the behavior and stability of the TCP/IP protocol. The most interesting section of the article is the section on packet marking strategies. One can find surprising connections between strategies for packet marking, packet shaping, and network QoS, with techniques in option pricing from financial engineering. This is particularly true for frame relay networks. This connection was not discussed in Kelly's article, but I have found these connections in developing my own network models.Read more ›
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Format: Hardcover
Maybe you like the idea of this book but you are wondering, does it live up to the promise, will you actually read much of it, is it just too big? The answers are yes, probably yes, and no.
I've browsed maybe half of the chapters. Each one is clear, easy to skim through, with a lot to dig into if you want. So far I've found not one "book report" just summarizing recent work. I've found fascinating helpful interpretations of subjects I don't know -- and challenging positions on subjects that I have my own view of.
Of course you can find fault. The book leans more to applied math than I'd like. And what about functional analysis?
Overall, I am stunned to think I wavered on buying this. I almost passed it up. It would have been a big mistake.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 3 reviews
17 of 17 people found the following review helpful
If you are interested, buy it. April 1 2002
By Colin McLarty - Published on Amazon.com
Format: Hardcover Verified Purchase
Maybe you like the idea of this book but you are wondering, does it live up to the promise, will you actually read much of it, is it just too big? The answers are yes, probably yes, and no.
I've browsed maybe half of the chapters. Each one is clear, easy to skim through, with a lot to dig into if you want. So far I've found not one "book report" just summarizing recent work. I've found fascinating helpful interpretations of subjects I don't know -- and challenging positions on subjects that I have my own view of.
Of course you can find fault. The book leans more to applied math than I'd like. And what about functional analysis?
Overall, I am stunned to think I wavered on buying this. I almost passed it up. It would have been a big mistake.
16 of 19 people found the following review helpful
An awesome look at the future of mathematics March 17 2001
By Dr. Lee D. Carlson - Published on Amazon.com
Format: Hardcover
This book is a look to the future of mathematics based on the trends in mathematical thinking at the present time. I did not read all the articles in the book, so my review will be limited to those I did. The article "Experimental Mathematics" by D. Bailey and J. Borwein is an overview of a somewhat controversial activity in mathematics. This activity, characterized as "experimental" mathematics, has, the authors argue, enabled very interesting mathematical problems to be eventually solved. They outline in the article the recent discovery of how to calculate the the nth digit of Pi without computing any of the first n-1 digits without multiple-precision arithmetic and needing only low memory. The calculation scheme was based on a formula that was discovered by a computer, the first time this has happened.according to the authors. Experimental mathematics can be viewed as "real-time" discovery of mathematics, as well as letting us visualize the mathematical structures involved using computer graphics. Mathematicians interested in network modeling will appreciate the article by F. Kelly entitled "Mathematical Modeling of the Internet". Interestingly, his approach makes use of dynamical systems, with the goal of studying the behavior and stability of the TCP/IP protocol. The most interesting section of the article is the section on packet marking strategies. One can find surprising connections between strategies for packet marking, packet shaping, and network QoS, with techniques in option pricing from financial engineering. This is particularly true for frame relay networks. This connection was not discussed in Kelly's article, but I have found these connections in developing my own network models. Kelly gives good insight on how to apply techniques from optimization theory and dynamical systems to study the behavior of modern networks. The network modeling of the 21st century will have to contend with wireless, DWDM, and other more exotic technologies. By far the most interesting articles in the book were the two articles "Geometric Aspects of Mirror Symmetry" by D. Morrison and "A Chapter in Physical Mathematics" by K. Marathe. The constructions that take place in the areas discussed in these two articles have to rank as the most fascinating in all of mathematics. And most interestingly, the ideas had a powerful influence from theoretical physics. One can say without question that physical ideas coming from quantum field theory/high energy physics justify a rephrasing of the words of the famous physicist Eugene Wigner. One could now speak of "the reasonable influence of physics in mathematics". Physical ideas have permeated many different areas of mathematics and will continue to do so. Some mathematicians have classified this influence as "physical mathematics" because some of the mathematical constructions have not been justified rigorously. Several brilliant mathematical developments have occurred in the last two decades resulting from ideas from high energy physics, such as quantum invariants of knots and three-dimensional manifolds, Seiberg-Witten theory, mirror symmetry in algebraic geometry, and supersymmetry and index theorems. These exciting results could be described best as kind of a "quantization of mathematics", and the future will hold more of the this line of thinking. Every construction in mathematics will have a quantum analog, with a correspondence between mappings/structures in "ordinary" or "classical" mathematics and unitary transformations/noncommutative structures in the "quantized" version. An example of this kind of development is occurring today in the field of non-commutative geometry. "Mathematics Unlimited-2001 And Beyond" is a brief glimpse of what will be an exciting century for mathematics. Quantum computation will no doubt become a reality soon, and its computational power, coupled with the needs of the information age, will push mathematics to new dizzying heights. What was called experimental and physical mathematics in the book will continue to have their niches; but "pure" mathematics will also hold its ground and continue to solidify and advance. The mathematical adventure is just beginning......
Unwieldy June 18 2014
By Kenneth A. Perko, Jr. - Published on Amazon.com
Format: Hardcover Verified Purchase
An unwieldy anthology of topics of interest at the end of the Second Millennium. The German edition is much lighter.


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