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Mathematics Unlimited Hardcover – January 25, 2001

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Editorial Reviews


"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

"[...] 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

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Product Details

  • Hardcover: 1236 pages
  • Publisher: Springer; 2001 edition (January 25, 2001)
  • Language: English
  • ISBN-10: 3540669132
  • ISBN-13: 978-3540669135
  • Product Dimensions: 9.8 x 7.9 x 2.6 inches
  • Shipping Weight: 6.8 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #246,781 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

17 of 17 people found the following review helpful By Colin McLarty on April 1, 2002
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.
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16 of 19 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on March 17, 2001
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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By Kenneth A. Perko, Jr. on June 18, 2014
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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