Mathematics Unlimited - 2001 and Beyond

1. Front Matter

   Pages I-XV

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2. Nonlinear Continuum Physics

   • Stuart S. Antman

   Pages 1-21

3. Computational Mechanics: Where Is It Going?

   • Ivo Babuška, J. Tinsley Oden

   Pages 23-28

4. From Finite Sets to Feynman Diagrams

   • John C. Baez, James Dolan

   Pages 29-50

5. Experimental Mathematics: Recent Developments and Future Outlook

   • David H. Bailey, Jonathan M. Borwein

   Pages 51-66

6. The Mathematical Aspects of Econometrics

   • Badi H. Baltagi

   Pages 67-81

7. Quantum Information

   • Ole E. Barndorff-Nielsen, Richard D. Gill, Peter E. Jupp

   Pages 83-107

8. The p-Adic L-Functions of Modular Elliptic Curves

   • Massimo Bertolini, Henri Darmon

   Pages 109-170

9. A Basis for a New Relationship Between Mathematics and Society

   • Jean Pierre Bourguignon

   Pages 171-188

10. New Issues in the Mathematics of Control

    • Roger Brockett

    Pages 189-219

11. Geometric Mechanics, Lagrangian Reduction, and Nonholonomic Systems

    • Hernán Cendra, Jerrold E. Marsden, Tudor S. Ratiu

    Pages 221-273

12. Mathematics: From the Outside Looking in

    • Achim Bachem, Vasco Alexander Schmidt

    Pages 275-281

13. Communicating Mathematics Across the Web

    • Arjeh M. Cohen

    Pages 283-300

14. Computational Aspects of Number Theory

    • Henri Cohen

    Pages 301-330

15. L-Functions and Random Matrices

    • J. Brian Conrey

    Pages 331-352

16. Some Open Problems and Research Directions in the Mathematical Study of Fluid Dynamics

    • Peter Constantin

    Pages 353-360

17. Mathematics of Financial Markets

    • Mark Davis

    Pages 361-380

18. Computational Neuroscience: More Math Is Needed to Understand the Human Brain

    • Erik De Schutter

    Pages 381-391

19. Probability Theory

    • Rick Durrett

    Pages 393-405

20. Selected Problems in Materials Science

    • E. Weinan

    Pages 407-432

This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty.

• computational science
• future
• mathematics

"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 wheremathematics 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 mathematischenLiteratur. 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

 

• Center for Parallel Computers, Royal Institute of Technology (KTH), Stockholm, Sweden

  Björn Engquist

• Department of Mathematics, University of California at Los Angeles, Los Angeles, USA

  Björn Engquist

• Department of Mathematics, Harvard University, Cambridge, USA

  Wilfried Schmid

Policies and ethics