Mathematics Unlimited - 2001 and Beyond" is a book guaranteed to delight the reader. This veritable treasure trove not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future development as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics, both pure and applied, to include contributions from other related sciences. Whatever your field of expertise, you will enjoy reading the many stimulating contributions and, in so doing, gain insights into the astounding progress of mathematics and the perspectives for its future over the next 100 years. One of the editors, Björn Engquist, is a world-renowned researcher in computational science and engineering, and professor at the University of California in Los Angeles, as well as a member of the Executive Committee of the International Mathematical Union. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewise, the authors are all foremost mathematicians and scientists, 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.
Author(s): Björn Engquist, Wilfried Schmid (eds)
Publisher: Springer
Year: 2001
Language: English
Commentary: (full book = 2 volumes of Collector’s Edition)
Pages: XV+1237
City: Berlin
Front Matter ....Pages I-XV
Nonlinear Continuum Physics (Stuart S. Antman)....Pages 1-21
Computational Mechanics: Where Is It Going? (Ivo Babuška, J. Tinsley Oden)....Pages 23-28
From Finite Sets to Feynman Diagrams (John C. Baez, James Dolan)....Pages 29-50
Experimental Mathematics: Recent Developments and Future Outlook (David H. Bailey, Jonathan M. Borwein)....Pages 51-66
The Mathematical Aspects of Econometrics (Badi H. Baltagi)....Pages 67-81
Quantum Information (Ole E. Barndorff-Nielsen, Richard D. Gill, Peter E. Jupp)....Pages 83-107
The p-Adic L-Functions of Modular Elliptic Curves (Massimo Bertolini, Henri Darmon)....Pages 109-170
A Basis for a New Relationship Between Mathematics and Society (Jean Pierre Bourguignon)....Pages 171-188
New Issues in the Mathematics of Control (Roger Brockett)....Pages 189-219
Geometric Mechanics, Lagrangian Reduction, and Nonholonomic Systems (Hernán Cendra, Jerrold E. Marsden, Tudor S. Ratiu)....Pages 221-273
Mathematics: From the Outside Looking in (Achim Bachem, Vasco Alexander Schmidt)....Pages 275-281
Communicating Mathematics Across the Web (Arjeh M. Cohen)....Pages 283-300
Computational Aspects of Number Theory (Henri Cohen)....Pages 301-330
L-Functions and Random Matrices (J. Brian Conrey)....Pages 331-352
Some Open Problems and Research Directions in the Mathematical Study of Fluid Dynamics (Peter Constantin)....Pages 353-360
Mathematics of Financial Markets (Mark Davis)....Pages 361-380
Computational Neuroscience: More Math Is Needed to Understand the Human Brain (Erik De Schutter)....Pages 381-391
Probability Theory (Rick Durrett)....Pages 393-405
Selected Problems in Materials Science (E. Weinan)....Pages 407-432
From Numerical Analysis to Computational Science (Björn Engquist, Gene Golub)....Pages 433-448
Diophantine Equations (Gerd Faltings)....Pages 449-454
After the ‘Golden Age’: What Next? (Lennart Carleson, Björn Engquist)....Pages 455-461
Shape (Gerald Farin)....Pages 463-477
Twistors and General Relativity (Jörg Frauendiener, Roger Penrose)....Pages 479-505
Computational Complexity (Oded Goldreich)....Pages 507-524
Possible Trends in Mathematics in the Coming Decades (Mikhael Gromov)....Pages 525-527
Quantum Computing Challenges (Jozef Gruska)....Pages 529-563
Statistical Science (Peter Hall)....Pages 565-575
Global Differential Geometry (Nigel Hitchin)....Pages 577-591
Evolution Equations in Geometry (Gerhard Huisken)....Pages 593-604
Computational Field Visualization (Christopher R. Johnson, Yarden Livnat, Leonid Zhukov, David Hart, Gordon Kindlmann)....Pages 605-630
Whither Applied Nonlinear Dynamics? (Christopher K. R. T. Jones)....Pages 631-645
Mathematics Comes from Many Sources… (David Eisenbud, Sara Robinson)....Pages 647-653
The Ubiquitous Heat Kernel (Jay Jorgenson, Serge Lang)....Pages 655-683
Mathematical Modelling of the Internet (Frank Kelly)....Pages 685-702
Developments in Insurance Mathematics (Claudia Klüppelberg)....Pages 703-722
Discontinuous Groups for Non-Riemannian Homogeneous Spaces (Toshiyuki Kobayashi)....Pages 723-747
Cryptography (Neal Koblitz)....Pages 749-769
Periods (Maxim Kontsevich, Don Zagier)....Pages 771-808
How Should We Prepare the Students of Science and Technology for a Life in the Computer Age? (Hans Petter Langtangen, Aslak Tveito)....Pages 809-825
Astrophysics and Cosmology in the 21st Century (Malcolm S. Longair)....Pages 827-857
L2-Invariants and Their Applications to Geometry, Group Theory and Spectral Theory (Wolfgang Lück)....Pages 859-871
A Chapter in Physical Mathematics: Theory of Knots in the Sciences (Kishore B. Marathe)....Pages 873-888
The Unity of Mathematics (Matthias Kreck, Vasco Alexander Schmidt)....Pages 889-897
Geometric Aspects of Mirror Symmetry (David R. Morrison)....Pages 899-918
What Is an Algorithm? (Yiannis N. Moschovakis)....Pages 919-936
From Number Crunching to Virtual Reality: Mathematics, Physics and Computation (Risto M. Nieminen)....Pages 937-959
Modeling the Cardiovascular System: A Mathematical Challenge (Alfio Quarteroni)....Pages 961-970
Math in the Entertainment Industry (Doug Roble, Tony Chan)....Pages 971-990
Three Problems in Real Algebraic Geometry and Their Descendants (Marie-Françoise Roy)....Pages 991-1001
Primitive Automorphic Forms (Kyoji Saito)....Pages 1003-1018
Mathematical Challenges from Molecular Evolution (Peter Schuster)....Pages 1019-1038
Mathematical Methods in Medical Imaging: Analysis of Vascular Structures for Liver Surgery Planning (Dirk Selle, Wolf Spindler, Bernhard Preim, Heinz-Otto Peitgen)....Pages 1039-1059
Systems of Conservation Laws: A Challenge for the XXIst Century (Denis Serre)....Pages 1061-1080
RIMS for the 21st Century (Masatake Mori, Kyoji Saito, Toshikazu Sunada)....Pages 1081-1093
Discrete Probability (Joel Spencer)....Pages 1095-1103
Probability Theory (Daniel W. Stroock)....Pages 1105-1113
Error-Correcting Codes and Curves over Finite Fields (Gerard van der Geer)....Pages 1115-1138
The Turing Machine Paradigm in Contemporary Computing (Jan van Leeuwen, Jiří Wiedermann)....Pages 1139-1155
Randomization of Algebra and Algebraization of Probability (Anatoly M. Vershik)....Pages 1157-1166
Dynamical Systems: Moving into the Next Century (Marcelo Viana)....Pages 1167-1178
Noise in the Climate System — Ubiquitous, Constitutive and Concealing (Hans von Storch, Jin-Song von Storch, Peter Müller)....Pages 1179-1194
Questions About Polytopes (Günter M. Ziegler)....Pages 1195-1211
Back Matter ....Pages 1213-1237
